yieldcurve/nelson-siegel-svensson.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "4753EEF952C84B03933ACBBC2915BBC5"
   },
   "source": [
    "# Nelson-Siegel-Svensson from the German Bundesbank\n",
    "Thomas Viehmann <tv@interesting-rates.de>\n",
    "\n",
    "We quickly implement the Nelson-Siegel-Svensson method and calculate the German Bundesbank's Bund yield curves from the parameters.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "cell_id": "8CCBAC2B868F43148C1F67370254CC8F"
   },
   "outputs": [],
   "source": [
    "import pandas\n",
    "import numpy\n",
    "import urllib.request\n",
    "from matplotlib import pyplot\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "9410D3813B124952853E046579DB94DD"
   },
   "source": [
    "We download the parameters from the Bundesbank in CSV format."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "cell_id": "3415D556CE794967819D18636F1726B4"
   },
   "outputs": [],
   "source": [
    "df = pandas.read_csv(urllib.request.urlopen(\"http://www.bundesbank.de/cae/servlet/StatisticDownload?tsId=BBK01.WZ9801&tsId=BBK01.WZ9802&tsId=BBK01.WZ9803&tsId=BBK01.WZ9804&tsId=BBK01.WZ9805&tsId=BBK01.WZ9806&its_csvFormat=en&its_fileFormat=csv&mode=its&its_dateFormat=dateOfDay\"), index_col=0)\n",
    "df.drop([x for x in df.columns if x.endswith(\"_FLAGS\")],axis=1, inplace=True)\n",
    "mapping = dict((df.iloc[0].dropna().apply(lambda x: x.split(\" / \")[1].split()[1])).items())\n",
    "df.columns = [mapping.get(x,x).lower() for x in df.columns]\n",
    "df = df.iloc[4:]\n",
    "df = df.apply(lambda x: x.astype(float))\n",
    "df.index = pandas.to_datetime(df.index)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "BE4E627FE5C44C8188CEC55FA9F1A6BD"
   },
   "source": [
    "Let us see what we got:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "cell_id": "42A3A48687464F118F3B204910085C07"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>beta0</th>\n",
       "      <th>beta1</th>\n",
       "      <th>beta2</th>\n",
       "      <th>tau1</th>\n",
       "      <th>beta3</th>\n",
       "      <th>tau2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1972-09-30</th>\n",
       "      <td>8.58387</td>\n",
       "      <td>30.00000</td>\n",
       "      <td>-29.88450</td>\n",
       "      <td>0.36495</td>\n",
       "      <td>-13.91200</td>\n",
       "      <td>0.36543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1972-10-31</th>\n",
       "      <td>8.52889</td>\n",
       "      <td>29.58953</td>\n",
       "      <td>28.98429</td>\n",
       "      <td>0.00481</td>\n",
       "      <td>-7.48676</td>\n",
       "      <td>0.26523</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1972-11-30</th>\n",
       "      <td>8.80418</td>\n",
       "      <td>29.92019</td>\n",
       "      <td>-20.51146</td>\n",
       "      <td>0.51241</td>\n",
       "      <td>-30.00000</td>\n",
       "      <td>0.24715</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1972-12-31</th>\n",
       "      <td>9.43739</td>\n",
       "      <td>-7.46531</td>\n",
       "      <td>-20.48638</td>\n",
       "      <td>1.29510</td>\n",
       "      <td>28.55031</td>\n",
       "      <td>1.01820</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-01-31</th>\n",
       "      <td>11.61329</td>\n",
       "      <td>-4.48145</td>\n",
       "      <td>-8.47201</td>\n",
       "      <td>0.52885</td>\n",
       "      <td>-7.08296</td>\n",
       "      <td>4.69237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-02-28</th>\n",
       "      <td>11.45540</td>\n",
       "      <td>13.02996</td>\n",
       "      <td>-30.00000</td>\n",
