VALIDATION BLACK SHOLES.ipynb

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   "source": [
    "# BLACK-SHOLES AND EIOPA RISK-FREE CURVE TERM STRUCTURE COVERAGE AND VARIANCE CHECK\n",
    "<a id=\"0\"></a> <br>\n",
    "ToDo\n",
    "The Hull-White model (HW) is a very popular choice when modeling interest rates. For example economic scenario generators can use the HW model to simulated risk-free curves. This notebook is devided into 4 sections. The first section uses the EIOPA Risk-Free-Rate (RFR) calibration to produce a yield curve. In the second section, this yield curve is used to produce a number of stochastic scenarios using a simple implementation of the HW model. The third section checks the goodness of fit of the simulated paths compared to the input term structure. The final section calculates the closed form variance and compares it to the simulated variance.\n",
    "\n",
    "HW model is presented in two different forms in literature. This script starts from the folowing diferential equation:\n",
    "\n",
    "$$ dr(t) = \\mu dt + \\sigma dW(t) $$\n",
    "\n",
    "Where:\n",
    " - t is time.\n",
    " - r(t) is the short rate at time t.\n",
    " - $\\theta (t)$ is the time-dependent parameter theta.\n",
    " - a is the mean reversion speed parameter.\n",
    " - $\\sigma$ is the volatility parameter.\n",
    " - $W(t)$ is a standard Brownian motion.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fec83f5",
   "metadata": {},
   "source": [
    "### Summary\n",
    "\n",
    "The goal of this script is to answer the following questions: \n",
    " - Is the HW simulation correctly implemented\n",
    " - Is the company is using a sufficienty large number of stochastic scenarios to aquaretly cover the term structure. \n",
    " - Are the parameters used in the simulation correctly implemented."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3d4aca5",
   "metadata": {},
   "source": [
    "# Table of Contents  \n",
    "1. [Note on Smith & Wilson algorithm](#1)\n",
    "2. [Success criteria](#2)\n",
    "3. [Data requirements](#3)\n",
    "4. [Hull-White Parameters](#4)\n",
    "5. [External dependencies](#5)\n",
    "6. [Importing data](#6)\n",
    "7. [Smith & Wilson](#7)\n",
    "8. [Hull-White interest rate simulation functions](#8)\n",
    "9. [Test 1; Comparison between ESG output and assumed term structure](#9)\n",
    "10. [Test 2; Comparison between simulated an calculated volatility](#10)\n",
    "11. [Conclusion](#11)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91cd8582",
   "metadata": {},
   "source": [
    "<a id=\"1\"></a> <br>\n",
    "## Note on Smith & Wilson algorithm\n",
    "\n",
    "The validation of RFR rate is performed in another script that checks the correct calibration of the EIOPA's RFR output, also available on OSM Github as a [Jupyter notebook](https://github.com/open-source-modelling/insurance_jupyter/tree/main/enough_stochastic_scenarios).\n",
    "\n",
    "This example uses a modified Smith&Wilson implementation (The original implementation is availible on [GitHub](https://github.com/open-source-modelling):\n",
    "-  [Python](https://github.com/open-source-modelling/insurance_python/tree/main/smith%26wilson)\n",
    "-  [Matlab](https://github.com/open-source-modelling/insurance_matlab/tree/main/smith%26wilson)\n",
    "-  [JavaScript](https://github.com/open-source-modelling/insurance_javascript/tree/main/smith-wilson)\n"
   ]
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   "id": "698030fb",
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    "#### Limitations of the implementation\n",
    "This script generates a synthetic dataset of ESG scenarios. It also simplifies the day-count convention with the assumption that each month represents 1/12-th of a year. The discretisation and numeric integration uses the simplest Euler scheme and the rectangular rule respectively.\n",
    "\n",
    "Only two checks are performed to verify the correctnes and the properties of the result.\n",
    "\n",
    "Only a single EIOPA curve is used (No volatility adjustment, Euro curve)."
