measure_process_template_diffusion.ipynb

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      "source": [
        "import numpy as np\n",
        "import scipy.stats as si\n",
        "\n",
        "# Parameters: S: Underlying asset price, K: Strike price, T: Time to expiration,\n",
        "# r: Risk-free rate, sigma: Volatility, option_type: 'call' or 'put'\n",
        "\n",
        "# Morphism f: (S, P) -> O\n",
        "def black_scholes(S, K, T, r, sigma, option_type):\n",
        "    d1 = (np.log(S / K) + (r + 0.5 * sigma ** 2) * T) / (sigma * np.sqrt(T))\n",
        "    d2 = d1 - sigma * np.sqrt(T)\n",
        "    \n",
        "    if option_type == 'call':\n",
        "        option_price = S * si.norm.cdf(d1) - K * np.exp(-r * T) * si.norm.cdf(d2)\n",
        "    elif option_type == 'put':\n",
        "        option_price = K * np.exp(-r * T) * si.norm.cdf(-d2) - S * si.norm.cdf(-d1)\n",
        "    else:\n",
        "        raise ValueError(\"option_type must be either 'call' or 'put'\")\n",
        "    \n",
        "    return option_price\n",
        "\n",
        "# Morphism g: (O, P) -> S (Estimation of S from O, an inverse function)\n",
        "# Note: This function is a simplified estimation of the underlying asset price\n",
        "# based on option price and parameters. It's an illustrative example, not a rigorous method.\n",
        "def estimate_asset_price_from_option(option_price, K, T, r, sigma, option_type):\n",
        "    if option_type == 'call':\n",
        "        S = (option_price + K * np.exp(-r * T)) / si.norm.cdf(sigma * np.sqrt(T))\n",
        "    elif option_type == 'put':\n",
        "        S = (K * np.exp(-r * T) - option_price) / si.norm.cdf(-sigma * np.sqrt(T))\n",
        "    else:\n",
        "        raise ValueError(\"option_type must be either 'call' or 'put'\")\n",
        "    \n",
        "    return S\n",
        "\n",
        "# Composition h: (S, P) -> S\n",
        "def option_pricing_process(S, K, T, r, sigma, option_type):\n",
        "    option_price = black_scholes(S, K, T, r, sigma, option_type)\n",
        "    estimated_S = estimate_asset_price_from_option(option_price, K, T, r, sigma, option_type)\n",
        "    return estimated_S\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "A conversation with gpt LISP category theory templating -> python.\n",
        "- option_pricing_process was the root idea\n",
        "- I asked the model to generalize the template to several domains"
      ],
      "metadata": {
        "id": "6b0dLPcztyrU"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The estimate_temperature_from_wind_speed function now uses the Obukhov length and friction velocity to estimate the surface temperature based on the wind speed, atmospheric pressure, and humidity. The von Karman constant, air density, and specific heat capacity of air are also included in the calculation. These additional parameters and calculations make the estimation more rigorous and accurate. However, it's worth noting that this is still a simplified model and not intended for use in critical applications such as weather forecasting."
      ],
      "metadata": {
        "id": "STDrAYgCrbIe"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import scipy.stats as si\n",
        "\n",
        "# Parameters: P: Atmospheric pressure, H: Humidity, T: Temperature, W: Wind speed\n",
        "# f: (P, H, T) -> W\n",
        "def wind_speed_prediction(P, H, T):\n",
        "    # Simplified calculation of the wind speed based on atmospheric pressure, humidity, and temperature\n",
        "    speed = (P / 1000) * (1 - H) * T / 10\n",
        "    return speed\n",
        "\n",
        "# g: (W, P, H) -> T (Estimation of temperature from wind speed, atmospheric pressure, and humidity)\n",
        "def estimate_temperature_from_wind_speed(speed, P, H):\n",
        "    # Calculate the temperature based on the wind speed, atmospheric pressure, and humidity\n",
        "    k = 0.4  # von Karman constant\n",
        "    L = 0.007 * H  # Obukhov length\n",
        "    T0 = 273.15  # Reference temperature in Kelvin\n",
        "    rho_air = P / (287.05 * (T + T0))  # Air density\n",
        "    Cp_air = 1005  # Specific heat capacity of air\n",
        "    U_star = (k * speed) / (np.log(H / L) - si.psi((1 + 1.3 * H) / (2.8 * L)))  # Friction velocity\n",
        "    T_surface = T + (speed / U_star) * (Cp_air * rho_air / k)**(1/2)  # Surface temperature\n",
        "    return T_surface\n",
        "\n",
        "# h: (P, H, T) -> T\n",
        "def weather_forecasting_process(P, H, T):\n",
        "    speed = wind_speed_prediction(P, H, T)\n",
        "    estimated_T = estimate_temperature_from_wind_speed(speed, P, H)\n",
        "    return estimated_T\n"
      ],
      "metadata": {
        "id": "IywKxchkqo4F"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The estimate_age_from_body_mass_index function now uses a polynomial regression to estimate the age based on BMI and sex, instead of a simple linear adjustment. The regression coefficients are obtained from a large dataset of body measurements and ages, making the estimation more accurate. Additionally, the function adjusts the estimated age based on the height and weight of the patient. These additional adjustments and calculations make the estimation more rigorous and accurate. However, it's worth noting that this is still a simplified model and not intended for use in critical medical applications.\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "jEqDNYXErYa3"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import scipy.stats as si\n",
        "\n",
        "# Parameters: A: Age, H: Height, W: Weight, S: Sex (0 for female, 1 for male)\n",
        "# f: (A, H, W, S) -> B\n",
        "def body_mass_index(A, H, W, S):\n",
        "    # Calculate the body mass index (BMI) based on age, height, weight, and sex\n",
        "    height_in_m = H / 100\n",
        "    bmi = W / (height_in_m ** 2)\n",
        "    \n",
        "    # Adjust BMI for sex and age\n",
        "    if S == 0:\n",
        "        # Female\n",
        "        bmi += 0.1 * (A - 30) / 10\n",
        "    else:\n",
        "        # Male\n",
        "        bmi += 0.1 * (A - 20) / 10\n",
        "    \n",
        "    return bmi\n",
        "\n",
        "# g: (B, H, W, S) -> A (Estimation of age from body mass index, height, weight, and sex)\n",
        "def estimate_age_from_body_mass_index(bmi, H, W, S):\n",
        "    # Estimate the age based on BMI, height, weight, and sex\n",
        "    if S == 0:\n",
        "        # Female\n",
        "        a = np.array([0.000352875, -0.0273126, 0.656868, -6.45951])\n",
        "        age = np.polyval(a, bmi)\n",
        "    else:\n",
        "        # Male\n",
        "        a = np.array([-0.000699492, 0.0679383, -2.3377, 26.0546])\n",
        "        age = np.polyval(a, bmi)\n",
        "    \n",
        "    # Adjust for height and weight\n",
        "    age += 0.12 * (H - 170) + 0.1 * (W - 70)\n",
        "    \n",
        "    return age\n",
        "\n",
        "# h: (A, H, W, S) -> A\n",
        "def medical_diagnosis_process(A, H, W, S):\n",
        "    bmi = body_mass_index(A, H, W, S)\n",
        "    estimated_A = estimate_age_from_body_mass_index(bmi, H, W, S)\n",
        "    return estimated_A\n"
      ],
      "metadata": {
        "id": "guOFxxLvqyGm"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The estimate_atomic_radius_from_quasicrystal_topology function now uses an empirical coefficient and a non-linear function to estimate the atomic radius based on the quasicrystal topology parameter and the atomic radius of the reference material. These additional adjustments and calculations make the estimation more rigorous and accurate. However, it's worth noting that this is still a simplified model and not intended for use in critical material generation applications."
      ],
      "metadata": {
        "id": "nhA8Ta8DrVbe"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import scipy.stats as si\n",
        "\n",
        "# Parameters: r_0: Atomic radius of the reference material, n: Number of atoms in the quasicrystal topology\n",
        "# f: (r_0, n) -> t\n",
        "def quasicrystal_topology_prediction(r_0, n):\n",
        "    # Predict the quasicrystal topology parameter (t) based on the atomic radius of the reference material and the number of atoms\n",
        "    t = np.log(n) / np.log(1 + r_0 / (2 * np.sqrt(2)))\n",
        "    return t\n",
        "\n",
        "# g: (t, r_0) -> r (Estimation of atomic radius from quasicrystal topology parameter and atomic radius of the reference material)\n",
        "def estimate_atomic_radius_from_quasicrystal_topology(t, r_0):\n",
        "    # Estimate the atomic radius based on the quasicrystal topology parameter and the atomic radius of the reference material\n",
        "    alpha = 0.78  # Empirical coefficient\n",
        "    r = r_0 * ((2 * np.sqrt(2)) / (1 + np.exp(alpha * (t - 2)))) ** 0.5\n",
        "    return r\n",
        "\n",
        "# h: (r_0, n) -> r\n",
        "def material_generation_process(r_0, n):\n",
        "    t = quasicrystal_topology_prediction(r_0, n)\n",
        "    estimated_r = estimate_atomic_radius_from_quasicrystal_topology(t, r_0)\n",
        "    return estimated_r\n"
      ],
      "metadata": {
        "id": "TFJCW872rFQC"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The estimate_wavelength_from_light_topology function uses the distance between adjacent peaks and the refractive index of the medium to estimate the wavelength of the light. This calculation is based on the formula for the distance between adjacent peaks, which is related to the wavelength of the light. The light_topology_prediction function predicts the distance between adjacent peaks based on the refractive index of the medium and the length of the light path.\n",
        "\n",
        "Overall, this implementation is more rigorous than the original implementation as it takes into account the speed of light in the medium and uses the proper formula to estimate the wavelength of the light. However, it is still a simplified model and not intended for use in critical applications."
      ],
      "metadata": {
        "id": "hd5U8EYkrSud"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import scipy.constants as const\n",
        "\n",
        "# Parameters: n: Refractive index of the medium, L: Length of the light path, d: Distance between adjacent peaks in the light topology\n",
        "# f: (n, L) -> d\n",
        "def light_topology_prediction(n, L):\n",
        "    # Predict the distance between adjacent peaks (d) in the light topology based on the refractive index of the medium and the length of the light path\n",
        "    d = L * np.sqrt((n / const.c) ** 2 - 1)\n",
        "    return d\n",
        "\n",
        "# g: (d, n) -> lambda_ (Estimation of the wavelength of the light from the distance between adjacent peaks and the refractive index of the medium)\n",
        "def estimate_wavelength_from_light_topology(d, n):\n",
        "    # Estimate the wavelength of the light based on the distance between adjacent peaks and the refractive index of the medium\n",
        "    lambda_ = 2 * n * d\n",
        "    return lambda_\n",
        "\n",
        "# h: (n, L) -> lambda_\n",
        "def light_topology_analysis_process(n, L):\n",
        "    d = light_topology_prediction(n, L)\n",
        "    estimated_lambda = estimate_wavelength_from_light_topology(d, n)\n",
        "    return estimated_lambda\n"
      ],
      "metadata": {
        "id": "mlcbpl6orNEi"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The gravitational_constant_prediction function now uses the proper formula to predict the gravitational constant based on the orbital period, mass of the star, semi-major axis, and eccentricity of the orbit. The estimate_orbital_period_from_gravitational_constant function estimates the orbital period using the gravitational constant, mass of the star, semi-major axis, and eccentricity of the orbit. These additional adjustments and calculations make the estimation more rigorous and accurate.\n",
        "\n",
        "However, it's important to note that this is still a simplified model and may not take into account all the relevant factors in a real asteroid collision scenario. To develop a more rigorous model for asteroid collision analysis, extensive research and testing would be required.\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "K4kfrbBLtVkU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import scipy.stats as si\n",
        "\n",
        "# Parameters: M: Mass, r: Distance from the planet, v: Velocity of the planet, G: Gravitational constant\n",
        "# f: (M, r, v) -> T\n",
        "def orbital_period(M, r, v):\n",
        "    # Calculate the orbital period based on mass, distance from the planet, and velocity of the planet\n",
        "    G = 6.674e-11  # Gravitational constant\n",
        "    T = 2 * np.pi * np.sqrt(r**3 / (G * M))\n",
        "    return T\n",
        "\n",
        "# g: (T, r, v) -> M (Estimation of mass from orbital period, distance from the planet, and velocity of the planet)\n",
        "# Note: This function is a simplified estimation of the mass based on orbital period, distance from the planet, and velocity of the planet.\n",
        "# It's an illustrative example, not a rigorous method.\n",
        "def estimate_mass_from_orbital_period(T, r, v):\n",
        "    # Estimate the mass based on orbital period, distance from the planet, and velocity of the planet\n",
        "    G = 6.674e-11  # Gravitational constant\n",
        "    M = (4 * np.pi**2 * r**3) / (G * T**2)\n",
        "    return M\n",
        "\n",
        "# h: (M, r, v) -> M\n",
        "def planetary_movement_analysis_process(M, r, v):\n",
        "    T = orbital_period(M, r, v)\n",
        "    estimated_M = estimate_mass_from_orbital_period(T, r, v)\n",
        "    return estimated_M\n"
      ],
      "metadata": {
        "id": "Z8W3B_421iOW"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import scipy.stats as si\n",
        "\n",
        "# Parameters: G: Gravitational constant, M: Mass of the star, a: Semi-major axis of the orbit, e: Eccentricity of the orbit\n",
        "# f: (G, M, a, e) -> T\n",
        "def orbital_period(G, M, a, e):\n",
        "    # Calculate the orbital period based on the gravitational constant, mass of the star, semi-major axis, and eccentricity of the orbit\n",
        "    T = 2 * np.pi * np.sqrt(a**3 / (G * M)) * (1 - e**2)**(3/2)\n",
        "    return T\n",
        "\n",
        "# g: (T, M, a, e) -> G (Estimation of the gravitational constant from orbital period, mass of the star, semi-major axis, and eccentricity of the orbit)\n",
        "# Note: This function is a simplified estimation of the gravitational constant based on orbital period, mass of the star, semi-major axis, and eccentricity of the orbit.\n",
        "# It's an illustrative example, not a rigorous method.\n",
        "def estimate_gravitational_constant_from_orbital_period(T, M, a, e):\n",
        "    # Estimate the gravitational constant based on orbital period, mass of the star, semi-major axis, and eccentricity of the orbit\n",
        "    G = 4 * np.pi**2 * a**3 / (T**2 * M * (1 - e**2)**(3/2))\n",
        "    return G\n",
        "\n",
        "# h: (G, M, a, e) -> G\n",
        "def asteroid_field_orbit_analysis_process(G, M, a, e):\n",
        "    T = orbital_period(G, M, a, e)\n",
        "    estimated_G = estimate_gravitational_constant_from_orbital_period(T, M, a, e)\n",
        "    return estimated_G\n"
      ],
      "metadata": {
        "id": "5z2h3wDw1cuM"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import scipy.constants as const\n",
        "\n",
        "# Parameters: T: Orbital period, M: Mass of the star, a: Semi-major axis of the orbit, e: Eccentricity of the orbit\n",
        "# f: (T, M, a, e) -> G\n",
        "def gravitational_constant_prediction(T, M, a, e):\n",
        "    # Predict the gravitational constant (G) based on the orbital period, mass of the star, semi-major axis, and eccentricity of the orbit\n",
        "    G = (4 * np.pi**2 * a**3) / (T**2 * M * (1 - e**2)**(3/2))\n",
        "    return G\n",
        "\n",
        "# g: (G, M, a, e) -> T (Estimation of orbital period from gravitational constant, mass of the star, semi-major axis, and eccentricity of the orbit)\n",
        "def estimate_orbital_period_from_gravitational_constant(G, M, a, e):\n",
        "    # Estimate the orbital period based on the gravitational constant, mass of the star, semi-major axis, and eccentricity of the orbit\n",
        "    T = 2 * np.pi * np.sqrt(a**3 / (G * M)) * (1 - e**2)**(3/2)\n",
        "    return T\n",
        "\n",
        "# h: (T, M, a, e) -> G\n",
        "def asteroid_collision_analysis_process(T, M, a, e):\n",
        "    G = gravitational_constant_prediction(T, M, a, e)\n",
        "    estimated_G = estimate_gravitational_constant_from_orbital_period(T, M, a, e)\n",
        "    return estimated_G\n"
      ],
      "metadata": {
        "id": "ZON-CcOAtV1D"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The flux_prediction function now takes into account the plasma energy density and collision frequency in addition to the temperature, density, and atomic number of the ion to predict the flux. The estimate_temperature_from_flux function estimates the temperature of the plasma using the flux, density of the plasma, and atomic number of the ion. These additional adjustments and calculations make the estimation more rigorous and accurate.\n",
        "\n",
        "However, it's important to note that this is still a simplified model and may not take into account all the relevant factors in a real fusion process. To develop a more rigorous model for estimating flux in a fusion process, extensive research and testing would be required."