       "      <td>0.39174</td>\n",
       "      <td>-7.29206</td>\n",
       "      <td>5.24815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-03-31</th>\n",
       "      <td>11.44706</td>\n",
       "      <td>-6.15884</td>\n",
       "      <td>28.95551</td>\n",
       "      <td>2.46182</td>\n",
       "      <td>-30.00000</td>\n",
       "      <td>3.09107</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-04-30</th>\n",
       "      <td>8.90814</td>\n",
       "      <td>-12.64824</td>\n",
       "      <td>-10.75908</td>\n",
       "      <td>0.58485</td>\n",
       "      <td>30.00000</td>\n",
       "      <td>0.42540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-05-31</th>\n",
       "      <td>10.36056</td>\n",
       "      <td>21.01261</td>\n",
       "      <td>-30.00000</td>\n",
       "      <td>0.12923</td>\n",
       "      <td>-2.28758</td>\n",
       "      <td>3.54882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-06-30</th>\n",
       "      <td>10.30138</td>\n",
       "      <td>19.20941</td>\n",
       "      <td>-24.00549</td>\n",
       "      <td>0.44307</td>\n",
       "      <td>-1.48525</td>\n",
       "      <td>1.65952</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-07-31</th>\n",
       "      <td>10.28803</td>\n",
       "      <td>-0.75852</td>\n",
       "      <td>-29.29636</td>\n",
       "      <td>1.69725</td>\n",
       "      <td>30.00000</td>\n",
       "      <td>1.54753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-08-31</th>\n",
       "      <td>9.45106</td>\n",
       "      <td>-1.76690</td>\n",
       "      <td>-30.00000</td>\n",
       "      <td>0.00685</td>\n",
       "      <td>-8.08538</td>\n",
       "      <td>0.01089</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-09-30</th>\n",
       "      <td>9.59896</td>\n",
       "      <td>30.00000</td>\n",
       "      <td>30.00000</td>\n",
       "      <td>0.02152</td>\n",
       "      <td>-15.45649</td>\n",
       "      <td>0.09899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-10-31</th>\n",
       "      <td>9.44673</td>\n",
       "      <td>-29.08596</td>\n",
       "      <td>30.00000</td>\n",
       "      <td>0.19653</td>\n",
       "      <td>-30.00000</td>\n",
       "      <td>0.01996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-11-30</th>\n",
       "      <td>10.43546</td>\n",
       "      <td>0.99556</td>\n",
       "      <td>-2.49649</td>\n",
       "      <td>1.83575</td>\n",
       "      <td>-2.80698</td>\n",
       "      <td>1.83550</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-12-31</th>\n",
       "      <td>10.61079</td>\n",
       "      <td>2.12365</td>\n",
       "      <td>-1.81761</td>\n",
       "      <td>1.39298</td>\n",
       "      <td>-5.90079</td>\n",
       "      <td>1.40155</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1974-01-31</th>\n",
       "      <td>6.48418</td>\n",
       "      <td>3.15442</td>\n",
       "      <td>30.00000</td>\n",
       "      <td>5.40143</td>\n",
       "      <td>-24.81542</td>\n",
       "      <td>4.35549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1974-02-28</th>\n",
       "      <td>12.02109</td>\n",
       "      <td>-1.05923</td>\n",
       "      <td>-3.28653</td>\n",
       "      <td>2.80130</td>\n",
       "      <td>-1.69805</td>\n",
       "      <td>2.81055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1974-03-31</th>\n",
       "      <td>11.06112</td>\n",
       "      <td>-1.21315</td>\n",
       "      <td>-30.00000</td>\n",
       "      <td>1.16008</td>\n",
       "      <td>28.33333</td>\n",
