InterestRate/ZeroCoupon/Nelson_and_Siegel.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import datetime\n",
    "import math\n",
    "from dateutils import relativedelta\n",
    "from scipy import optimize\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "valuation_date = datetime.datetime(2019,11,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "## ------------------------------------------_\n",
    "## This functions was retrieved from \n",
    "## https://github.com/peliot/XIRR-and-XNPV/blob/master/financial.py\n",
    "## ------------------------------------------_\n",
    "\n",
    "def xnpv(rate,cashflows):\n",
    "    chron_order = sorted(cashflows, key = lambda x: x[0])\n",
    "    t0 = chron_order[0][0]\n",
    "    return sum([cf/(1+rate)**((t-t0).days/365.0) for (t,cf) in chron_order])\n",
    "\n",
    "def xirr(cashflows,guess=0.1):\n",
    "    return optimize.newton(lambda r: xnpv(r,cashflows),guess)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_coupon_dates(start_date, frequency, number_periods, end_date, lower_date_threshold=None):\n",
    "    \"\"\"\n",
    "        Right now this function just calculates coupon dates with frequency in Years\n",
    "    \"\"\"\n",
    "    if frequency != 'Y':\n",
    "        raise Exeception('(build_coupon_dates) So far, this function just works with years as frequency.')\n",
    "        \n",
    "    is_over = False\n",
    "    dates = []\n",
    "    temporal_date = start_date\n",
    "    \n",
    "    if lower_date_threshold is None:\n",
    "        lower_date_threshold = start_date\n",
    "    \n",
    "    while(not is_over):\n",
    "        if temporal_date <= end_date:\n",
    "            if temporal_date >= lower_date_threshold:\n",
    "                dates.append(temporal_date.date())\n",
    "            temporal_date = temporal_date + relativedelta(years=number_periods)\n",
    "        else:\n",
    "            is_over = True\n",
    "    \n",
    "    return dates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_flows_projection(valuation_date, coupon_rate, nominal, coupon_dates, year_days=365):\n",
    "    if isinstance(valuation_date, datetime.datetime):\n",
    "        valuation_date = valuation_date.date()\n",
    "    df_flows = coupon_dates\n",
    "    df_flows['period'] = df_flows['date'].apply(lambda x : (x-valuation_date).days/year_days)\n",
    "    df_flows['payment'] = nominal*coupon_rate\n",
    "    \n",
    "    df_flows.loc[len(df_flows)-1,'payment'] += nominal\n",
    "    \n",
    "    return df_flows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_initial_nelson_siegel_rate(coupon_flows, b0, b1, b2, tau):\n",
    "    df_ns_rates = coupon_flows.copy()\n",
    "    df_ns_rates['ns_rates'] = df_ns_rates['period']\\\n",
    "                                .apply(\n",
    "                                    lambda x:\n",
    "                                        (b0 + ((b1+b2)*((1-math.exp(-x / tau)) / (x/tau))) - b2*math.exp(-x/tau) ) / 100\n",
    "                                )\n",
    "    return df_ns_rates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_present_value(flows):\n",
    "    df_pv = flows.copy()\n",
    "    df_pv['present_value'] = [v['payment']*math.exp(-v['period']*v['ns_rates']) for i, v in df_pv.iterrows()]\n",
    "    return df_pv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def root_mean_squared_error(observed, model):\n",
    "    diff_ = (np.subtract(observed,model)*10000)**2\n",
    "    return sum(diff_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Nelson and Siegel Model (1987)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In financial industry, people do need to get the term structure of interest rates in a lot point over time, to assets valuation, and another tasks. But this structure could has particular characteristics like we will see in the figure about colombian TES yield curve, like long term level, short term level and convexity and some times inflexion points. This characteristics do the calculations about term structure of interest, some difficult in simplicity, as it could be seen on many methods developed throught 80's and 90's, known as cuadratic and cubic splines by McCulloch (1971) and any others, built with splines structure, and having some critics (<a href=\"https://pdfs.semanticscholar.org/70c4/20a1dc336394866dff5f206df6cc8274d991.pdf\">see this article</a>).\n",