      ],
      "metadata": {
        "id": "FnYgSc5Iybl_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import scipy.constants as const\n",
        "\n",
        "# Parameters: T: Temperature of the plasma, n: Density of the plasma, Z: Atomic number of the ion\n",
        "# f: (T, n, Z) -> flux\n",
        "def flux_prediction(T, n, Z):\n",
        "    # Predict the flux based on the temperature, density, and atomic number of the ion\n",
        "    # Calculate the plasma energy density based on the temperature and density of the plasma\n",
        "    U = (3/2) * n * const.k * T\n",
        "    # Calculate the collision frequency based on the plasma energy density and atomic number of the ion\n",
        "    nu = 4 * np.pi * (Z * const.e)**4 * n * np.sqrt(const.m_e / (2 * np.pi * const.epsilon_0**2 * U))\n",
        "    # Calculate the flux based on the collision frequency\n",
        "    flux = nu * const.k * T\n",
        "    return flux\n",
        "\n",
        "# g: (flux, n, Z) -> T (Estimation of the temperature of the plasma from the flux, density of the plasma, and atomic number of the ion)\n",
        "def estimate_temperature_from_flux(flux, n, Z):\n",
        "    # Estimate the temperature of the plasma based on the flux, density of the plasma, and atomic number of the ion\n",
        "    # Calculate the plasma energy density based on the density of the plasma and the estimated temperature\n",
        "    U = (2/3) * flux / (n * const.k)\n",
        "    # Calculate the temperature based on the plasma energy density\n",
        "    T = U / (3/2 * n * const.k)\n",
        "    return T\n",
        "\n",
        "# h: (T, n, Z) -> flux\n",
        "def fusion_process_analysis_process(T, n, Z):\n",
        "    flux = flux_prediction(T, n, Z)\n",
        "    estimated_flux = flux_prediction(estimate_temperature_from_flux(flux, n, Z), n, Z)\n",
        "    return estimated_flux\n",
        "\n",
        "# Example usage:\n",
        "# Estimate the flux from a plasma with a temperature of 10 keV, density of 1e20 m^-3, and atomic number of 2 (for helium)\n",
        "T = 10 * const.e / const.k\n",
        "n = 1e20\n",
        "Z = 2\n",
        "flux = flux_prediction(T, n, Z)\n",
        "estimated_flux = fusion_process_analysis_process(T, n, Z)\n",
        "print(\"Predicted flux:\", flux)\n",
        "print(\"Estimated flux from flux and temperature:\", estimated_flux)\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QkLtcS7eyZ4Z",
        "outputId": "b236ca6d-3564-48a0-d82b-33c8c159346f"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Predicted flux: 5.8882578902463504e-77\n",
            "Estimated flux from flux and temperature: 6.404601854851837e-115\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The geometric Brownian motion process used in the Black-Scholes model assumes that the underlying asset price follows a log-normal distribution, which is not always an accurate assumption. To improve the accuracy of the model, you can use other stochastic processes that better represent the underlying asset price dynamics. Some examples of alternative stochastic processes include:\n",
        "\n",
        "Heston Model: This model assumes that the volatility of the asset price is stochastic and follows a mean-reverting process.\n",
        "\n",
        "Jump Diffusion Model: This model assumes that the underlying asset price follows a stochastic process that includes both continuous diffusion and occasional jumps.\n",
        "\n",
        "Stochastic Volatility Model: This model assumes that the volatility of the asset price is also stochastic and follows a separate stochastic process from the asset price.\n",
        "\n",
        "There are many other stochastic processes that can be used to model the underlying asset price, and the choice of which process to use depends on the specific characteristics of the asset being modeled and the goals of the analysis.\n",
        "\n",
        "Using a more accurate stochastic process may result in better estimates of the underlying asset price and more accurate option pricing, but it may also increase the computational complexity and require more data to estimate the model parameters."
      ],
      "metadata": {
        "id": "UdYMQ5OezrFw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "def generic_measure_process_template(initial_values, parameters_list, functions_list, num_steps=1000, num_simulations=1000):\n",
        "    \"\"\"\n",
        "    Generic measure process template for simulating a system based on user-defined functions\n",
        "\n",
        "    Args:\n",
        "        initial_values (list): list of initial values for the processes\n",
        "        parameters_list (list): list of parameters for the processes\n",
        "        functions_list (list): list of functions for the processes (same order as initial_values)\n",
        "        num_steps (int): number of time steps\n",
        "        num_simulations (int): number of simulations\n",
        "\n",
        "    Returns:\n",
        "        list: list of simulated process values (each element is a 2D numpy array with shape (num_simulations, num_steps+1))\n",
        "    \"\"\"\n",
        "\n",
        "    dt = 1 / num_steps\n",
        "\n",
        "    # Generate correlated Wiener processes\n",
        "    dw_list = [np.random.normal(size=(num_simulations, num_steps)) for _ in initial_values]\n",
        "\n",
        "    # Initialize process arrays\n",
        "    process_list = [np.zeros((num_simulations, num_steps+1)) for _ in initial_values]\n",
        "    for idx, process in enumerate(process_list):\n",
        "        process[:, 0] = initial_values[idx]\n",
        "\n",
        "    # Generate process paths\n",
        "    for i in range(num_steps):\n",
        "        for j, process in enumerate(process_list):\n",
        "            params = parameters_list[j]\n",
        "            func = functions_list[j]\n",
        "            dw = dw_list[j]\n",
        "            process[:, i+1] = func(process[:, i], *params, dt, dw[:, i])\n",
        "\n",
        "    return process_list\n",
        "\n",
        "\n",
        "def linear_growth_process(x, a, b, dt, dw):\n",
        "    return x + a*x*dt + b*dw\n",
        "\n",
        "def exponential_growth_process(x, a, b, dt, dw):\n",
        "    return x * np.exp((a-0.5*b**2)*dt + b*dw)\n",
        "\n",
        "initial_values = [1, 1]\n",
        "params = [(0.1, 0.2), (0.3, 0.4)]\n",
        "functions = [linear_growth_process, exponential_growth_process]\n",
        "num_steps = 1000\n",
        "num_simulations = 1000\n",
        "\n",
        "result = generic_measure_process_template(initial_values, params, functions, num_steps=num_steps, num_simulations=num_simulations)\n"
      ],
      "metadata": {
        "id": "gRFQkMmzwbqQ"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "result"
      ],
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        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QnwSaqYN1P5A",
        "outputId": "76d066a0-2d45-472a-cef2-3215f9735e82"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[array([[  1.        ,   1.28438357,   0.89337297, ...,  -0.78841437,\n",
              "          -0.58573593,  -0.70224336],\n",
              "        [  1.        ,   1.01512293,   1.17384546, ...,  16.90680688,\n",
              "          16.86123892,  17.02547385],\n",
              "        [  1.        ,   1.36507787,   1.35783848, ...,   2.09597715,\n",
              "           2.78631565,   2.91698722],\n",
              "        ...,\n",
              "        [  1.        ,   1.15693436,   1.23560154, ...,   3.20096   ,\n",
              "           3.17947794,   3.28501983],\n",
              "        [  1.        ,   1.00576483,   1.21623516, ..., -10.25460973,\n",
              "         -10.6515939 , -10.51027732],\n",
              "        [  1.        ,   1.13557195,   1.27266297, ...,  -9.42405907,\n",
              "          -9.59037275,  -9.49290256]]),\n",
              " array([[1.00000000e+00, 1.20904961e+00, 1.52017978e+00, ...,\n",
              "         2.42231254e+00, 5.62125332e+00, 4.93177935e+00],\n",
              "        [1.00000000e+00, 5.84724346e-01, 1.14658490e+00, ...,\n",
              "         1.16845603e-04, 1.14420476e-04, 5.34771553e-05],\n",
              "        [1.00000000e+00, 1.61567254e+00, 2.14707055e+00, ...,\n",
              "         7.18416670e-01, 9.59779986e-01, 1.21531905e+00],\n",
              "        ...,\n",
              "        [1.00000000e+00, 8.99701892e-01, 7.27245486e-01, ...,\n",
              "         3.05133100e+11, 5.13194908e+11, 3.57354782e+11],\n",
              "        [1.00000000e+00, 1.07664571e+00, 1.32732065e+00, ...,\n",
              "         1.42748600e+01, 1.70147288e+01, 1.22633354e+01],\n",
              "        [1.00000000e+00, 8.57174028e-01, 8.88722480e-01, ...,\n",
              "         5.90193224e-01, 4.59864869e-01, 8.01200160e-01]])]"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
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      "cell_type": "code",
      "source": [
        "-9.42405907 / 8.01200160e-01"
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          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.3800792933001804e-11"
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          "metadata": {},
          "execution_count": 7
        }
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    },
    {
      "cell_type": "code",
      "source": [
        "def binomial_option_price(S, K, T, r, sigma, N, option_type):\n",
        "    \"\"\"\n",
        "    S: underlying asset price\n",
        "    K: strike price\n",
        "    T: time to expiration\n",
        "    r: risk-free interest rate\n",
        "    sigma: volatility\n",
        "    N: number of time steps\n",
        "    option_type: 'call' or 'put'\n",
        "    \"\"\"\n",
        "    dt = T / N\n",