       "      <td>1.08420</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1974-04-30</th>\n",
       "      <td>10.99285</td>\n",
       "      <td>-1.22774</td>\n",
       "      <td>28.59509</td>\n",
       "      <td>1.18632</td>\n",
       "      <td>-30.00000</td>\n",
       "      <td>1.26113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1974-05-31</th>\n",
       "      <td>11.01159</td>\n",
       "      <td>11.30677</td>\n",
       "      <td>-30.00000</td>\n",
       "      <td>0.16399</td>\n",
       "      <td>30.00000</td>\n",
       "      <td>0.02584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1974-06-30</th>\n",
       "      <td>12.87856</td>\n",
       "      <td>19.85707</td>\n",
       "      <td>-30.00000</td>\n",
       "      <td>0.31596</td>\n",
       "      <td>-6.77646</td>\n",
       "      <td>2.07747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1974-07-31</th>\n",
       "      <td>12.88140</td>\n",
       "      <td>-3.34980</td>\n",
       "      <td>-1.47883</td>\n",
       "      <td>2.18805</td>\n",
       "      <td>-2.67353</td>\n",
       "      <td>2.18630</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1974-08-31</th>\n",
       "      <td>12.89372</td>\n",
       "      <td>-3.17628</td>\n",
       "      <td>-1.23712</td>\n",
       "      <td>2.66876</td>\n",
       "      <td>-2.54253</td>\n",
       "      <td>2.69818</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1974-09-30</th>\n",
       "      <td>12.30008</td>\n",
       "      <td>-2.44785</td>\n",
       "      <td>-2.61271</td>\n",
       "      <td>1.85613</td>\n",
       "      <td>-1.14738</td>\n",
       "      <td>1.86477</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1974-10-31</th>\n",
       "      <td>13.67133</td>\n",
       "      <td>-4.67172</td>\n",
       "      <td>-2.69482</td>\n",
       "      <td>2.27010</td>\n",
       "      <td>-8.12225</td>\n",
       "      <td>30.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1974-11-30</th>\n",
       "      <td>11.30768</td>\n",
       "      <td>-1.91948</td>\n",
       "      <td>-3.04720</td>\n",
       "      <td>1.17281</td>\n",
       "      <td>-2.15114</td>\n",
       "      <td>1.16793</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1974-12-31</th>\n",
       "      <td>10.73064</td>\n",
       "      <td>-1.82234</td>\n",
       "      <td>-3.11141</td>\n",
       "      <td>1.30525</td>\n",
       "      <td>-0.36643</td>\n",
       "      <td>1.31588</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1975-01-31</th>\n",
       "      <td>10.35981</td>\n",
       "      <td>-1.54463</td>\n",
       "      <td>-3.05494</td>\n",
       "      <td>0.98556</td>\n",
       "      <td>-4.16007</td>\n",
       "      <td>1.00195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1975-02-28</th>\n",
       "      <td>10.61680</td>\n",
       "      <td>-3.79682</td>\n",
       "      <td>-2.86949</td>\n",
       "      <td>1.14062</td>\n",
       "      <td>-3.48496</td>\n",
       "      <td>1.13985</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-05-31</th>\n",
       "      <td>0.46930</td>\n",
       "      <td>-0.67415</td>\n",
       "      <td>30.00000</td>\n",
       "      <td>6.48595</td>\n",
       "      <td>-28.30952</td>\n",
       "      <td>5.78670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-30</th>\n",
       "      <td>0.61250</td>\n",
       "      <td>-0.84021</td>\n",
       "      <td>-26.78858</td>\n",
       "      <td>5.64995</td>\n",
       "      <td>29.29365</td>\n",
       "      <td>6.65600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-07-31</th>\n",