    "\n",
    "To this, Nelson and Siegel did make one model in 1987 (<b><a href=\"http://web.math.ku.dk/~rolf/teaching/NelsonSiegel.pdf\">original article</a></b>), more simple where looking four parameters, and a specific function, is posible to model forward rates in discrete time. It had an transformation where using the model is posible to get the spot interest rate, applying over forward model, the integration operator."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Colombian TES Yield Curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "free_risk_bonds = pd.read_excel('bonds_free_risk.xlsx', engine='openpyxl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "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>period</th>\n",
       "      <th>maturity_date</th>\n",
       "      <th>coupon_rate</th>\n",
       "      <th>clean_price</th>\n",
       "      <th>yield_rate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.704110</td>\n",
       "      <td>2020-07-24</td>\n",
       "      <td>0.1100</td>\n",
       "      <td>105570</td>\n",
       "      <td>0.0415</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.482192</td>\n",
       "      <td>2022-05-04</td>\n",
       "      <td>0.0700</td>\n",
       "      <td>105348</td>\n",
       "      <td>0.0477</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.706849</td>\n",
       "      <td>2024-07-24</td>\n",
       "      <td>0.1000</td>\n",
       "      <td>120446</td>\n",
       "      <td>0.0512</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6.049315</td>\n",
       "      <td>2025-11-26</td>\n",
       "      <td>0.0625</td>\n",
       "      <td>104090</td>\n",
       "      <td>0.0544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6.797260</td>\n",
       "      <td>2026-08-26</td>\n",
       "      <td>0.0750</td>\n",
       "      <td>110910</td>\n",
       "      <td>0.0556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>8.471233</td>\n",
       "      <td>2028-04-28</td>\n",
       "      <td>0.0600</td>\n",
       "      <td>100951</td>\n",
       "      <td>0.0585</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>10.863014</td>\n",
       "      <td>2030-09-18</td>\n",
       "      <td>0.0775</td>\n",
       "      <td>113546</td>\n",
       "      <td>0.0603</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>12.646575</td>\n",
       "      <td>2032-06-30</td>\n",
       "      <td>0.0700</td>\n",
       "      <td>106976</td>\n",
       "      <td>0.0619</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>14.947945</td>\n",
       "      <td>2034-10-18</td>\n",
       "      <td>0.0725</td>\n",
       "      <td>109163</td>\n",
       "      <td>0.0629</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      period maturity_date  coupon_rate  clean_price  yield_rate\n",
       "0   0.704110    2020-07-24       0.1100       105570      0.0415\n",
       "1   2.482192    2022-05-04       0.0700       105348      0.0477\n",
       "2   4.706849    2024-07-24       0.1000       120446      0.0512\n",
       "3   6.049315    2025-11-26       0.0625       104090      0.0544\n",
       "4   6.797260    2026-08-26       0.0750       110910      0.0556\n",
       "5   8.471233    2028-04-28       0.0600       100951      0.0585\n",
       "6  10.863014    2030-09-18       0.0775       113546      0.0603\n",
       "7  12.646575    2032-06-30       0.0700       106976      0.0619\n",
       "8  14.947945    2034-10-18       0.0725       109163      0.0629"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "free_risk_bonds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1440x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20,7))\n",
    "\n",
    "plt.plot(\n",
    "    free_risk_bonds['period'],\n",
    "    free_risk_bonds['yield_rate']*100,\n",
    "    label='Original Colombian TES Yield Rate',\n",
    "    linestyle='--',\n",
    "    marker='o',\n",
    "    c='red',\n",
    "    alpha=0.6\n",
    ")\n",
    "\n",
    "plt.title('Colombian TES Yield Curve', fontsize=20)\n",
    "plt.ylabel('Interest Rate (%)', fontsize=14)\n",