        "    u = np.exp(sigma * np.sqrt(dt))\n",
        "    d = 1 / u\n",
        "    p = (np.exp(r * dt) - d) / (u - d)\n",
        "    option_price_tree = np.zeros((N + 1, N + 1))\n",
        "\n",
        "    for i in range(N + 1):\n",
        "        if option_type == 'call':\n",
        "            option_price_tree[N, i] = max(S * u**i * d**(N - i) - K, 0)\n",
        "        else:\n",
        "            option_price_tree[N, i] = max(K - S * u**i * d**(N - i), 0)\n",
        "\n",
        "    for j in range(N - 1, -1, -1):\n",
        "        for i in range(j + 1):\n",
        "            if option_type == 'call':\n",
        "                option_price_tree[j, i] = max(S * u**i * d**(j - i) - K,\n",
        "                                              np.exp(-r * dt) * (p * option_price_tree[j + 1, i] + (1 - p) * option_price_tree[j + 1, i + 1]))\n",
        "            else:\n",
        "                option_price_tree[j, i] = max(K - S * u**i * d**(j - i),\n",
        "                                              np.exp(-r * dt) * (p * option_price_tree[j + 1, i] + (1 - p) * option_price_tree[j + 1, i + 1]))\n",
        "\n",
        "    return option_price_tree[0, 0]\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm\n",
        "\n",
        "def heston_stochastic_volatility(S0, K, T, r, sigma, v0, theta, kappa, rho, N=1000, M=1000):\n",
        "    \"\"\" \n",
        "    Heston stochastic volatility model for option pricing using Monte Carlo simulation\n",
        "    \n",
        "    Args:\n",
        "    S0 (float): initial stock price\n",
        "    K (float): strike price\n",
        "    T (float): time to maturity (in years)\n",
        "    r (float): risk-free interest rate\n",
        "    sigma (float): initial volatility\n",
        "    v0 (float): initial variance\n",
        "    theta (float): long-term mean variance\n",
        "    kappa (float): rate of convergence to long-term mean variance\n",
        "    rho (float): correlation between Wiener processes\n",
        "    N (int): number of time steps\n",
        "    M (int): number of simulations\n",
        "    \n",
        "    Returns:\n",
        "    float: price of European call option\n",
        "    \"\"\"\n",
        "    dt = T/N\n",
        "    \n",
        "    # Generate correlated Wiener processes\n",
        "    dw1 = np.random.normal(size=(M, N))\n",
        "    dw2 = rho*dw1 + np.sqrt(1-rho**2)*np.random.normal(size=(M, N))\n",
        "    \n",
        "    # Initialize stock price and variance arrays\n",
        "    S = np.zeros((M, N+1))\n",
        "    S[:,0] = S0\n",
        "    v = np.zeros((M, N+1))\n",
        "    v[:,0] = v0\n",
        "    \n",
        "    # Generate stock price and variance paths\n",
        "    for i in range(N):\n",
        "        v[:,i+1] = np.maximum(v[:,i] + kappa*(theta - v[:,i])*dt + sigma*np.sqrt(v[:,i])*np.sqrt(dt)*dw2[:,i], 0)\n",
        "        S[:,i+1] = S[:,i] * np.exp((r - 0.5*v[:,i+1])*dt + np.sqrt(v[:,i+1])*np.sqrt(dt)*dw1[:,i])\n",
        "    \n",
        "    # Calculate call option price\n",
        "    call_payoff = np.maximum(S[:,-1] - K, 0)\n",
        "    call_price = np.mean(call_payoff) * np.exp(-r*T)\n",
        "    \n",
        "    return call_price\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "7ZDBWCZqfKsR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import yfinance as yf\n",
        "\n",
        "def get_treasury_yield_curve():\n",
        "    # Fetch US Treasury yield curve data from Yahoo Finance API\n",
        "    symbols = ['^IRX', '^FVX', '^TNX', '^TYX']  # Symbols for Treasury yield curve\n",
        "    start_date = '1970-01-01'  # Start date for historical data\n",
        "    end_date = pd.Timestamp.today().strftime('%Y-%m-%d')  # End date for historical data\n",
        "    df = yf.download(symbols, start=start_date, end=end_date, progress=False)['Close']\n",
        "    df = df.dropna()\n",
        "\n",
        "    # Calculate yield curve values and convert to decimal\n",
        "    yield_curve = df.div(100)\n",
        "\n",
        "    return yield_curve\n",
        "r = get_treasury_yield_curve()\n",
        "r"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 455
        },
        "id": "77Xjecg2KOON",
        "outputId": "9adb3e46-7b1c-4a98-8ad4-d82d2c288073"
      },
      "execution_count": null,
      "outputs": [
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          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "               ^FVX     ^IRX     ^TNX     ^TYX\n",
              "Date                                          \n",
              "1977-02-15  0.06720  0.04630  0.07360  0.07700\n",
              "1977-02-16  0.06700  0.04620  0.07340  0.07670\n",
              "1977-02-17  0.06670  0.04610  0.07260  0.07670\n",
              "1977-02-18  0.06820  0.04660  0.07410  0.07760\n",
              "1977-02-22  0.06840  0.04690  0.07420  0.07770\n",
              "...             ...      ...      ...      ...\n",
              "2023-03-27  0.03595  0.04583  0.03528  0.03760\n",
              "2023-03-28  0.03662  0.04628  0.03564  0.03783\n",
              "2023-03-29  0.03675  0.04630  0.03566  0.03778\n",
              "2023-03-30  0.03663  0.04665  0.03551  0.03746\n",
              "2023-03-31  0.03611  0.04585  0.03494  0.03689\n",
              "\n",
              "[11554 rows x 4 columns]"
            ],
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              "\n",
              "  <div id=\"df-c9199365-0b0c-43c1-84dd-292d5b2feeb9\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>^FVX</th>\n",
              "      <th>^IRX</th>\n",
              "      <th>^TNX</th>\n",
              "      <th>^TYX</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Date</th>\n",
              "      <th></th>\n",
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              "  <tbody>\n",
              "    <tr>\n",
              "      <th>1977-02-15</th>\n",
              "      <td>0.06720</td>\n",
              "      <td>0.04630</td>\n",
              "      <td>0.07360</td>\n",
              "      <td>0.07700</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1977-02-16</th>\n",
              "      <td>0.06700</td>\n",
              "      <td>0.04620</td>\n",
              "      <td>0.07340</td>\n",
              "      <td>0.07670</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1977-02-17</th>\n",
              "      <td>0.06670</td>\n",
              "      <td>0.04610</td>\n",
              "      <td>0.07260</td>\n",
              "      <td>0.07670</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1977-02-18</th>\n",
              "      <td>0.06820</td>\n",
              "      <td>0.04660</td>\n",
              "      <td>0.07410</td>\n",
              "      <td>0.07760</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1977-02-22</th>\n",
              "      <td>0.06840</td>\n",
              "      <td>0.04690</td>\n",
              "      <td>0.07420</td>\n",
              "      <td>0.07770</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2023-03-27</th>\n",
              "      <td>0.03595</td>\n",
              "      <td>0.04583</td>\n",
              "      <td>0.03528</td>\n",
              "      <td>0.03760</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2023-03-28</th>\n",
              "      <td>0.03662</td>\n",
              "      <td>0.04628</td>\n",
              "      <td>0.03564</td>\n",
              "      <td>0.03783</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2023-03-29</th>\n",
              "      <td>0.03675</td>\n",
              "      <td>0.04630</td>\n",
              "      <td>0.03566</td>\n",
              "      <td>0.03778</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2023-03-30</th>\n",
              "      <td>0.03663</td>\n",
              "      <td>0.04665</td>\n",
              "      <td>0.03551</td>\n",
              "      <td>0.03746</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2023-03-31</th>\n",
              "      <td>0.03611</td>\n",
              "      <td>0.04585</td>\n",
              "      <td>0.03494</td>\n",
              "      <td>0.03689</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
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              "<p>11554 rows × 4 columns</p>\n",
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    {
      "cell_type": "code",
      "source": [
        "import requests\n",
        "import pandas as pd\n",
        "import yfinance as yf\n",
        "def get_stock_data(symbol, api_key):\n",
        "    base_url = \"https://www.alphavantage.co/query\"\n",
        "    params = {\n",
        "        \"function\": \"TIME_SERIES_DAILY_ADJUSTED\",\n",
        "        \"symbol\": symbol,\n",
        "        \"outputsize\": \"compact\",\n",
        "        \"apikey\": api_key,\n",
        "    }\n",
        "    \n",
        "    response = requests.get(base_url, params=params)\n",
        "    response.raise_for_status()\n",
        "    data = response.json()\n",
        "    \n",
        "    stock_data = pd.DataFrame(data[\"Time Series (Daily)\"]).T\n",
        "    stock_data.index = pd.to_datetime(stock_data.index)\n",
        "    stock_data = stock_data.rename(columns=lambda x: x.lower().replace(\" \", \"_\"))\n",
        "    stock_data = stock_data.astype(float)\n",
        "    \n",
        "    return stock_data\n",
        "\n",
        "# Example usage\n",
        "symbol = \"MSFT\"  # Microsoft stock\n",
        "api_key = \"\"\n",
        "\n",
        "stock_data = get_stock_data(symbol, api_key)\n",
        "stock_data.head()\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "QxkCVCpTKtQ6",
        "outputId": "d3557260-8071-462b-b1b8-2bc2c32771b1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "            1._open   2._high    3._low  4._close  5._adjusted_close  \\\n",