       "      <td>0.74211</td>\n",
       "      <td>-0.95124</td>\n",
       "      <td>-7.58198</td>\n",
       "      <td>4.78797</td>\n",
       "      <td>8.96615</td>\n",
       "      <td>7.70390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-08-31</th>\n",
       "      <td>0.00010</td>\n",
       "      <td>-0.21490</td>\n",
       "      <td>12.85983</td>\n",
       "      <td>8.49736</td>\n",
       "      <td>-9.23206</td>\n",
       "      <td>5.46717</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-09-30</th>\n",
       "      <td>0.00021</td>\n",
       "      <td>-0.22090</td>\n",
       "      <td>30.00000</td>\n",
       "      <td>7.61921</td>\n",
       "      <td>-26.70343</td>\n",
       "      <td>6.45672</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-10-31</th>\n",
       "      <td>0.00039</td>\n",
       "      <td>-0.27454</td>\n",
       "      <td>9.84537</td>\n",
       "      <td>9.05896</td>\n",
       "      <td>-6.79839</td>\n",
       "      <td>5.10291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-11-30</th>\n",
       "      <td>0.00044</td>\n",
       "      <td>-0.31131</td>\n",
       "      <td>30.00000</td>\n",
       "      <td>7.42196</td>\n",
       "      <td>-26.98974</td>\n",
       "      <td>6.17789</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-31</th>\n",
       "      <td>0.00698</td>\n",
       "      <td>-0.38685</td>\n",
       "      <td>29.98993</td>\n",
       "      <td>7.76139</td>\n",
       "      <td>-25.97234</td>\n",
       "      <td>6.47600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-31</th>\n",
       "      <td>0.00010</td>\n",
       "      <td>-0.37225</td>\n",
       "      <td>-27.65478</td>\n",
       "      <td>6.07779</td>\n",
       "      <td>30.00000</td>\n",
       "      <td>7.11502</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-02-29</th>\n",
       "      <td>0.00010</td>\n",
       "      <td>-0.41949</td>\n",
       "      <td>21.01928</td>\n",
       "      <td>7.29171</td>\n",
       "      <td>-19.37407</td>\n",
       "      <td>5.97233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-03-31</th>\n",
       "      <td>0.00022</td>\n",
       "      <td>-0.43630</td>\n",
       "      <td>-28.10668</td>\n",
       "      <td>6.64137</td>\n",
       "      <td>30.00000</td>\n",
       "      <td>7.56583</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-04-30</th>\n",
       "      <td>1.60800</td>\n",
       "      <td>-2.21031</td>\n",
       "      <td>26.38437</td>\n",
       "      <td>1.77300</td>\n",
       "      <td>-29.98360</td>\n",
       "      <td>1.91008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-05-31</th>\n",
       "      <td>1.48722</td>\n",
       "      <td>-2.10391</td>\n",
       "      <td>24.20078</td>\n",
       "      <td>1.80138</td>\n",
       "      <td>-27.65378</td>\n",
       "      <td>1.94603</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-06-30</th>\n",
       "      <td>0.83366</td>\n",
       "      <td>-1.51991</td>\n",
       "      <td>27.20025</td>\n",
       "      <td>1.80380</td>\n",
       "      <td>-29.81352</td>\n",
       "      <td>1.89838</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-07-31</th>\n",
       "      <td>0.79072</td>\n",
       "      <td>-1.49237</td>\n",
       "      <td>-0.00445</td>\n",
       "      <td>0.70120</td>\n",
       "      <td>-3.80696</td>\n",
       "      <td>2.38485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-08-31</th>\n",
       "      <td>0.86296</td>\n",
       "      <td>-1.53240</td>\n",
       "      <td>-21.10021</td>\n",
       "      <td>1.95991</td>\n",
