examples/notebook/heavylight_basic.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "62a375d3-e011-4f97-863f-399660e3a3d0",
   "metadata": {},
   "source": [
    "# Heavylight example notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2c0620e8-f047-4c82-b924-a8a88f6efef7",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from heavylight import Model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "223844b8-0e8f-4fd6-b8e4-d72a3bd3f3c8",
   "metadata": {},
   "source": [
    "Define the model as a class - note that it doesn't need to be defined in terms of `t` for time, but this is fairly standard"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2fa05b8f-c670-43c8-8a2a-dbe050661c64",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "class Annuity(Model):\n",
    "    def t(self, t):\n",
    "        return t\n",
    "\n",
    "    def expected_claim(self, t):\n",
    "        return self.number_alive(t) * self.data[\"annuity_per_period\"]\n",
    "\n",
    "    def number_alive(self, t):\n",
    "        if t == 0:\n",
    "            return self.data[\"initial_policies\"]\n",
    "        else:\n",
    "            return self.number_alive(t - 1) - self.deaths(t - 1)\n",
    "    \n",
    "    def deaths(self, t):\n",
    "        return self.number_alive(t) * self.mortality_rate(t)\n",
    "\n",
    "    def mortality_rate(self, t):\n",
    "        return self.basis[\"q_x\"](t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72ed411e-5706-4fdb-ac04-a395fd3b522a",
   "metadata": {},
   "source": [
    "Define the data for the model, as a python dictionary (can use any storage object)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a5497421-ce9d-44b7-991f-df61dc3a2db3",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "policy_data = {\n",
    "    \"initial_policies\": 10,\n",
    "    \"annuity_per_period\": 55,\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bfa9f0c9-1c62-423d-973f-ff57a9269182",
   "metadata": {},
   "source": [
    "Rather than using a table of mortality rates, we could define a function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "46737aba-0264-4795-8edb-1ba95ff25598",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def q_x(t):\n",
    "    return 0.02*2.64**(0.04 * (t + 30)) + 0.002"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "983ff576-cd33-44f9-b207-567f2f6d6d4f",
   "metadata": {},
   "source": [
    "Store this function in a basis dictionary so we can pass into the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f6f4aa4a-6d10-467e-a715-a0cdbf84a7b9",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "basis = {\n",
    "    \"q_x\": q_x,\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca5ed51e-fcb1-4329-bff7-d7e75c07962a",
   "metadata": {},
   "source": [
    "Create an instance of the model, passing in the data and basis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6684b54a-fafd-4c28-bae2-6c9196d24064",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "model = Annuity(data = policy_data,\n",
    "                basis = basis,\n",
    "                do_run = True,\n",
    "                proj_len = 40,\n",
    "                )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe23fa8c-c58b-4991-b4d9-2af0eb2b15ca",
   "metadata": {},
   "source": [
    "We can look-up individual results of the model directly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2460b718-9c85-4cae-8779-b42d6031726e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "379.7484060121289"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.expected_claim(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84d43a47-d7e9-4893-82f3-02c894a10b81",
   "metadata": {},
   "source": [
    "Pull all single parameter functions into a dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "77c5845a-a119-4476-aa47-f0403c1450c8",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>deaths</th>\n",
       "      <th>expected_claim</th>\n",
       "      <th>mortality_rate</th>\n",
       "      <th>number_alive</th>\n",
       "      <th>t</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.661143</td>\n",
       "      <td>550.000000</td>\n",
       "      <td>0.066114</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.641139</td>\n",
       "      <td>513.637151</td>\n",
       "      <td>0.068653</td>\n",
       "      <td>9.338857</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.620078</td>\n",
       "      <td>478.374486</td>\n",
       "      <td>0.071292</td>\n",
       "      <td>8.697718</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.598033</td>\n",
       "      <td>444.270217</td>\n",
       "      <td>0.074036</td>\n",
       "      <td>8.077640</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.575091</td>\n",
       "      <td>411.378405</td>\n",
       "      <td>0.076888</td>\n",
       "      <td>7.479607</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     deaths  expected_claim  mortality_rate  number_alive  t\n",
       "0  0.661143      550.000000        0.066114     10.000000  0\n",
       "1  0.641139      513.637151        0.068653      9.338857  1\n",
       "2  0.620078      478.374486        0.071292      8.697718  2\n",
       "3  0.598033      444.270217        0.074036      8.077640  3\n",
       "4  0.575091      411.378405        0.076888      7.479607  4"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_cashflows = model.ToDataFrame()\n",
    "model_cashflows.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38da052e-6a1f-4075-9621-da401e9561ac",
   "metadata": {},
   "source": [
    "Plot the key output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ee35f832-25c3-4d16-abed-23704666ae45",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_cashflows.plot(x=\"t\", y=\"expected_claim\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "60355de2-d475-40d7-9cef-119abbd6507a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_cashflows.plot(x=\"t\", y=\"mortality_rate\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "71f0a83e-9430-4cc3-8675-254611e60fe7",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "## Calculate the present value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "eefd51a4-9050-4e45-a1e8-77206cafe9d0",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def npv(cashflows, rate):\n",
    "    return sum(cashflow / ((1 + rate) ** t) for t, cashflow in enumerate(cashflows, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "cd8ff8bb-1674-4f8c-809a-540456c571e6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4364.808437169173"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npv(model_cashflows[\"expected_claim\"], 0.04)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b745b14-2426-48cb-97b7-5b5343da2dd3",
   "metadata": {},
   "source": [
    "Quick check that the NPV formula is sensible"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "537d294e-184c-414c-b927-84d53eb3ec92",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5963.772020370224"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npv(model_cashflows[\"expected_claim\"], 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "aabb14a3-77c9-41e6-a302-6e9955ccbd2c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5963.772020370224"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_cashflows.expected_claim.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b6805aec-90ff-49fa-b8a7-bd1dcc737edd",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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