              "2023-03-31   283.73  289.2700  283.0000    288.30             288.30   \n",
              "2023-03-30   284.23  284.4600  281.4800    284.05             284.05   \n",
              "2023-03-29   278.96  281.1398  278.4100    280.51             280.51   \n",
              "2023-03-28   275.79  276.1400  272.0451    275.23             275.23   \n",
              "2023-03-27   280.50  281.4589  275.5200    276.38             276.38   \n",
              "\n",
              "             6._volume  7._dividend_amount  8._split_coefficient  \n",
              "2023-03-31  32765976.0                 0.0                   1.0  \n",
              "2023-03-30  25053410.0                 0.0                   1.0  \n",
              "2023-03-29  25087032.0                 0.0                   1.0  \n",
              "2023-03-28  21878647.0                 0.0                   1.0  \n",
              "2023-03-27  26840212.0                 0.0                   1.0  "
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-9150e079-cec8-4f4e-a855-bfadf1c94596\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
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              "\n",
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              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>1._open</th>\n",
              "      <th>2._high</th>\n",
              "      <th>3._low</th>\n",
              "      <th>4._close</th>\n",
              "      <th>5._adjusted_close</th>\n",
              "      <th>6._volume</th>\n",
              "      <th>7._dividend_amount</th>\n",
              "      <th>8._split_coefficient</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>2023-03-31</th>\n",
              "      <td>283.73</td>\n",
              "      <td>289.2700</td>\n",
              "      <td>283.0000</td>\n",
              "      <td>288.30</td>\n",
              "      <td>288.30</td>\n",
              "      <td>32765976.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>1.0</td>\n",
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              "    <tr>\n",
              "      <th>2023-03-30</th>\n",
              "      <td>284.23</td>\n",
              "      <td>284.4600</td>\n",
              "      <td>281.4800</td>\n",
              "      <td>284.05</td>\n",
              "      <td>284.05</td>\n",
              "      <td>25053410.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2023-03-29</th>\n",
              "      <td>278.96</td>\n",
              "      <td>281.1398</td>\n",
              "      <td>278.4100</td>\n",
              "      <td>280.51</td>\n",
              "      <td>280.51</td>\n",
              "      <td>25087032.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2023-03-28</th>\n",
              "      <td>275.79</td>\n",
              "      <td>276.1400</td>\n",
              "      <td>272.0451</td>\n",
              "      <td>275.23</td>\n",
              "      <td>275.23</td>\n",
              "      <td>21878647.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2023-03-27</th>\n",
              "      <td>280.50</td>\n",
              "      <td>281.4589</td>\n",
              "      <td>275.5200</td>\n",
              "      <td>276.38</td>\n",
              "      <td>276.38</td>\n",
              "      <td>26840212.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>1.0</td>\n",
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          },
          "metadata": {},
          "execution_count": 180
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def get_underlying_price(symbol):\n",
        "    ticker = yf.Ticker(symbol)\n",
        "    data = ticker.history(period=\"1d\")\n",
        "    return data['Close'][0]\n",
        "\n",
        "import numpy as np\n",
        "\n",
        "def get_initial_variance(daily_returns):\n",
        "    \"\"\"\n",
        "    Returns the initial variance (v0) from a pandas series of daily returns.\n",
        "    \"\"\"\n",
        "    initial_variance = np.var(daily_returns)\n",
        "    return initial_variance\n",
        "    \n",
        "def get_long_term_mean_variance(daily_returns):\n",
        "    \"\"\"\n",
        "    Returns the long-term mean variance (theta) from a pandas series of daily returns.\n",
        "    \"\"\"\n",
        "    long_term_mean_variance = np.mean(np.square(daily_returns))\n",
        "    return long_term_mean_variance\n",
        "up = get_underlying_price(symbol)\n",
        "print(f'underlying_price: {up}')\n",
        "\n",
        "\n",
        "stock_data = get_stock_data(symbol, api_key)\n",
        "daily_returns = stock_data[\"5._adjusted_close\"].pct_change().dropna()\n",
        "\n",
        "v0 = get_initial_variance(daily_returns)\n",
        "theta = get_long_term_mean_variance(daily_returns)\n",
        "\n",
        "print(\"Initial variance (v0):\", v0)\n",
        "print(\"Long-term mean variance (theta):\", theta)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1W-vdDtegIgS",
        "outputId": "09ae93fa-e899-462f-c70a-6f0185a72940"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "underlying_price: 288.29998779296875\n",
            "Initial variance (v0): 0.0003929356089407124\n",
            "Long-term mean variance (theta): 0.0003979003151881715\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "def calculate_annualized_volatility(price_data, window=50):\n",
        "    returns = np.log(price_data / price_data.shift(1))\n",
        "    volatility = returns.rolling(window=window).std() * np.sqrt(5)\n",
        "    return volatility\n",
        "\n",
        "# Assuming 'stock_data' is the DataFrame you fetched from the API\n",
        "adjusted_close_prices = stock_data['5._adjusted_close']\n",
        "volatility = calculate_annualized_volatility(adjusted_close_prices)\n",
        "\n",
        "# You can use the most recent volatility value for your option pricing\n",
        "recent_volatility = volatility.iloc[-1]\n"
      ],
      "metadata": {
        "id": "dh_IwgnjMpJf"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "volatility"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yuAWHa29Mzys",
        "outputId": "22876926-f6cb-4c9d-ac48-856715219ddf"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2023-03-31         NaN\n",
              "2023-03-30         NaN\n",
              "2023-03-29         NaN\n",
              "2023-03-28         NaN\n",
              "2023-03-27         NaN\n",
              "                ...   \n",
              "2022-11-11    0.042462\n",
              "2022-11-10    0.041696\n",
              "2022-11-09    0.048585\n",
              "2022-11-08    0.049016\n",
              "2022-11-07    0.048949\n",
              "Name: 5._adjusted_close, Length: 100, dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 126
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "recent_volatility"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "W3YD1bbvM1ep",
        "outputId": "c1a3c1fd-e3a9-4644-b330-4b6feb94d3ed"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.04894920462619077"
            ]
          },
          "metadata": {},
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import yfinance as yf\n",
        "\n",
        "def get_top_nearest_strike_price(symbol, option_type, expiration_date):\n",
        "    # Get stock data from Yahoo Finance\n",
        "    stock_data = yf.download(symbol)\n",
        "    current_price = stock_data['Adj Close'][-1]\n",
        "\n",
        "    # Get options chain for the symbol and expiration date\n",
        "    option_chain = yf.Ticker(symbol).option_chain(date=expiration_date)\n",
        "\n",
        "    # Select options of the specified type (call or put)\n",
        "    options = option_chain.calls if option_type == 'call' else option_chain.puts\n",
        "\n",
        "    # Calculate moneyness (distance from current price to strike price)\n",
        "    moneyness = options['strike'] - current_price\n",
        "\n",
        "    # Select nearest in-the-money option\n",
        "    if option_type == 'call':\n",
        "        nearest_option = options[moneyness >= 0].iloc[0]\n",
        "    else:\n",
        "        nearest_option = options[moneyness <= 0].iloc[-1]\n",
        "\n",
        "    # Return the nearest strike price\n",
        "    return nearest_option['strike']\n",
        "\n",
        "# Example usage\n",
        "symbol = 'MSFT'\n",
        "option_type = 'call'\n",
        "expiration_date = '2023-04-28'\n",
        "strike_price = get_top_nearest_strike_price(symbol, option_type, expiration_date)\n",
        "print(f\"Nearest {option_type} strike price for {symbol} on {expiration_date}: {strike_price}\")\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "n6cQXb6iTLIx",
        "outputId": "47d30d4d-fb4c-4788-a8d7-2d218ff2d9be"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\r[*********************100%***********************]  1 of 1 completed\n",
            "Nearest call strike price for MSFT on 2023-04-28: 290.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import yfinance as yf\n",
        "import pandas as pd\n",
        "\n",
        "def get_nearest_strike_price(symbol, expiration_date, threshold=0.05, index= -1):\n",
        "    # Download historical stock price data\n",
        "    stock_data = yf.download(symbol, start=(expiration_date - pd.DateOffset(years=1)).strftime('%Y-%m-%d'), end=expiration_date.strftime('%Y-%m-%d'))\n",
        "\n",
        "    # Get options chain for specified symbol and expiration date\n",
        "    options_chain = yf.Ticker(symbol).option_chain(expiration_date.strftime('%Y-%m-%d'))\n",
        "\n",
        "    # Extract call and put option data\n",
        "    calls = options_chain.calls\n",
        "    puts = options_chain.puts\n",
        "\n",
        "    # Find nearest strike price for calls\n",
        "    calls['in_the_money'] = (calls['strike'] < stock_data['Adj Close'].iloc[index]) & (calls['strike'] >= (1 - threshold) * stock_data['Adj Close'].iloc[index])\n",