       "      <td>18.52108</td>\n",
       "      <td>1.80823</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-09-30</th>\n",
       "      <td>0.85359</td>\n",
       "      <td>-1.61903</td>\n",
       "      <td>-29.35170</td>\n",
       "      <td>1.91671</td>\n",
       "      <td>26.67020</td>\n",
       "      <td>1.80187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-10-31</th>\n",
       "      <td>1.33061</td>\n",
       "      <td>-2.18835</td>\n",
       "      <td>-0.14068</td>\n",
       "      <td>0.70931</td>\n",
       "      <td>-4.81700</td>\n",
       "      <td>2.31295</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-11-30</th>\n",
       "      <td>0.55600</td>\n",
       "      <td>-1.37525</td>\n",
       "      <td>26.25197</td>\n",
       "      <td>5.62709</td>\n",
       "      <td>-25.38540</td>\n",
       "      <td>5.03144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-31</th>\n",
       "      <td>1.46745</td>\n",
       "      <td>-2.60460</td>\n",
       "      <td>-21.05146</td>\n",
       "      <td>1.53950</td>\n",
       "      <td>17.74190</td>\n",
       "      <td>1.33560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-31</th>\n",
       "      <td>1.78318</td>\n",
       "      <td>-2.44890</td>\n",
       "      <td>25.60004</td>\n",
       "      <td>1.51221</td>\n",
       "      <td>-30.00000</td>\n",
       "      <td>1.61925</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-02-28</th>\n",
       "      <td>1.63301</td>\n",
       "      <td>-2.57413</td>\n",
       "      <td>16.24321</td>\n",
       "      <td>1.56949</td>\n",
       "      <td>-20.73842</td>\n",
       "      <td>1.75779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-03-31</th>\n",
       "      <td>1.71984</td>\n",
       "      <td>-2.48265</td>\n",
       "      <td>18.12741</td>\n",
       "      <td>1.70136</td>\n",
       "      <td>-22.27206</td>\n",
       "      <td>1.84439</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-04-30</th>\n",
       "      <td>1.74353</td>\n",
       "      <td>-2.37674</td>\n",
       "      <td>-1.33117</td>\n",
       "      <td>0.63335</td>\n",
       "      <td>-5.61103</td>\n",
       "      <td>2.22454</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-05-31</th>\n",
       "      <td>1.80291</td>\n",
       "      <td>-2.42013</td>\n",
       "      <td>-1.65132</td>\n",
       "      <td>0.45237</td>\n",
       "      <td>-6.39828</td>\n",
       "      <td>2.11766</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-06-30</th>\n",
       "      <td>1.78529</td>\n",
       "      <td>-2.59107</td>\n",
       "      <td>-27.24948</td>\n",
       "      <td>1.71336</td>\n",
       "      <td>23.68634</td>\n",
       "      <td>1.58797</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-07-31</th>\n",
       "      <td>1.76955</td>\n",
       "      <td>-2.40812</td>\n",
       "      <td>4.41393</td>\n",
       "      <td>4.68211</td>\n",
       "      <td>-5.79222</td>\n",
       "      <td>3.23586</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-08-31</th>\n",
       "      <td>1.73866</td>\n",
       "      <td>-2.52889</td>\n",
       "      <td>0.03024</td>\n",
       "      <td>0.91346</td>\n",
       "      <td>-5.70445</td>\n",
       "      <td>2.14135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-30</th>\n",
       "      <td>1.88347</td>\n",
       "      <td>-2.34000</td>\n",
       "      <td>-4.06436</td>\n",
       "      <td>2.33709</td>\n",
       "      <td>-1.38362</td>\n",
       "      <td>0.05894</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-10-31</th>\n",