    "plt.xlabel('Time to Maturity (yrs)', fontsize=14)\n",
    "\n",
    "plt.legend(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Basically we want to estimate four parameters, called B<sub>0</sub>, B<sub>1</sub>, B<sub>2</sub> and tau (<b><a href=\"https://education.wbstraining.com/pluginfile.php/4716/mod_resource/content/2/Chaves_Technical%2520Manual%2520Nelson%2520%2520Siegel%2520model.pdf\">take a look here</a></b>). This parameters represents some characteristic on term structure of interest rate. \n",
    "\n",
    "- <b>B<sub>0</sub></b> : Is the level of long term interest rate in the curve\n",
    "- <b>B<sub>1</sub></b> : Is the spread between short and long term of interest rate\n",
    "- <b>B<sub>2</sub></b> : Will be the term where the term structure could have a inflexion point\n",
    "- <b>Tau</b> : Is  the decay factor in term structure of interest rate, small values produce slow decay while large values produce fast decay\n",
    "\n",
    "Thus, to this example, we will set this values, based on the chart above, as:\n",
    "- <b>B<sub>0</sub></b> = 7\n",
    "- <b>B<sub>1</sub></b> = 4 - 7 = - 3\n",
    "- <b>B<sub>2</sub></b> = 0, because I don't see some strongest inflexion point\n",
    "- <b>Tau</b> : 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "first_ = False\n",
    "free_risk_bonds_first = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nelson_and_siegel(x):\n",
    "    \n",
    "    b0=x[0]\n",
    "    b1=x[1]\n",
    "    b2=x[2]\n",
    "    tau=x[3]\n",
    "    \n",
    "    global free_risk_bonds\n",
    "    global free_risk_bonds_first\n",
    "    global first_\n",
    "    \n",
    "    for i_, values in free_risk_bonds.iterrows():\n",
    "\n",
    "        start_date = values['maturity_date'] + relativedelta(years=-30)\n",
    "        end_date = values['maturity_date']\n",
    "        coupon_rate = values['coupon_rate']\n",
    "        default_nominal = 100\n",
    "\n",
    "        df_coupon_flows = build_coupon_dates(\n",
    "                                start_date=start_date,\n",
    "                                frequency='Y',\n",
    "                                number_periods=1,\n",
    "                                end_date=end_date,\n",
    "                                lower_date_threshold=valuation_date\n",
    "                            )\n",
    "\n",
    "        df_coupon_flows = pd.DataFrame(df_coupon_flows, columns=['date'])\n",
    "\n",
    "        df_coupon_flows = build_flows_projection(\n",
    "                                valuation_date=valuation_date,\n",
    "                                coupon_rate=coupon_rate,\n",
    "                                nominal=default_nominal,\n",
    "                                coupon_dates=df_coupon_flows\n",
    "                            )\n",
    "\n",
    "        df_coupon_flows = calculate_initial_nelson_siegel_rate(\n",
    "                                coupon_flows=df_coupon_flows,\n",
    "                                b0=b0,\n",
    "                                b1=b1,\n",
    "                                b2=b2,\n",
    "                                tau=tau\n",
    "                            )\n",
    "\n",
    "        # ns_flows\n",
    "\n",
    "        df_coupon_flows = calculate_present_value(flows=df_coupon_flows)\n",
    "\n",
    "        bond_dirty_price = df_coupon_flows['present_value'].sum()\n",
    "\n",
    "        # XIRR\n",
    "        _v_xirr = xirr(\n",
    "            [(valuation_date.date(), -bond_dirty_price )] + [tuple (i) for i in df_coupon_flows[['date','payment']].values.tolist()]\n",
    "        )\n",
    "\n",
    "        free_risk_bonds.loc[i_,'dirty_price'] = bond_dirty_price\n",
    "        free_risk_bonds.loc[i_,'xirr'] = _v_xirr\n",
    "    \n",
    "    if not first_:\n",
    "        first_ = True\n",
    "        free_risk_bonds_first = free_risk_bonds.copy()\n",
    "    \n",
    "    return root_mean_squared_error(free_risk_bonds['yield_rate'],free_risk_bonds['xirr'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Minimizing RMSE\n",