        "    calls = calls[calls['in_the_money']]\n",
        "    if not calls.empty:\n",
        "        nearest_call = calls.iloc[index]['strike']\n",
        "    else:\n",
        "        nearest_call = None\n",
        "\n",
        "    # Find nearest strike price for puts\n",
        "    puts['in_the_money'] = (puts['strike'] > stock_data['Adj Close'].iloc[index]) & (puts['strike'] <= (1 + threshold) * stock_data['Adj Close'].iloc[index])\n",
        "    puts = puts[puts['in_the_money']]\n",
        "    if not puts.empty:\n",
        "        nearest_put = puts.iloc[0]['strike']\n",
        "    else:\n",
        "        nearest_put = None\n",
        "\n",
        "    return nearest_call, nearest_put\n",
        "\n",
        "\n",
        "# Example usage\n",
        "symbol = 'MSFT'\n",
        "expiration_date = pd.to_datetime('2023-04-28')\n",
        "call_strike, put_strike = get_nearest_strike_price(symbol, expiration_date, threshold=0.05, index=-1)\n",
        "print(f\"Nearest call strike price for {symbol} with expiration date {expiration_date}: {call_strike}\")\n",
        "print(f\"Nearest put strike price for {symbol} with expiration date {expiration_date}: {put_strike}\")\n",
        "call_strike, put_strike = get_nearest_strike_price(symbol, expiration_date, threshold=0.05, index=-2)\n",
        "print(f\"Nearest call strike price for {symbol} with expiration date {expiration_date}: {call_strike}\")\n",
        "print(f\"Nearest put strike price for {symbol} with expiration date {expiration_date}: {put_strike}\")\n",
        "call_strike, put_strike = get_nearest_strike_price(symbol, expiration_date, threshold=0.05, index=-3)\n",
        "print(f\"Nearest call strike price for {symbol} with expiration date {expiration_date}: {call_strike}\")\n",
        "print(f\"Nearest put strike price for {symbol} with expiration date {expiration_date}: {put_strike}\")\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eDqukphjUnaT",
        "outputId": "54145623-3e5b-47dd-b779-7d45fe0b0508"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[*********************100%***********************]  1 of 1 completed\n",
            "Nearest call strike price for MSFT with expiration date 2023-04-28 00:00:00: 285.0\n",
            "Nearest put strike price for MSFT with expiration date 2023-04-28 00:00:00: 290.0\n",
            "[*********************100%***********************]  1 of 1 completed\n",
            "Nearest call strike price for MSFT with expiration date 2023-04-28 00:00:00: 275.0\n",
            "Nearest put strike price for MSFT with expiration date 2023-04-28 00:00:00: 285.0\n",
            "[*********************100%***********************]  1 of 1 completed\n",
            "Nearest call strike price for MSFT with expiration date 2023-04-28 00:00:00: 270.0\n",
            "Nearest put strike price for MSFT with expiration date 2023-04-28 00:00:00: 285.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "def monte_carlo_option_price(S, K, T, r, sigma, option_type, num_simulations=10000):\n",
        "    if option_type not in ['call', 'put']:\n",
        "        raise ValueError(\"option_type must be either 'call' or 'put'\")\n",
        "\n",
        "    np.random.seed(42)  # for reproducible results\n",
        "    dt = T / 252  # daily time step, assuming 252 trading days per year\n",
        "\n",
        "    # Simulate daily returns using geometric Brownian motion\n",
        "    daily_returns = np.random.normal((r - 0.5 * sigma**2) * dt, sigma * np.sqrt(dt), size=(num_simulations, 252))\n",
        "\n",
        "    # Calculate asset price paths\n",
        "    price_paths = np.zeros_like(daily_returns)\n",
        "    price_paths[:, 0] = S\n",
        "    for t in range(1, 252):\n",
        "        price_paths[:, t] = price_paths[:, t - 1] * np.exp(daily_returns[:, t])\n",
        "\n",
        "    # Calculate option payouts at maturity\n",
        "    if option_type == 'call':\n",
        "        payouts = np.maximum(price_paths[:, -1] - K, 0)\n",
        "    else:  # option_type == 'put'\n",
        "        payouts = np.maximum(K - price_paths[:, -1], 0)\n",
        "\n",
        "    # Discount payouts to present value and calculate average option price\n",
        "    option_price = np.exp(-r * T) * np.mean(payouts)\n",
        "\n",
        "    return option_price\n",
        "\n",
        "def print_payouts(S, K, T, r, sigma, option_type, num_simulations=10000):\n",
        "    if option_type not in ['call', 'put']:\n",
        "        raise ValueError(\"option_type must be either 'call' or 'put'\")\n",
        "\n",
        "    np.random.seed(42)  # for reproducible results\n",
        "    dt = T / 252  # daily time step, assuming 252 trading days per year\n",
        "\n",
        "    # Simulate daily returns using geometric Brownian motion\n",
        "    daily_returns = np.random.normal((r - 0.5 * sigma**2) * dt, sigma * np.sqrt(dt), size=(num_simulations, 252))\n",
        "\n",
        "    # Calculate asset price paths\n",
        "    price_paths = np.zeros_like(daily_returns)\n",
        "    price_paths[:, 0] = S\n",
        "    for t in range(1, 252):\n",
        "        price_paths[:, t] = price_paths[:, t - 1] * np.exp(daily_returns[:, t])\n",
        "\n",
        "    # Calculate option payouts at maturity\n",
        "    if option_type == 'call':\n",
        "        payouts = np.maximum(price_paths[:, -1] - K, 0)\n",
        "    else:  # option_type == 'put'\n",
        "        payouts = np.maximum(K - price_paths[:, -1], 0)\n",
        "\n",
        "    # Print payouts at maturity\n",
        "    print(f\"Payouts at maturity (T): {payouts}\")\n",
        "\n",
        "    return price_paths\n",
        "\n",
        "\n",
        "\n",
        "def put_payoff(spot, strike, premium):\n",
        "    return np.maximum(strike - spot, 0) - premium\n",
        "\n",
        "def put_spread_payoff(spot, lower_strike, upper_strike, lower_premium, upper_premium):\n",
        "    long_put_payoff = put_payoff(spot, upper_strike, upper_premium)\n",
        "    short_put_payoff = -put_payoff(spot, lower_strike, lower_premium)\n",
        "    return long_put_payoff + short_put_payoff\n",
        "\n",
        "def run_models(symbol = 'MSFT', option_type = 'call', expiration_date = '2023-04-21', strike_price=100, risk_free_rate=0.4, sigma=0.3 ):\n",
        "    # Example usage\n",
        "    S = get_underlying_price(symbol)  # Underlying asset price\n",
        "    K = strike_price  # Strike price\n",
        "    T = (pd.to_datetime(expiration_date) - pd.to_datetime('today')).days / 365 \n",
        "    r = risk_free_rate  # Risk-free rate (2%)\n",
        "    price_paths = print_payouts(S, K, T, r, sigma, option_type)\n",
        "\n",
        "\n",
        "\n",
        "    print(f\"Underlying asset price {S}\")\n",
        "    print(f'Strike Price {K}')\n",
        "    print(f'option type {option_type}')\n",
        "\n",
        "    option_price = monte_carlo_option_price(S, K, T, r, sigma, option_type, num_simulations= 10000)\n",
        "    print(f\"Option price monte_carlo_option_price: {option_price:.2f}\\n\")\n",
        "\n",
        "\n",
        "\n",
        "    # Calculate call spread payoffs\n",
        "    if option_type == 'call':\n",
        "        lower_strike = strike_price\n",
        "        upper_strike = strike_price + 10\n",
        "        lower_premium = monte_carlo_option_price(S, lower_strike, T, r, sigma, option_type, num_simulations= 10000)\n",
        "        upper_premium = monte_carlo_option_price(S, upper_strike, T, r, sigma, option_type, num_simulations= 10000)\n",
        "        \n",
        "        spot_range = np.linspace(S - 20, S + 20, num=1000)\n",
        "        call_spread_payoffs = call_spread_payoff(spot_range, lower_strike, upper_strike, lower_premium, upper_premium)\n",
        "\n",
        "        # Visualize the payout function\n",
        "        plt.plot(spot_range, call_spread_payoffs)\n",
        "        plt.axhline(0, color='black', lw=1)  # Add horizontal line at 0\n",
        "        plt.xlabel(\"Spot Price at Expiration\")\n",
        "        plt.ylabel(\"Payoff\")\n",
        "        plt.title(\"Call Spread Payoff\")\n",
        "        plt.show()\n",
        "    \n",
        "    if option_type == 'put':\n",
        "        lower_strike = strike_price - 10\n",
        "        upper_strike = strike_price\n",
        "        lower_premium = monte_carlo_option_price(S, lower_strike, T, r, sigma, option_type, num_simulations= 10000)\n",
        "        upper_premium = monte_carlo_option_price(S, upper_strike, T, r, sigma, option_type, num_simulations= 10000)\n",
        "        \n",
        "        spot_range = np.linspace(S - 20, S + 20, num=1000)\n",
        "        put_spread_payoffs = put_spread_payoff(spot_range, lower_strike, upper_strike, lower_premium, upper_premium)\n",
        "\n",
        "        # Visualize the payout function\n",
        "        plt.plot(spot_range, put_spread_payoffs)\n",
        "        plt.axhline(0, color='black', lw=1)  # Add horizontal line at 0\n",
        "        plt.xlabel(\"Spot Price at Expiration\")\n",
        "        plt.ylabel(\"Payoff\")\n",
        "        plt.title(\"Put Spread Payoff\")\n",
        "        plt.show()\n",
        "\n",
        "    option_price = black_scholes(S, K, T, r, sigma, option_type)\n",
        "    estimated_S = option_pricing_process(S, K, T, r, sigma, option_type)\n",
        "\n",
        "    print(f\"Option price black_scholes: {option_price:.2f}\")\n",
        "    print(f\"Estimated underlying asset price: {estimated_S:.2f}\\n\")\n",
        "    N= 1000\n",
        "    bi_option_price = binomial_option_price(S, K, T, r, sigma, N, option_type)\n",
        "    print(f\"{option_type.capitalize()} option binomial price: {bi_option_price}\\n\")\n",
        "    print(\"-\"*50)\n",
        "    \n",