       "      <td>1.60514</td>\n",
       "      <td>-2.34387</td>\n",
       "      <td>11.26804</td>\n",
       "      <td>4.53295</td>\n",
       "      <td>-12.62120</td>\n",
       "      <td>3.83460</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>542 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               beta0     beta1     beta2     tau1     beta3      tau2\n",
       "1972-09-30   8.58387  30.00000 -29.88450  0.36495 -13.91200   0.36543\n",
       "1972-10-31   8.52889  29.58953  28.98429  0.00481  -7.48676   0.26523\n",
       "1972-11-30   8.80418  29.92019 -20.51146  0.51241 -30.00000   0.24715\n",
       "1972-12-31   9.43739  -7.46531 -20.48638  1.29510  28.55031   1.01820\n",
       "1973-01-31  11.61329  -4.48145  -8.47201  0.52885  -7.08296   4.69237\n",
       "1973-02-28  11.45540  13.02996 -30.00000  0.39174  -7.29206   5.24815\n",
       "1973-03-31  11.44706  -6.15884  28.95551  2.46182 -30.00000   3.09107\n",
       "1973-04-30   8.90814 -12.64824 -10.75908  0.58485  30.00000   0.42540\n",
       "1973-05-31  10.36056  21.01261 -30.00000  0.12923  -2.28758   3.54882\n",
       "1973-06-30  10.30138  19.20941 -24.00549  0.44307  -1.48525   1.65952\n",
       "1973-07-31  10.28803  -0.75852 -29.29636  1.69725  30.00000   1.54753\n",
       "1973-08-31   9.45106  -1.76690 -30.00000  0.00685  -8.08538   0.01089\n",
       "1973-09-30   9.59896  30.00000  30.00000  0.02152 -15.45649   0.09899\n",
       "1973-10-31   9.44673 -29.08596  30.00000  0.19653 -30.00000   0.01996\n",
       "1973-11-30  10.43546   0.99556  -2.49649  1.83575  -2.80698   1.83550\n",
       "1973-12-31  10.61079   2.12365  -1.81761  1.39298  -5.90079   1.40155\n",
       "1974-01-31   6.48418   3.15442  30.00000  5.40143 -24.81542   4.35549\n",
       "1974-02-28  12.02109  -1.05923  -3.28653  2.80130  -1.69805   2.81055\n",
       "1974-03-31  11.06112  -1.21315 -30.00000  1.16008  28.33333   1.08420\n",
       "1974-04-30  10.99285  -1.22774  28.59509  1.18632 -30.00000   1.26113\n",
       "1974-05-31  11.01159  11.30677 -30.00000  0.16399  30.00000   0.02584\n",
       "1974-06-30  12.87856  19.85707 -30.00000  0.31596  -6.77646   2.07747\n",
       "1974-07-31  12.88140  -3.34980  -1.47883  2.18805  -2.67353   2.18630\n",
       "1974-08-31  12.89372  -3.17628  -1.23712  2.66876  -2.54253   2.69818\n",
       "1974-09-30  12.30008  -2.44785  -2.61271  1.85613  -1.14738   1.86477\n",
       "1974-10-31  13.67133  -4.67172  -2.69482  2.27010  -8.12225  30.00000\n",
       "1974-11-30  11.30768  -1.91948  -3.04720  1.17281  -2.15114   1.16793\n",
       "1974-12-31  10.73064  -1.82234  -3.11141  1.30525  -0.36643   1.31588\n",
       "1975-01-31  10.35981  -1.54463  -3.05494  0.98556  -4.16007   1.00195\n",
       "1975-02-28  10.61680  -3.79682  -2.86949  1.14062  -3.48496   1.13985\n",
       "...              ...       ...       ...      ...       ...       ...\n",
       "2015-05-31   0.46930  -0.67415  30.00000  6.48595 -28.30952   5.78670\n",
       "2015-06-30   0.61250  -0.84021 -26.78858  5.64995  29.29365   6.65600\n",
       "2015-07-31   0.74211  -0.95124  -7.58198  4.78797   8.96615   7.70390\n",
       "2015-08-31   0.00010  -0.21490  12.85983  8.49736  -9.23206   5.46717\n",
       "2015-09-30   0.00021  -0.22090  30.00000  7.61921 -26.70343   6.45672\n",
       "2015-10-31   0.00039  -0.27454   9.84537  9.05896  -6.79839   5.10291\n",
       "2015-11-30   0.00044  -0.31131  30.00000  7.42196 -26.98974   6.17789\n",
       "2015-12-31   0.00698  -0.38685  29.98993  7.76139 -25.97234   6.47600\n",
       "2016-01-31   0.00010  -0.37225 -27.65478  6.07779  30.00000   7.11502\n",