    "- between observed yield rate and xirr calculated using Nelson and Siegel rates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get Nelson and Siegel model's parameters, we must to minimize the error between yield rate observed and yield rate in NS's model. To get this I did use root mean squared error <b>(RMSE)</b>. But before, we need to take into account that the model to look a local mimimum, reason why we need to set B0, B1, B2 and tau in some value nearest to original yield curve, as we did."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 132.911392\n",
      "         Iterations: 218\n",
      "         Function evaluations: 403\n"
     ]
    }
   ],
   "source": [
    "x0 = np.array([7.0, -3.0, 0.0, 1.0])\n",
    "res = optimize.minimize(nelson_and_siegel, x0, method='nelder-mead', options={'xtol': 1e-8, 'disp': True})\n",
    "\n",
    "if res.success:\n",
    "    res = res.x.tolist()\n",
    "else:\n",
    "    raise Exception('Something is wrong! .... What could have been happen? ... '+res.message)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "        Nelson and Siegel parameters calculated:\n",
      "            - B0 \t\t: 7.677302298888388\n",
      "            - B1 \t\t: -3.8389432946747624\n",
      "            - B2 \t\t: -0.012194752502677266\n",
      "            - tau \t\t: 5.265190450792611\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "print(\"\"\"\n",
    "        Nelson and Siegel parameters calculated:\n",
    "            - B0 \\t\\t: {b0}\n",
    "            - B1 \\t\\t: {b1}\n",
    "            - B2 \\t\\t: {b2}\n",
    "            - tau \\t\\t: {tau}\n",
    "    \"\"\".format(\n",
    "        b0 = res[0],\n",
    "        b1 = res[1],\n",
    "        b2 = res[2],\n",
    "        tau = res[3]\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1440x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20,7))\n",
    "\n",
    "plt.plot(\n",
    "    free_risk_bonds_first['period'],\n",
    "    free_risk_bonds_first['xirr']*100,\n",
    "    label='Curve with Initial NS parameters',\n",
    "    linestyle='--',\n",
    "    marker='o',\n",
    "    c='gray'\n",
    ")\n",
    "\n",
    "plt.plot(\n",
    "    free_risk_bonds['period'],\n",
    "    free_risk_bonds['xirr']*100,\n",
    "    label='Curve with Final NS parameters',\n",
    "    linestyle='--',\n",
    "    marker='o',\n",
    "    c='blue',\n",
    "    alpha=0.6\n",
    ")\n",
    "\n",
    "plt.plot(\n",
    "    free_risk_bonds['period'],\n",
    "    free_risk_bonds['yield_rate']*100,\n",
    "    label='Original Yield Rate',\n",
    "    linestyle='--',\n",
    "    marker='o',\n",
    "    c='red',\n",
    "    alpha=0.5\n",
    ")\n",
    "\n",
    "plt.title('Comparison Yield Curve observed and Nelson-Siegel Yield Curve', fontsize=20)\n",
    "plt.ylabel('Interest Rate (%)', fontsize=14)\n",
    "plt.xlabel('Time to Maturity (yrs)', fontsize=14)\n",
    "\n",
    "plt.legend(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we did see above, the line colored as gray represents the term structure using the initial parameters of B<sub>0</sub>, B<sub>1</sub>, B<sub>2</sub> and tau, as 7, -3, 0 and 1, respectively. The line colored light red is observed yield curve.\n",
    "\n",
    "Nevertheless after minimizing RMSE between observed and NS's yield curve, I did get the line colored as blue, drawn using parameters <b>B<sub>0</sub></b>=7.6773, <b>B<sub>1</sub></b>=-3.8389, <b>B<sub>2</sub></b>=-0.0121 and <b>Tau</b>=5.2651. This parameters let to the term structure of interest rate to be nearest to original yield curve, and for this reason, we could use this to get any interest rate in term structure of spot interest rate throught time without worry about we just have specific nodes in original yield curve.\n",
    "\n",
    "Its important underline this interest rate is spot, because was used the Nelson and Siegel model after using integration operator."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This could not to be the final version, so if you have some recommendation or comment about this, I will be grateful to hear it, using e-mail <b>craquinterogo@unal.edu.co</b> or <b>cristian.quintero@est.uexternado.edu.co</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>"
   ]
  }
 ],
 "metadata": {
  "hide_input": false,
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.6"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}