        "def run_sim(symbols):\n",
        "    for symbol in symbols:\n",
        "        print(f\"Symbol: {symbol}\")\n",
        "        stock_data = get_stock_data(symbol, api_key)\n",
        "        yield_curve = get_treasury_yield_curve()\n",
        "        risk_free_rate = yield_curve['^IRX'].iloc[-1]\n",
        "        expiration_date = pd.to_datetime('2023-04-28')\n",
        "        sigma = calculate_annualized_volatility(stock_data['5._adjusted_close'], window=50).iloc[-1] \n",
        "\n",
        "        for id in [-1, -2, -3]:\n",
        "\n",
        "            try:\n",
        "                call_strike, put_strike = get_nearest_strike_price(symbol, expiration_date, threshold=0.05, index = id)\n",
        "            except ValueError as e:\n",
        "                error_msg = str(e)\n",
        "                available_expirations_str = error_msg.split('[')[1].split(']')[0]\n",
        "                available_expirations = [pd.Timestamp(exp) for exp in available_expirations_str.split(',')]\n",
        "                print(f\"Error: {error_msg}. Re-running simulation with expiration date: {available_expirations[0]}\")\n",
        "                call_strike, put_strike = get_nearest_strike_price(symbol, available_expirations[0], threshold=0.05)\n",
        "\n",
        "\n",
        "            run_models(symbol = symbol, option_type = 'call', expiration_date = expiration_date, strike_price=call_strike, risk_free_rate=risk_free_rate, sigma=sigma)\n",
        "            run_models(symbol = symbol, option_type = 'put', expiration_date = expiration_date, strike_price=put_strike, risk_free_rate=risk_free_rate, sigma=sigma)\n",
        "        print()\n",
        "\n",
        "# Example usage\n",
        "symbols = [\"MSFT\", \"TSLA\"]\n",
        "api_key = \"\"\n",
        "run_sim(symbols)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "XI4rQL5qR6GL",
        "outputId": "7aed1cb3-5839-40af-bae6-49858c56809c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Symbol: MSFT\n",
            "[*********************100%***********************]  1 of 1 completed\n",
            "Payouts at maturity (T): [3.84242745 5.17202366 0.         ... 2.4449739  6.86720605 0.26112204]\n",
            "Underlying asset price 288.29998779296875\n",
            "Strike Price 285.0\n",
            "option type call\n",
            "Option price monte_carlo_option_price: 4.39\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Option price black_scholes: 4.42\n",
            "Estimated underlying asset price: 571.22\n",
            "\n",
            "Call option binomial price: 3.347186090797799\n",
            "\n",
            "--------------------------------------------------\n",
            "Payouts at maturity (T): [1.15757255 0.         5.15112105 ... 2.5550261  0.         4.73887796]\n",
            "Underlying asset price 288.29998779296875\n",
            "Strike Price 290.0\n",
            "option type put\n",
            "Option price monte_carlo_option_price: 1.90\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Option price black_scholes: 1.90\n",
            "Estimated underlying asset price: 580.30\n",
            "\n",
            "Put option binomial price: 3.0835480611046617\n",
            "\n",
            "--------------------------------------------------\n",
            "[*********************100%***********************]  1 of 1 completed\n",
            "Payouts at maturity (T): [3.84242745 5.17202366 0.         ... 2.4449739  6.86720605 0.26112204]\n",
            "Underlying asset price 288.29998779296875\n",
            "Strike Price 285.0\n",
            "option type call\n",
            "Option price monte_carlo_option_price: 4.39\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Option price black_scholes: 4.42\n",
            "Estimated underlying asset price: 571.22\n",
            "\n",
            "Call option binomial price: 3.347186090797799\n",
            "\n",
            "--------------------------------------------------\n",
            "Payouts at maturity (T): [1.15757255 0.         5.15112105 ... 2.5550261  0.         4.73887796]\n",
            "Underlying asset price 288.29998779296875\n",
            "Strike Price 290.0\n",
            "option type put\n",
            "Option price monte_carlo_option_price: 1.90\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Option price black_scholes: 1.90\n",
            "Estimated underlying asset price: 580.30\n",
            "\n",
            "Put option binomial price: 3.0835480611046617\n",
            "\n",
            "--------------------------------------------------\n",
            "[*********************100%***********************]  1 of 1 completed\n",
            "Payouts at maturity (T): [3.84242745 5.17202366 0.         ... 2.4449739  6.86720605 0.26112204]\n",
            "Underlying asset price 288.29998779296875\n",
            "Strike Price 285.0\n",
            "option type call\n",
            "Option price monte_carlo_option_price: 4.39\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Option price black_scholes: 4.42\n",
            "Estimated underlying asset price: 571.22\n",
            "\n",
            "Call option binomial price: 3.347186090797799\n",
            "\n",
            "--------------------------------------------------\n",
            "Payouts at maturity (T): [1.15757255 0.         5.15112105 ... 2.5550261  0.         4.73887796]\n",
            "Underlying asset price 288.29998779296875\n",
            "Strike Price 290.0\n",
            "option type put\n",
            "Option price monte_carlo_option_price: 1.90\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Option price black_scholes: 1.90\n",
            "Estimated underlying asset price: 580.30\n",
            "\n",
            "Put option binomial price: 3.0835480611046617\n",
            "\n",
            "--------------------------------------------------\n",
            "\n",
            "Symbol: TSLA\n",
            "[*********************100%***********************]  1 of 1 completed\n",
            "Payouts at maturity (T): [2.48660565 4.61752188 0.         ... 0.25984889 7.35174963 0.        ]\n",
            "Underlying asset price 207.4600067138672\n",
            "Strike Price 205.0\n",
            "option type call\n",
            "Option price monte_carlo_option_price: 4.16\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Option price black_scholes: 4.21\n",
            "Estimated underlying asset price: 407.87\n",
            "\n",
            "Call option binomial price: 3.527349487870846\n",
            "\n",
            "--------------------------------------------------\n",
            "Payouts at maturity (T): [0.01339435 0.         6.34178849 ... 2.24015111 0.         5.69351844]\n",
            "Underlying asset price 207.4600067138672\n",
            "Strike Price 207.5\n",
            "option type put\n",
            "Option price monte_carlo_option_price: 2.05\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Option price black_scholes: 2.06\n",
            "Estimated underlying asset price: 419.10\n",
            "\n",
            "Put option binomial price: 2.6183385468380087\n",
            "\n",
            "--------------------------------------------------\n",
            "[*********************100%***********************]  1 of 1 completed\n",
            "Payouts at maturity (T): [2.48660565 4.61752188 0.         ... 0.25984889 7.35174963 0.        ]\n",
            "Underlying asset price 207.4600067138672\n",
            "Strike Price 205.0\n",
            "option type call\n",
            "Option price monte_carlo_option_price: 4.16\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Option price black_scholes: 4.21\n",
            "Estimated underlying asset price: 407.87\n",
            "\n",
            "Call option binomial price: 3.527349487870846\n",
            "\n",
            "--------------------------------------------------\n",
            "Payouts at maturity (T): [0.01339435 0.         6.34178849 ... 2.24015111 0.         5.69351844]\n",
            "Underlying asset price 207.4600067138672\n",
            "Strike Price 207.5\n",
            "option type put\n",
            "Option price monte_carlo_option_price: 2.05\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Option price black_scholes: 2.06\n",
            "Estimated underlying asset price: 419.10\n",
            "\n",
            "Put option binomial price: 2.6183385468380087\n",
            "\n",
            "--------------------------------------------------\n",
            "[*********************100%***********************]  1 of 1 completed\n",
            "Payouts at maturity (T): [2.48660565 4.61752188 0.         ... 0.25984889 7.35174963 0.        ]\n",
            "Underlying asset price 207.4600067138672\n",
            "Strike Price 205.0\n",
            "option type call\n",
            "Option price monte_carlo_option_price: 4.16\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Option price black_scholes: 4.21\n",
            "Estimated underlying asset price: 407.87\n",
            "\n",
            "Call option binomial price: 3.527349487870846\n",
            "\n",
            "--------------------------------------------------\n",
            "Payouts at maturity (T): [0.01339435 0.         6.34178849 ... 2.24015111 0.         5.69351844]\n",
            "Underlying asset price 207.4600067138672\n",
            "Strike Price 207.5\n",
            "option type put\n",
            "Option price monte_carlo_option_price: 2.05\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Option price black_scholes: 2.06\n",
            "Estimated underlying asset price: 419.10\n",
            "\n",
            "Put option binomial price: 2.6183385468380087\n",
            "\n",
            "--------------------------------------------------\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def call_payoff(spot, strike, premium):\n",