       "2016-02-29   0.00010  -0.41949  21.01928  7.29171 -19.37407   5.97233\n",
       "2016-03-31   0.00022  -0.43630 -28.10668  6.64137  30.00000   7.56583\n",
       "2016-04-30   1.60800  -2.21031  26.38437  1.77300 -29.98360   1.91008\n",
       "2016-05-31   1.48722  -2.10391  24.20078  1.80138 -27.65378   1.94603\n",
       "2016-06-30   0.83366  -1.51991  27.20025  1.80380 -29.81352   1.89838\n",
       "2016-07-31   0.79072  -1.49237  -0.00445  0.70120  -3.80696   2.38485\n",
       "2016-08-31   0.86296  -1.53240 -21.10021  1.95991  18.52108   1.80823\n",
       "2016-09-30   0.85359  -1.61903 -29.35170  1.91671  26.67020   1.80187\n",
       "2016-10-31   1.33061  -2.18835  -0.14068  0.70931  -4.81700   2.31295\n",
       "2016-11-30   0.55600  -1.37525  26.25197  5.62709 -25.38540   5.03144\n",
       "2016-12-31   1.46745  -2.60460 -21.05146  1.53950  17.74190   1.33560\n",
       "2017-01-31   1.78318  -2.44890  25.60004  1.51221 -30.00000   1.61925\n",
       "2017-02-28   1.63301  -2.57413  16.24321  1.56949 -20.73842   1.75779\n",
       "2017-03-31   1.71984  -2.48265  18.12741  1.70136 -22.27206   1.84439\n",
       "2017-04-30   1.74353  -2.37674  -1.33117  0.63335  -5.61103   2.22454\n",
       "2017-05-31   1.80291  -2.42013  -1.65132  0.45237  -6.39828   2.11766\n",
       "2017-06-30   1.78529  -2.59107 -27.24948  1.71336  23.68634   1.58797\n",
       "2017-07-31   1.76955  -2.40812   4.41393  4.68211  -5.79222   3.23586\n",
       "2017-08-31   1.73866  -2.52889   0.03024  0.91346  -5.70445   2.14135\n",
       "2017-09-30   1.88347  -2.34000  -4.06436  2.33709  -1.38362   0.05894\n",
       "2017-10-31   1.60514  -2.34387  11.26804  4.53295 -12.62120   3.83460\n",
       "\n",
       "[542 rows x 6 columns]"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "EC0B802777F541DA889759024F962F0D"
   },
   "source": [
    "We define the [Nelson-Siegel-Svensson](https://en.wikipedia.org/wiki/Fixed-income_attribution#Modeling_the_yield_curve) function:\n",
    "$$\n",
    "y(t) = \\beta_0 + \\beta_1 \\frac{1-\\exp(-t/\\tau_1)}{t/\\tau_1}\n",
    "               + \\beta_2 (\\frac{1-\\exp(-t/\\tau_1)}{t/\\tau_1} - \\exp(-t/\\tau_1))\n",
    "               + \\beta_3 (\\frac{1-\\exp(-t/\\tau_2)}{t/\\tau_2} - \\exp(-t/\\tau_2))\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "cell_id": "87E83A984CE442F1A68D1F1AC7D4D664"
   },
   "outputs": [],
   "source": [
    "def nelson_siegel_svensson(term, beta0, beta1, beta2, beta3, tau1, tau2):\n",
    "    return ( beta0\n",
    "            +beta1*(1-numpy.exp(-term/tau1))/(term/tau1)\n",
    "            +beta2*((1-numpy.exp(-term/tau1))/(term/tau1)-numpy.exp(-term/tau1))\n",
    "            +beta3*((1-numpy.exp(-term/tau2))/(term/tau2)-numpy.exp(-term/tau2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "9E0EA35E49554D708AE4A6E23D2D28CF"
   },
   "source": [
    "Let us apply it with the Bundesbank parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "cell_id": "3737D09AFB6D4136870AEFA3E6B839A2"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1972-09     6.699762\n",
       "1972-10     7.043209\n",
       "1972-11     9.094030\n",
       "1972-12     6.917985\n",
       "1973-01     6.419964\n",
       "1973-02     7.048853\n",
       "1973-03     6.969552\n",
       "1973-04     8.327831\n",
       "1973-05     8.945003\n",
       "1973-06    10.608796\n",
       "dtype: float64"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nelson_siegel_svensson(1.0, *[df[i] for i in [\"beta0\",\"beta1\",\"beta2\",\"beta3\",\"tau1\",\"tau2\"]]).iloc[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "E39273F29C4646EF8194D615A1593921"
   },
   "source": [
    "And check against the Bundesbank's own calculations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "cell_id": "13E08117A566436FB730D72B87D64BEC"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>20</th>\n",
       "      <th>30</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1972-09-01</th>\n",
       "      <td>6.70</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1972-10-01</th>\n",
       "      <td>7.04</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1972-11-01</th>\n",
       "      <td>9.09</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1972-12-01</th>\n",
       "      <td>6.92</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-01-01</th>\n",
       "      <td>6.42</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-02-01</th>\n",
       "      <td>7.05</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-03-01</th>\n",
       "      <td>6.97</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-04-01</th>\n",
       "      <td>8.33</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-05-01</th>\n",
       "      <td>8.95</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1973-06-01</th>\n",
       "      <td>10.61</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               1   20  30\n",
       "1972-09-01   6.70 NaN NaN\n",
       "1972-10-01   7.04 NaN NaN\n",
       "1972-11-01   9.09 NaN NaN\n",
       "1972-12-01   6.92 NaN NaN\n",
       "1973-01-01   6.42 NaN NaN\n",
       "1973-02-01   7.05 NaN NaN\n",
       "1973-03-01   6.97 NaN NaN\n",
       "1973-04-01   8.33 NaN NaN\n",
       "1973-05-01   8.95 NaN NaN\n",
       "1973-06-01  10.61 NaN NaN"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "check_df = pandas.read_csv(urllib.request.urlopen(\"http://www.bundesbank.de/cae/servlet/StatisticDownload?tsId=BBK01.WZ9808&tsId=BBK01.WZ3449&tsId=BBK01.WZ3500&its_csvFormat=en&its_fileFormat=csv&mode=its\"), index_col=0)\n",
    "check_df.drop([x for x in check_df.columns if x.endswith(\"_FLAGS\")],axis=1, inplace=True)\n",
    "mapping = dict((check_df.iloc[0].dropna().apply(lambda x: int(float(x.split(\" / \")[1].split()[3])))).items())\n",
    "check_df.columns = [mapping.get(x,x) for x in check_df.columns]\n",
    "check_df = check_df.iloc[4:]\n",
    "check_df = check_df.apply(lambda x: x.astype(float))\n",
    "check_df.index = pandas.to_datetime(check_df.index)\n",
    "check_df.iloc[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "14E8A39C932A4E21BE9320F55CC98C38"
   },
   "source": [
    "In the 70's and 80's there were no long-running Bunds.\n",
    "We can get a taste of how it is not a good idea to use Nelson-Siegel-Svensson for extrapolation when we compare\n",
    "the movements of (existing) 10-year rates with the (extrapolated) 30-year rates for that period."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "cell_id": "8991BC6673454423B3521DFD4CC5EF87"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f539c514c88>"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD8CAYAAABn919SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f539c514da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.plot(nelson_siegel_svensson(10.0, *[df[i] for i in [\"beta0\",\"beta1\",\"beta2\",\"beta3\",\"tau1\",\"tau2\"]]).loc[:'1990-01-01'],label=\"10\")\n",
    "pyplot.plot(nelson_siegel_svensson(30.0, *[df[i] for i in [\"beta0\",\"beta1\",\"beta2\",\"beta3\",\"tau1\",\"tau2\"]]).loc[:'1990-01-01'],label=\"30\")\n",
    "pyplot.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "cell_id": "5D4B2172AB7C4D9991A2BA715BC18B41"
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}