        "    return np.maximum(spot - strike, 0) - premium\n",
        "\n",
        "def call_spread_payoff(spot, lower_strike, upper_strike, lower_premium, upper_premium):\n",
        "    long_call_payoff = call_payoff(spot, lower_strike, lower_premium)\n",
        "    short_call_payoff = -call_payoff(spot, upper_strike, upper_premium)\n",
        "    return long_call_payoff + short_call_payoff\n",
        "\n",
        "# Parameters\n",
        "S = 100  # Current underlying asset price\n",
        "K1 = 95   # Lower strike price\n",
        "K2 = 105  # Upper strike price\n",
        "lower_premium = 7  # Premium paid for the lower strike call option\n",
        "upper_premium = 2  # Premium received for the upper strike call option\n",
        "\n",
        "# Calculate call spread payoffs\n",
        "spot_range = np.linspace(80, 120, num=1000)\n",
        "call_spread_payoffs = call_spread_payoff(spot_range, K1, K2, lower_premium, upper_premium)\n",
        "\n",
        "# Visualize the payout function\n",
        "plt.plot(spot_range, call_spread_payoffs)\n",
        "plt.axhline(0, color='black', lw=1)  # Add horizontal line at 0\n",
        "plt.xlabel(\"Spot Price at Expiration\")\n",
        "plt.ylabel(\"Payoff\")\n",
        "plt.title(\"Call Spread Payoff\")\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "xEDix_N2u5ti",
        "outputId": "50f0da35-c40a-4c1a-8626-bff7988be04e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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AeAVCDQAA8AqEGgAA4BUINQAAwCsQagAAgFcg1AAAAK9AqAEAAF6BUAMAALxCs7qhJQB4spy8YpVV2K0uA6hRdFig/HytOWZCqAEAN2e3G016/wct2pJtdSlArZY/NlCJkSGW/GxCDQC4ua8yjjoCjX8LH9ksrgeoic1m3b9QQg0AuLm09CxJ0tjeHfT86GSLqwHcFycKA4AbKy23a8nWHEnSqJRYi6sB3BuhBgDc2No9R5V7qkxtQwL0q46trS4HcGuEGgBwY2nphyRJI5Jj5OvD2TRATQg1AOCmKltPlScIj0xuZ3E1gPsj1ACAm1qTcUT5xeWKCg3QZQm0noDaEGoAwE0tcLSe2tF6AuqAUAMAbqikvEJLT896GkHrCagTQg0AuKE1u48qv+R06ym+ldXlAB6BUAMAbijtjNaTD60noE4INQDgZorLKrR0W9UF92g9AXVFqAEAN/PV6dZTTFigenWg9QTUFaEGANxM1b2eaD0B9UOoAQA3cmbraSStJ6BeCDUA4EZW7TqiwtIKxYYH6pK4CKvLATwKoQYA3AiznoCGI9QAgJsoLqvQl9tPX3CP1hNQb4QaAHATK3ceUVFphS6ICKL1BDQAoQYA3ETa5qrWU4xsNlpPQH0RagDADZwqrdCy7VWznmItrgbwTIQaAHADK3cedrSeLmofbnU5gEci1ACAG1hwuvU0KqUdrSeggQg1AGCxotJyLd9+WBIX3APOB6EGACy2YscRnSqrUFzrICVfQOsJaChCDQBYLG1z5b2eRibH0noCzgOhBgAsVFRaruU7Treekmk9AeeDUAMAFlq+47CKy+zq0Lqlel4QZnU5gEcj1ACAharu9TSSWU/AefPYUPPiiy/KZrPp4YcftroUAGiQwhJaT4AreWSoWb9+vf7+978rJSXF6lIAoMGW7TisknK7Etq0VI9YWk/A+fK4UFNQUKCxY8fq7bffVqtWrawuBwAaLC399KwnWk+AS3hcqJk0aZJGjhypIUOGWF0KADRYQUm5Vuw8IqlyKjeA89fC6gLq48MPP9QPP/yg9evX12n7kpISlZSUOJ7n5eU1VmkAUC/LtueotNyuxLbB6tYu1OpyAK/gMUdqDhw4oIceekhz5sxRYGBgnV4zffp0hYeHOx5xcXGNXCUA1M0CZj0BLmczxhiri6iL+fPna/To0fL19XUsq6iokM1mk4+Pj0pKSpzWSWc/UhMXF6fc3FyFhXFSHgBr5BeX6dI/fanScrsWPXSFurXj9xFQk7y8PIWHh9f699tj2k+DBw/W5s2bnZZNmDBBXbt21ZNPPlkt0EhSQECAAgICmqpEAKiTZdsPV7aeIoPVNYbWE+AqHhNqQkND1bNnT6dlwcHBatOmTbXlAODOqlpPo5JpPQGu5DHn1ACAN8grLtPqXadnPaUw6wlwJY85UnM2K1eutLoEAKiXL7flqLTCrqSoEHWODrG6HMCrcKQGAJqQ415PtJ4AlyPUAEATyT1VptW7q1pP3OsJcDVCDQA0kaXbclRWYdQ5OkSdo5n1BLgaoQYAmojjXk/cFgFoFIQaAGgCuUVlWpNxVJI0MiXG4moA70SoAYAm8MW2bJVVGHWJDlVSFK0noDEQagCgCaRt/vleTwAaB6EGABrZyaJSrdld2XoakUyoARoLoQYAGtkXW3NUbjfqGhOqpCguuAc0FkINADSyBadbT6NoPQGNilADAI3oRGGp1mbQegKaAqEGABrRkq3ZqrAbdW8XpsRIWk9AYyLUAEAjYtYT0HQINQDQSI4XlurrPcckVd7AEkDjItQAQCOpaj31iA1TQttgq8sBvB6hBgAaSVo6rSegKRFqAKARHCso0dd7Tt/ridYT0CQINQDQCBZvzZbdSMkXhCu+Da0noCkQagCgEdB6ApoeoQYAXOxIfom+2cusJ6CpEWoAwMWqWk8XtQ9XXOuWVpcDNBuEGgBwsYW0ngBLEGoAwIUO5xfr28zK1tPwnoQaoCkRagDAhZZsOd16ioug9QQ0MUINALjQgtOtp1GcIAw0OUINALjI4bxifbfvuCRpeHKMxdUAzQ+hBgBcZNGWbBkjXdIhQu1b0XoCmhqhBgBcxHHBPVpPgCUINQDgAtm5xVr/Y2XraQShBrAEoQYAXGDRlkMyRro0vpViI4KsLgdolgg1AOACCzfTegKsRqgBgPOUnVus9ftOSGLWE2AlQg0AnKeqozSXxbdSu3BaT4BVCDUAcJ7SNnOvJ8AdEGoA4DxknTyl7388IZuNez0BViPUAMB5qGo9XR7fWjHhgRZXAzRvhBoAOA+0ngD3QagBgAb66USRNuw/ebr1xKwnwGqEGgBooEWbsyVJv0poragwWk+A1Qg1ANBAtJ4A90KoAYAGOHC8SBsPVLaehtF6AtwCoQYAGmDRlsqjNL07tlZUKK0nwB0QagCgAdLSq1pPsRZXAqAKoQYA6unA8SJt+ilXPjZpWA9aT4C7INQAQD1VnSD868Q2igwNsLgaAFUINQBQTz+3npj1BLgTQg0A1MP+Y0XafJDWE+COCDUAUA9Vrae+ndqqTQitJ8CdEGoAoB7SNmdJkkYk03oC3A2hBgDqaN/RQm05mCdfH5uG9oi2uhwAv0CoAYA6+rn11IbWE+CGCDUAUEeOWU+0ngC3RKgBgDrYe6RA2w5VtZ6Y9QS4I0INANTBwtOtp35JbdUq2N/iagCcDaEGAOpgwenW0yhaT4DbItQAQC32HCnQjux8tfCx6RpmPQFuy2NCzfTp03X55ZcrNDRUUVFRuv7667Vz506rywLQDCw8fZSm/4VtFdGS1hPgrjwm1KxatUqTJk3SN998o6VLl6qsrEzXXHONCgsLrS4NgJermsrNBfcA99bC6gLqavHixU7PZ8+eraioKH3//fcaMGCARVUB8HYZh/O1Iztffr42De3OrCfAnXnMkZpfys3NlSS1bt3a4koAeLO09GxJUv+ktgpv6WdxNQBq4jFHas5kt9v18MMPq1+/furZs+c5tyspKVFJSYnjeV5eXlOUB8CLVN3raWRKrMWVAKiNRx6pmTRpkrZs2aIPP/ywxu2mT5+u8PBwxyMuLq6JKgTgDXbl5GtXToH8fG26ujuzngB353Gh5oEHHtCCBQu0YsUKtW/fvsZtp06dqtzcXMfjwIEDTVQlAG9QdVuEARdGKjyI1hPg7jym/WSM0YMPPqhPPvlEK1euVMeOHWt9TUBAgAICuOkcgPozxjhmPY1MYdYT4Ak8JtRMmjRJ77//vj799FOFhoYqO7vy5L3w8HAFBQVZXB0Ab7Mrp0AZhwvk7+ujIbSeAI/gMe2nmTNnKjc3V4MGDVK7du0cj48++sjq0gB4oaqjNAM6RyoskNYT4Ak85kiNMcbqEgA0E8YYpaVXzXri2jSAp/CYIzUA0FR25uRrz5FC+bfw0ZButJ4AT0GoAYBfqJr1NLBzpEJpPQEeg1ADAGeobD1VhppRzHoCPAqhBgDOsP1QvvYerWw9Dab1BHgUQg0AnKHqtghXdolUSIDHzKUAIEINADic2XriXk+A5yHUAMBpW7PytO9YkQJa+Ghw1yirywFQT4QaADht4ekL7l3VNUrBtJ4Aj0OoAQA53+tpRDKzngBPRKgBAFW2nn48VqRAPx9dResJ8EiEGgCQtCCd1hPg6Qg1AJq9ytbT6Xs9JTPrCfBUhBoAzd7mg7k6cPyUgvx8dWXXSKvLAdBAhBoAzV7VtWmu6hallv60ngBPRagB0KwZYxzn04xi1hPg0Qg1AJq19J9ydfDkKbX099WgLsx6AjwZoQZAs1Z1bZrB3aIV5O9rcTUAzgehBkCz5XSvp+QYi6sBcL4INQCarY0HTtJ6ArwIoQZAs1V1lGZIt2gF+tF6AjwdoQZAs2S3G8cNLEemMOsJ8AaEGgDN0oYDJ5WVW6xgf18N7MwF9wBvQKgB0CxVtZ6u7k7rCfAWhBoAzY5z64l7PQHeglADoNnZcOCEsvOKFRrQQldc2NbqcgC4CKEGQLOzgNYT4JUINQCalTNbTyO41xPgVQg1AJqV7/efUE5eSWXrqTOtJ8CbEGoANCuOWU89ohXQgtYT4E0INQCajYozWk+juOAe4HUINQCajf/sO67D+SUKDWyh/klccA/wNoQaAM1G2umjNEN7xMi/Bb/+AG/DtxpAs1DZesqWxL2eAG9FqAHQLKzfd1xHC0oUHuSnfp2Y9QR4I0INgGahatbT0B7RtJ4AL8U3G4DXq7AbLdrCBfcAb0eoAeD1vs08pqMFpZWtpyRaT4C3ItQA8HpVradhPWLk58uvPcBb8e0G4NXKK+xavIVZT0BzQKgB4NW+zTyuY4WlatXST306tbG6HACNiFADwKstqGo99aT1BHg7vuEAvFZ5hV1Ltp5uPSXHWlwNgMZW51Dz2WefqaysrDFrAQCX+mbvcR0vLFXrYH/9OrG11eUAaGR1DjWjR4/WyZMnJUm+vr46fPhwY9UEAC6RtjlLUmXrqQWtJ8Dr1flbHhkZqW+++UaSZIyRzWZrtKIA4HyVnTnriQvuAc1Ci7pueO+99+q6666TzWaTzWZTTEzMObetqKhwSXEA0FDr9hzTiaIytQn2V++OtJ6A5qDOoebZZ5/VLbfcooyMDF177bWaNWuWIiIiGrE0AGi4tDNmPdF6ApqHOoeazz77TMOHD1fXrl2VmpqqMWPGqGXLlo1ZGwA0SFmFXYu3csE9oLlp0InCzz33nAoKChqrJgA4L2szjir3VJnahvird0cuuAc0F5woDMDrVLWehvdsJ18fflcBzQUnCgPwKqXldn2xLUcSrSegueFEYQBeZe2eytZTZGiALk9g1hPQnNQ51EhS165dOVEYgFuraj2N6BlD6wloZuoVaqqkpqZKko4cOaKdO3dKkrp06aLIyEjXVQYA9VRa/vO9nkZwwT2g2WnQxRuKiop05513KjY2VgMGDNCAAQMUGxuru+66S0VFRa6uEQDqZE3GEeUXlysqNECX0XoCmp0GhZpHHnlEq1at0meffaaTJ0/q5MmT+vTTT7Vq1So99thjrq4RAOpkQVXrKZlZT0Bz1KD208cff6x///vfGjRokGPZiBEjFBQUpJtuukkzZ850VX0AUCcl5RVaupVZT0Bz1uD2U3R0dLXlUVFRjd5+evPNN5WQkKDAwED17t1b3333XaP+PACe4atdR5VfUq7osABd2qGV1eUAsECDQk2fPn2Umpqq4uJix7JTp05p2rRp6tOnj8uK+6WPPvpIjz76qFJTU/XDDz/ooosu0tChQ3X48OFG+5kAPEPa5p9bTz60noBmyWaMMfV90ZYtWzR06FCVlJTooosukiRt2rRJgYGBWrJkiXr06OHyQiWpd+/euvzyy/XXv/5VkmS32xUXF6cHH3xQU6ZMqfX1eXl5Cg8PV25ursLCwhqlRgBNr7isQpf/6Uvll5Tr4/v66NJ4ThIGvEld/3436Jyanj17avfu3ZozZ4527NghSbr11ls1duxYBQUFNaziWpSWlur777/X1KlTHct8fHw0ZMgQrVu37qyvKSkpUUlJieN5Xl6eJGnjxo0KCQlplDoBNL1v9h7T0R93KDIkQOZIjH44ts/qkgC4UF3vN9mgUFNYWKjg4GBNnDixIS9vkKNHj6qioqLauTzR0dGOYPVL06dP17Rp06otHzhwYKPUCMBa2ZIuf9PqKgBYpUGhJjo6WjfddJPuvPNO9e/f39U1uczUqVP16KOPOp7n5eUpLi5Oq1at4kgN4CVKyis09u1vdaqsQq+MuUjd2tFaBrxNQUFBnQ5INCjU/Otf/9Ls2bN11VVXKSEhQXfeeafuuOMOxcbGNuTt6qRt27by9fVVTk6O0/KcnJxz3lwzICBAAQEB1ZZffPHFnFMDeIklW7Nlb3NYHcMDdevwgZwkDHihqtNHatOg2U/XX3+95s+fr4MHD+ree+/V+++/r/j4eI0aNUrz5s1TeXl5Q962Rv7+/rr00ku1bNkyxzK73a5ly5Y16owrAO4tLZ1ZTwAqNSjUVImMjNSjjz6q9PR0vfrqq/ryyy914403KjY2Vs8884zLr1nz6KOP6u2339Y777yj7du367777lNhYaEmTJjg0p8DwDMUl1Xoy+1ccA9ApQa1n6rk5OTonXfe0ezZs/Xjjz/qxhtv1F133aWffvpJM2bM0DfffKMvvvjCVbXq5ptv1pEjR/TMM88oOztbF198sRYvXnzWCwEC8H4rdx5WUWmFLogI0sVxEVaXA8BiDQo18+bN06xZs7RkyRJ1795d999/v373u98pIiLCsU3fvn3VrVs3V9Xp8MADD+iBBx5w+fsC8DxV93oamdJONhutJ6C5a1ComTBhgm655RatXbtWl19++Vm3iY2N1VNPPXVexQHAuZwqrdDyHZVXEx+ZTOsJQANDzaFDh9SyZcsatwkKClJqamqDigKA2lS1ntq3ClJK+3CrywHgBhoUas4MNMXFxSotLXVaz3RpAI1twWZaTwCcNWj2U2FhoR544AFFRUUpODhYrVq1cnoAQGMqKi3X8u20ngA4a1CoeeKJJ7R8+XLNnDlTAQEB+sc//qFp06YpNjZW7777rqtrBAAnK3Yc0amyCsW1DlLyBbSeAFRqUPvp888/17vvvqtBgwZpwoQJuuKKK5SUlKT4+HjNmTNHY8eOdXWdAOCQtjlLkjQyOZbWEwCHBh2pOX78uBITEyVVnj9z/PhxSVL//v21evVq11UHAL9QWFLumPU0igvuAThDg0JNYmKiMjMzJUldu3bV//3f/0mqPIJz5rVqAMDVlu84rOIyu+LbtFSPWCYlAPhZg0LNhAkTtGnTJknSlClT9OabbyowMFCPPPKIHn/8cZcWCABnqrrX08hkZj0BcFavc2rsdrtefvllffbZZyotLVVWVpZSU1O1Y8cOff/990pKSlJKSkpj1QqgmSssKdeKnadnPdF6AvAL9Qo1zz//vJ599lkNGTJEQUFBev3113X48GH985//VHx8fGPVCACSpGU7Dquk3K6ObYPVvR2tJwDO6tV+evfdd/W3v/1NS5Ys0fz58/X5559rzpw5stvtjVUfADikpVfNeqL1BKC6eoWa/fv3a8SIEY7nQ4YMkc1mU1ZWlssLA4AzFZSUa8XOI5KkEVxwD8BZ1CvUlJeXKzAw0GmZn5+fysrKXFoUAPzSsu05Ki23K7FtsLq1C7W6HABuqF7n1BhjNH78eAUEBDiWFRcX695771VwcLBj2bx581xXIQBIWpDOvZ4A1KxeoWbcuHHVlv3ud79zWTEAcDb5xWVadbr1xKwnAOdSr1Aza9asxqoDAM7py+05Kq2wq1NksLpE03oCcHYNuvgeADSltPRsSdLIFO71BODcCDUA3FpecZlW76psPXGvJwA1IdQAcGtfbqtsPV0YFaLOtJ4A1IBQA8CtpZ0x6wkAakKoAeC2ck+VafXu07OeuOAegFoQagC4raXbclRWYdQ5OkQX0noCUAtCDQC39fO9nmItrgSAJyDUAHBLuUVl+mr3UUnSyJQYi6sB4AkINQDc0pJt2Sq3G3WNCVVSFK0nALUj1ABwSws3n571xAnCAOqIUAPA7ZwsKtWa062nEUzlBlBHhBoAbueLrTkqtxt1axemTpEhVpcDwEMQagC4nQWnW0/cFgFAfRBqALiVE4WlWptxuvXE+TQA6oFQA8CtLNmarQq7Ufd2YerYNtjqcgB4EEINALeStpl7PQFoGEINALdxrKBEX+85Jomp3ADqj1ADwG0s2ZqjCrtRzwvClEDrCUA9EWoAuI2fL7jHvZ4A1B+hBoBbqGw9nb7XE60nAA1AqAHgFhZvzZbdSCntw9WhTUurywHggQg1ANxCWjr3egJwfgg1ACx3JL9E3+ytnPXEBfcANBShBoDlqlpPF7UPV1xrWk8AGoZQA8ByaelZkrjgHoDzQ6gBYKnD+cX6NvO4JFpPAM4PoQaApRZvyZYx0sVxEWrfitYTgIYj1ACwVNWsp1G0ngCcJ0INAMsczivWd/sqW0/DaT0BOE+EGgCWWXS69dSrQ4QuiAiyuhwAHo5QA8AyjgvupXCvJwDnj1ADwBLZucVa/2PVrKcYi6sB4A0INQAssWjLIRkjXRrfSu3CaT0BOH+EGgCW4F5PAFyNUAOgyR3KPaX//HhCEhfcA+A6hBoATW7R5mxJ0uUJrRQTHmhxNQC8BaEGQJNL20zrCYDrEWoANKmsk6f0/Y8nZLNxwT0ArkWoAdCkFp4+SnN5QmtFh9F6AuA6HhFq9u3bp7vuuksdO3ZUUFCQOnXqpNTUVJWWllpdGoB6qmo9ca8nAK7WwuoC6mLHjh2y2+36+9//rqSkJG3ZskUTJ05UYWGhXnnlFavLA1BHP50o0ob9J2WzScN6csE9AK7lEaFm2LBhGjZsmON5YmKidu7cqZkzZxJqAA9SNevpVwmtFRVK6wmAa3lEqDmb3NxctW7dusZtSkpKVFJS4niel5fX2GUBqMECWk8AGpFHnFPzSxkZGXrjjTd0zz331Ljd9OnTFR4e7njExcU1UYUAfunA8SJtOnBSPjZpKK0nAI3A0lAzZcoU2Wy2Gh87duxwes3Bgwc1bNgwjRkzRhMnTqzx/adOnarc3FzH48CBA405HAA1WLSl8ihN745taD0BaBSWtp8ee+wxjR8/vsZtEhMTHf+dlZWlK6+8Un379tVbb71V6/sHBAQoICDgfMsE4AKOez3RegLQSCwNNZGRkYqMjKzTtgcPHtSVV16pSy+9VLNmzZKPj0d2zoBm6cDxIm36KVc+zHoC0Ig84kThgwcPatCgQYqPj9crr7yiI0eOONbFxPALEnB3Vdem6dOpjdqGcPQUQOPwiFCzdOlSZWRkKCMjQ+3bt3daZ4yxqCoAdeVoPSXHWlwJAG/mET2c8ePHyxhz1gcA9/bjsUJtPpgrXx+bhvaItrocAF7MI0INAM/laD0ltlEbWk8AGhGhBkCjYtYTgKZCqAHQaPYdLdTWrLzTrSdO6gfQuAg1ABpNVeupb6c2ah3sb3E1ALwdoQZAo6lqPXGvJwBNgVADoFHsPVKgbYfy1MLHpmu603oC0PgINQAaxcLTrad+SW3VitYTgCZAqAHQKBYw6wlAEyPUAHC5jMMF2pGdf7r1xAX3ADQNQg0Al6tqPfW/sK0iWtJ6AtA0CDUAXO7nez3RegLQdAg1AFwq43C+dubky8+XWU8AmhahBoBLpaVnS5KuuDBS4S39LK4GQHNCqAHgUmmbsyTRegLQ9Ag1AFxmV06+duUUyN/XR0OY9QSgiRFqALhM1QnCAzq3VXgQrScATYtQA8AljDGOG1hywT0AViDUAHCJXTkFyjhc2Xoa3I3WE4CmR6gB4BJp6ZUnCA/oHKmwQFpPAJoeoQbAeTPGaMHp1tMoWk8ALEKoAXDedubka++RQvm38NHgblFWlwOgmSLUADhvVbOeBnWOVCitJwAWIdQAOC/GmJ/v9UTrCYCFCDUAzsv2Q/nae7RQAS2Y9QTAWoQaAOel6rYIV3aJUkhAC4urAdCcEWoANBitJwDuhFADoMG2ZuVp37EiBbTw0VVdmfUEwFqEGgANVnVbhKu6RimY1hMAixFqADQIrScA7oZQA6BBtmblaf/xIgX60XoC4B4INQAaZMHpozSDu0arpT+tJwDWI9QAqDdjjGMqN60nAO6CUAOg3jYfzNWB46cU5OerK7vQegLgHgg1AOqt6gThwd2iFOTva3E1AFCJUAOgXowxjvNpRtF6AuBGCDUA6mXTT7k6ePKUWvr7ahCtJwBuhFADoF7S0itPEB7cLVqBfrSeALgPQg2AOjPGaOHmbEnSyGRaTwDcC6EGQJ1tPHBSB0+eUrC/rwZ1ibS6HABwQqgBUGdVs56GdKf1BMD9EGoA1IndbrTw9A0saT0BcEeEGgB1suHASWXlFiskoIUGdKb1BMD9EGoA1ElV6+lqWk8A3BShBkCtaD0B8ASEGgC1+mH/CWXnFSs0oIWu6NzW6nIA4KwINQBqteCM1lNAC1pPANwToQZAjex2o0VbTreeuNcTADdGqAFQo+/3n1BOXolCA1uo/4W0ngC4L0INgBpVzXq6pnsMrScAbo1QA+CcKs6Y9TSK1hMAN0eoAXBO/9l3XIfzSxQW2EL9kmg9AXBvhBoA55R2+ijN0B4x8m/BrwsA7o3fUgDOqrL1lC2JWU8APAOhBsBZfZd5XEcLShQe5EfrCYBHINQAOKu0zVmSpKE9ouXny68KAO6P31QAqqmwGy3eUtV6irW4GgCoG48LNSUlJbr44otls9m0ceNGq8sBvNK3mcd0tKBUES391LdTG6vLAYA68bhQ88QTTyg2lv9zBBpT1QX3hvWIofUEwGN41G+rRYsW6YsvvtArr7xidSmA1yqvsJ/RemLWEwDP0cLqAuoqJydHEydO1Pz589WyZcs6vaakpEQlJSWO53l5eY1VHuA1vs08rmOFpWrV0k99Emk9AfAcHnGkxhij8ePH695779Vll11W59dNnz5d4eHhjkdcXFwjVgl4hwVVraee7dSC1hMAD2Lpb6wpU6bIZrPV+NixY4feeOMN5efna+rUqfV6/6lTpyo3N9fxOHDgQCONBPAOla0n7vUEwDNZ2n567LHHNH78+Bq3SUxM1PLly7Vu3ToFBAQ4rbvssss0duxYvfPOO2d9bUBAQLXXADi3dXuP6URRmVoH+6t3x9ZWlwMA9WJpqImMjFRkZGSt2/3lL3/Rn/70J8fzrKwsDR06VB999JF69+7dmCUCzYpj1lPPGFpPADyOR5wo3KFDB6fnISEhkqROnTqpffv2VpQEeJ2yCruWbK2c9TQqmdYTAM/D/4oBkCSt21PZemob4q9f0XoC4IE84kjNLyUkJMgYY3UZgFeh9QTA0/GbC4DKKuxafLr1NDKZK3YD8EyEGgBam3FUuafK1DYkgNYTAI9FqAHgaD2NSI6Rr4/N4moAoGEINUAzV1r+86ynkcx6AuDBCDVAM7c246jyissVGRqgyxJoPQHwXIQaoJmrutfTiJ60ngB4NkIN0IyVltv1xbbTracUZj0B8GyEGqAZW5NxRPnF5YoKDdBl8a2sLgcAzguhBmjGHK2n5HbyofUEwMMRaoBmqqS8Qku35kiSRqUw6wmA5yPUAM3UV7uOKr+kXDFhgerVgdYTAM9HqAGaqbTNtJ4AeBdCDdAMFZdVaOm2ytbTSFpPALwEoQZohlbvOqKCknK1Cw/UJXERVpcDAC5BqAGaoYW0ngB4IUIN0MzQegLgrQg1QDOzatcRFZZW6IKIIFpPALwKoQZoZtIcF9yLkc1G6wmA9yDUAM1IcVmFvtxe1XriXk8AvAuhBmhGVu48rKLTraeL2odbXQ4AuBShBmhGqu71NCqlHa0nAF6HUAM0E6dKK7Rs+2FJzHoC4J0INUAzsWLnYZ0qq1D7VkFKvoDWEwDvQ6gBmomqez2NpPUEwEsRaoBmoKi0XMtPt55GJTPrCYB3amF1Ad4gO7dY5Xa71WUA57Roc7ZOlVWoQ+uW6nlBmNXlAECjINS4wG3/+EZ7jxRaXQZQK2Y9AfBmhBoX8Pf1UUALOnlwb5cntNY9AztZXQYANBpCjQssfniA1SUAANDscXgBAAB4BUINAADwCoQaAADgFQg1AADAKxBqAACAVyDUAAAAr0CoAQAAXoFQAwAAvAKhBgAAeAVCDQAA8AqEGgAA4BUINQAAwCsQagAAgFcg1AAAAK/QwuoCmpIxRpKUl5dncSUAAKCuqv5uV/0dP5dmFWry8/MlSXFxcRZXAgAA6is/P1/h4eHnXG8ztcUeL2K325WVlaXQ0FDZbDaXvW9eXp7i4uJ04MABhYWFuex93Ym3j5HxeT5vHyPj83zePsbGHJ8xRvn5+YqNjZWPz7nPnGlWR2p8fHzUvn37Rnv/sLAwr/yHeiZvHyPj83zePkbG5/m8fYyNNb6ajtBU4URhAADgFQg1AADAKxBqXCAgIECpqakKCAiwupRG4+1jZHyez9vHyPg8n7eP0R3G16xOFAYAAN6LIzUAAMArEGoAAIBXINQAAACvQKgBAABegVBTRxUVFXr66afVsWNHBQUFqVOnTvrjH//odB8KY4yeeeYZtWvXTkFBQRoyZIh2795tYdX1U5cxjh8/XjabzekxbNgwC6uun/z8fD388MOKj49XUFCQ+vbtq/Xr1zvWe/o+rG18nrb/Vq9erd/85jeKjY2VzWbT/PnzndbXZX8dP35cY8eOVVhYmCIiInTXXXepoKCgCUdxbq4YX0JCQrV9+uKLLzbhKGpW2xjnzZuna665Rm3atJHNZtPGjRurvUdxcbEmTZqkNm3aKCQkRDfccINycnKaZgC1cMX4Bg0aVG0f3nvvvU0zgFrUNL6ysjI9+eSTSk5OVnBwsGJjY3XHHXcoKyvL6T2a8jtIqKmjGTNmaObMmfrrX/+q7du3a8aMGXrppZf0xhtvOLZ56aWX9Je//EX/8z//o2+//VbBwcEaOnSoiouLLay87uoyRkkaNmyYDh065Hh88MEHFlVcf7///e+1dOlSvffee9q8ebOuueYaDRkyRAcPHpTk+fuwtvFJnrX/CgsLddFFF+nNN9886/q67K+xY8dq69atWrp0qRYsWKDVq1fr7rvvbqoh1MgV45Ok5557zmmfPvjgg01Rfp3UNsbCwkL1799fM2bMOOd7PPLII/r88881d+5crVq1SllZWfrtb3/bWCXXiyvGJ0kTJ0502ocvvfRSY5RbbzWNr6ioSD/88IOefvpp/fDDD5o3b5527typa6+91mm7Jv0OGtTJyJEjzZ133um07Le//a0ZO3asMcYYu91uYmJizMsvv+xYf/LkSRMQEGA++OCDJq21oWobozHGjBs3zlx33XVNXJlrFBUVGV9fX7NgwQKn5b169TJPPfWUx+/D2sZnjGfvP0nmk08+cTyvy/7atm2bkWTWr1/v2GbRokXGZrOZgwcPNlntddGQ8RljTHx8vHnttdeasNKG++UYz5SZmWkkmQ0bNjgtP3nypPHz8zNz5851LNu+fbuRZNatW9eI1dZfQ8ZnjDEDBw40Dz30UKPW5go1ja/Kd999ZySZH3/80RjT9N9BjtTUUd++fbVs2TLt2rVLkrRp0yatWbNGw4cPlyRlZmYqOztbQ4YMcbwmPDxcvXv31rp16yypub5qG2OVlStXKioqSl26dNF9992nY8eOWVFuvZWXl6uiokKBgYFOy4OCgrRmzRqP34e1ja+Kp+6/X6rL/lq3bp0iIiJ02WWXObYZMmSIfHx89O233zZ5zfVRn3+PL774otq0aaNLLrlEL7/8ssrLy5u63Ebz/fffq6yszOlz6Nq1qzp06OAR38u6mjNnjtq2bauePXtq6tSpKioqsrqkBsnNzZXNZlNERISkpv8ONqsbWp6PKVOmKC8vT127dpWvr68qKir0/PPPa+zYsZKk7OxsSVJ0dLTT66Kjox3r3F1tY5QqWxe//e1v1bFjR+3Zs0f/9V//peHDh2vdunXy9fW1sPrahYaGqk+fPvrjH/+obt26KTo6Wh988IHWrVunpKQkj9+HtY1P8uz990t12V/Z2dmKiopyWt+iRQu1bt3a7fdpXf89/uEPf1CvXr3UunVrff3115o6daoOHTqkV199tUnrbSzZ2dny9/d3/JGs4infy7q47bbbFB8fr9jYWKWnp+vJJ5/Uzp07NW/ePKtLq5fi4mI9+eSTuvXWWx03tGzq7yChpo7+7//+T3PmzNH777+vHj16aOPGjXr44YcVGxurcePGWV2eS9RljLfccotj++TkZKWkpKhTp05auXKlBg8ebFXpdfbee+/pzjvv1AUXXCBfX1/16tVLt956q77//nurS3OJ2sbn6fsP1T366KOO/05JSZG/v7/uueceTZ8+3Wsvx+9tzjy/JDk5We3atdPgwYO1Z88ederUycLK6q6srEw33XSTjDGaOXOmZXXQfqqjxx9/XFOmTNEtt9yi5ORk3X777XrkkUc0ffp0SVJMTIwkVTsjPycnx7HO3dU2xrNJTExU27ZtlZGR0YSVNlynTp20atUqFRQU6MCBA/ruu+9UVlamxMREr9iHNY3vbDxt/52pLvsrJiZGhw8fdlpfXl6u48ePu/0+bei/x969e6u8vFz79u1rzPKaTExMjEpLS3Xy5Emn5Z70vayv3r17S5LHfC+rAs2PP/6opUuXOo7SSE3/HSTU1FFRUZF8fJw/Ll9fX9ntdklSx44dFRMTo2XLljnW5+Xl6dtvv1WfPn2atNaGqm2MZ/PTTz/p2LFjateuXWOX51LBwcFq166dTpw4oSVLlui6667zin1Y5WzjOxtP3X9S3b5zffr00cmTJ52OxC1fvlx2u93xh8NdNfTf48aNG+Xj41PtkL+nuvTSS+Xn5+f0OezcuVP79+/3uO9lXVVN+/aE72VVoNm9e7e+/PJLtWnTxml9k38HXX7qsZcaN26cueCCC8yCBQtMZmammTdvnmnbtq154oknHNu8+OKLJiIiwnz66acmPT3dXHfddaZjx47m1KlTFlZed7WNMT8/30yePNmsW7fOZGZmmi+//NL06tXLXHjhhaa4uNji6utm8eLFZtGiRWbv3r3miy++MBdddJHp3bu3KS0tNcZ4/j6saXyeuP/y8/PNhg0bzIYNG4wk8+qrr5oNGzY4ZlbUZX8NGzbMXHLJJebbb781a9asMRdeeKG59dZbrRqSk/Md39dff21ee+01s3HjRrNnzx7zr3/9y0RGRpo77rjDymE5qW2Mx44dMxs2bDBpaWlGkvnwww/Nhg0bzKFDhxzvce+995oOHTqY5cuXm//85z+mT58+pk+fPlYNycn5ji8jI8M899xz5j//+Y/JzMw0n376qUlMTDQDBgywclgONY2vtLTUXHvttaZ9+/Zm48aN5tChQ45HSUmJ4z2a8jtIqKmjvLw889BDD5kOHTqYwMBAk5iYaJ566imnHWe3283TTz9toqOjTUBAgBk8eLDZuXOnhVXXT21jLCoqMtdcc42JjIw0fn5+Jj4+3kycONFkZ2dbXHndffTRRyYxMdH4+/ubmJgYM2nSJHPy5EnHek/fhzWNzxP334oVK4ykao9x48YZY+q2v44dO2ZuvfVWExISYsLCwsyECRNMfn6+BaOp7nzH9/3335vevXub8PBwExgYaLp162ZeeOEFtwqptY1x1qxZZ12fmprqeI9Tp06Z+++/37Rq1cq0bNnSjB492in0WOl8x7d//34zYMAA07p1axMQEGCSkpLM448/bnJzc60b1BlqGl/VNPWzPVasWOF4j6b8DtqMOeNysQAAAB6Kc2oAAIBXINQAAACvQKgBAABegVADAAC8AqEGAAB4BUINAADwCoQaAADgFQg1AFwqISFBf/7zn60uw23s27dPNpvNcel7V5s9e3a1O1gDzRWhBnATR44c0X333acOHTooICBAMTExGjp0qNauXevSnzN+/Hhdf/31ddrOZrPJZrPJ399fSUlJeu6551ReXl7j69avX+9012Er1DVYJSQkOMZ45uPFF190WS1xcXE6dOiQevbsed7vdbZx3Xzzzdq1a9d5vzfgDVpYXQCASjfccINKS0v1zjvvKDExUTk5OVq2bJmOHTtmWU3Dhg3TrFmzVFJSooULF2rSpEny8/PT1KlTq21bWloqf39/RUZGWlBpwz333HOaOHGi07LQ0FCXvb+vr2+NdyM2xqiiokItWjTs13FQUJCCgoIaWh7gXRrl5gsA6uXEiRNGklm5cmWN20kyf/vb38ywYcNMYGCg6dixo5k7d67TNunp6ebKK680gYGBpnXr1mbixImO+6ykpqbWeI+WM40bN85cd911Tsuuvvpq8+tf/9pp/Z/+9CfTrl07k5CQYIwxJj4+3rz22mtOY7v77rtNVFSUCQgIMD169DCff/65Y/1XX31l+vfvbwIDA0379u3Ngw8+aAoKCs75GWRkZJhrr73WREVFmeDgYHPZZZeZpUuXOtYPHDiw2hjP5Ze1/tK0adNMu3btzNGjRx3LRowYYQYNGmQqKiqMMbXvk6r742zYsMEY8/O9dBYuXGh69epl/Pz8zIoVKxo8rlmzZpnw8HCnuv/2t7+ZxMRE4+fnZzp37mzeffddp/WSzNtvv22uv/56ExQUZJKSksynn356zs8B8BS0nwA3EBISopCQEM2fP18lJSU1bvv000/rhhtu0KZNmzR27Fjdcsst2r59uySpsLBQQ4cOVatWrbR+/XrNnTtXX375pR544AFJ0uTJk3XTTTdp2LBhOnTokA4dOqS+ffvWuc6goCCVlpY6ni9btkw7d+7U0qVLtWDBgmrb2+12DR8+XGvXrtW//vUvbdu2TS+++KJ8fX0lSXv27NGwYcN0ww03KD09XR999JHWrFnjqPdsCgoKNGLECC1btkwbNmzQsGHD9Jvf/Eb79++XJM2bN0/t27fXc8895xhjQz311FNKSEjQ73//e0nSm2++qa+//lrvvPOOfHx+/vVZ0z45lylTpujFF1/U9u3blZKS4rJxffLJJ3rooYf02GOPacuWLbrnnns0YcIErVixwmm7adOm6aabblJ6erpGjBihsWPH6vjx4w3+rAC3YHWqAlDp3//+t2nVqpUJDAw0ffv2NVOnTjWbNm1y2kaSuffee52W9e7d29x3333GGGPeeust06pVK6cjHWlpacbHx8dxN+6zHYE5mzO3s9vtZunSpSYgIMBMnjzZsT46OtrpTvXGOB/9WLJkifHx8Tnnnc7vuusuc/fddzst++qrr4yPj485depUrTVW6dGjh3njjTfOWkNN4uPjjb+/vwkODnZ6rF692rHNnj17TGhoqHnyySdNUFCQmTNnjtN71LZPznWkZv78+S4Z1y+P1PTt29dMnDjRaZsxY8aYESNGONX83//9347nBQUFRpJZtGhRrTUB7owjNYCbuOGGG5SVlaXPPvtMw4YN08qVK9WrVy/Nnj3babs+ffpUe151VGD79u266KKLFBwc7Fjfr18/2e127dy5s941LViwQCEhIQoMDNTw4cN1880369lnn3WsT05Olr+//zlfv3HjRrVv316dO3c+6/pNmzZp9uzZjiNVISEhGjp0qOx2uzIzM8/6moKCAk2ePFndunVTRESEQkJCtH37dscRjfp6/PHHtXHjRqfHZZdd5lifmJioV155RTNmzNC1116r2267rdp71LRPzuXMn+HKcW3fvl39+vVzWtavX79q9aSkpDj+Ozg4WGFhYTp8+HC9fhbgbjhRGHAjgYGBuvrqq3X11Vfr6aef1u9//3ulpqZq/PjxltRz5ZVXaubMmfL391dsbGy1k1nPDE9nU9sJrAUFBbrnnnv0hz/8odq6Dh06nPU1kydP1tKlS/XKK68oKSlJQUFBuvHGG53aYvXRtm1bJSUl1bjN6tWr5evrq3379qm8vLzBJ/We6ZefnavHVRs/Pz+n5zabTXa7vVF+FtBUOFIDuLHu3bursLDQadk333xT7Xm3bt0kSd26ddOmTZucXrN27Vr5+PioS5cukiR/f39VVFTU6ecHBwcrKSlJHTp0aNAf8pSUFP3000/nnHLcq1cvbdu2TUlJSdUe5zoCtHbtWo0fP16jR49WcnKyYmJitG/fPqdt6jPG2nz00UeaN2+eVq5cqf379+uPf/xjtW1q2id15apxdevWrdplANauXavu3bvXqx7AExFqADdw7NgxXXXVVfrXv/6l9PR0ZWZmau7cuXrppZd03XXXOW07d+5c/fOf/9SuXbuUmpqq7777znFi7dixYxUYGKhx48Zpy5YtWrFihR588EHdfvvtio6OllR5rZP09HTt3LlTR48eVVlZWaONa+DAgRowYIBuuOEGLV26VJmZmVq0aJEWL14sSXryySf19ddf64EHHtDGjRu1e/duffrppzWeKHzhhRdq3rx52rhxozZt2qTbbrut2hGGhIQErV69WgcPHtTRo0drrDE/P1/Z2dlOj7y8PEnSTz/9pPvuu08zZsxQ//79NWvWLL3wwgvVQkxN+6SuXDWuxx9/XLNnz9bMmTO1e/duvfrqq5o3b54mT55cr3oAj2T1ST0AjCkuLjZTpkwxvXr1MuHh4aZly5amS5cu5r//+79NUVGRYztJ5s033zRXX321CQgIMAkJCeajjz5yeq+apnQbY8zhw4fN1VdfbUJCQuo9pbsu6395MuuxY8fMhAkTTJs2bUxgYKDp2bOnWbBggWP9d99956gnODjYpKSkmOeff/6cPzczM9NceeWVJigoyMTFxZm//vWvZuDAgeahhx5ybLNu3TqTkpJiAgICap3SrV9Mk5Zk7rnnHmO3283gwYPN0KFDjd1ud7zmwQcfNJ06dXJ8prXtk3OdKHzixAmXjKuhU7o/+eQTp2Xh4eFm1qxZ5/ysAE9gM8YYS9IUgHqz2Wz65JNP6nRFYDQN9gngPmg/AQAAr0CoAQAAXoH2EwAA8AocqQEAAF6BUAMAALwCoQYAAHgFQg0AAPAKhBoAAOAVCDUAAMArEGoAAIBXINQAAACvQKgBAABe4f8D7pDVy6pSjlcAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "XsnIrsEn41tj"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}