   ]
  },
  {
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   "id": "a302c5b4",
   "metadata": {},
   "source": [
    "<a id=\"2\"></a> <br>\n",
    "## Success criteria\n",
    "\n",
    "The following success criteria is defined:\n",
    "-  Maximum difference between the average simulated yield curve and the one provided as input is less than 0.1 bps.\n",
    "-  Average difference between the average simulated curve and the one provided as input is less than 0.05 bps.\n",
    "-  Maximum difference between the empirical volatility of the simulated yield curve and the theoretical volatility is less than 0.1 bps.\n",
    "-  Average difference between the empirical volatility of the simulated yield curve and the theoretical volatility is less than 0.05 bps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "6d6e95b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "statistics_mean_max_diff_in_bps = 500\n",
    "statistics_mean_average_diff_in_bps = 100\n",
    "statistics_vol_max_diff_in_bps = 2\n",
    "statistics_vol_average_diff_in_bps = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a060ea9c",
   "metadata": {},
   "source": [
    "The success function that is called at the end of every check is the following (With the threasholds that are defined above)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "b624aa9a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def SuccessTest(TestStatistics, threshold_max, threshold_mean):\n",
    "    out1 = False\n",
    "    out2 = False\n",
    "    if max(TestStatistics)<threshold_max:\n",
    "        print(\"Test passed\")\n",
    "        out1 = True\n",
    "    else:\n",
    "        print(\"Test failed\")\n",
    "\n",
    "    if np.mean(TestStatistics)<threshold_mean:\n",
    "        print(\"Test passed\")\n",
    "        out2 = True\n",
    "    else:\n",
    "        print(\"Test failed\")\n",
    "    return [out1, out2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "649ad6eb",
   "metadata": {},
   "source": [
    "This implementation looks at two kinds of test statistics. The average deviation and the maximum deviation. \n",
    "\n",
    "The average deviation is defined as:\n",
    "\n",
    "<font size=4>\n",
    "$$S_{AVERAGE} = \\frac{1}{N} \\sum_{t = 0}^T \\left|x_{THEORETICAL}(t) - x_{EST}(t) \\right|$$\n",
    "</font> <br>\n",
    "\n",
    "The maximum deviation is defined as:\n",
    "<font size=4>\n",
    "$$ S_{MAX} = \\max_t \\left| x_{THEORETICAL}(t) - x_{EST}(t) \\right| $$\n",
    "</font> <br>\n",
    "\n",
    "Where `N` is the number of time increments and `T` is the maximum maturity \n",
    "</font> <br>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07e93aac",
   "metadata": {},
   "source": [
    "<a id=\"3\"></a> <br>\n",
    "## Data requirements\n",
    "\n",
    "This script contains the EIOPA RFR published for March 2023. The publication can be found on the [EIOPA RFR website](https://www.eiopa.europa.eu/tools-and-data/risk-free-interest-rate-term-structures_en)."
   ]
  },
  {
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   "id": "31d36679",
   "metadata": {},
   "source": [
    "The observed maturities `m_obs` and the calibrated vector `Qb` can be found in the published Excel workbook *EIOPA_RFR_20230331_Qb_SW.xlsx*.\n",
    "\n",
    "The Euro curve without the volatility adjustment (VA) is used. It can be found in the sheet *SW_Qb_no_VA*. This example is focused on the EUR curve, but can be easily extended to other curves."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2f16f4f",
   "metadata": {},
   "source": [
    "Target maturities (`t_obs`), the additional parameters (`UFR` and `alpha`), and the given curve can be found in the Excel *EIOPA_RFR_20230331_Term_Structures.xlsx*. Sheet *RFR_spot_no_VA* looks at the curve without the Volatility Adjustment."
   ]
  },
  {
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   "id": "b50e7ce9",
   "metadata": {},
   "source": [
    "<a id=\"4\"></a> <br>\n",
    "## Black-Sholes Parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc59fb82",
   "metadata": {},
   "source": [
    "This script provides validation for a single output of the Hull White modell. The run specification is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "5c729201",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "param_raw = pd.read_csv(\"Parameters.csv\", sep=',', index_col=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "ada58f3b",
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>model</th>\n",
       "      <th>Type</th>\n",
       "      <th>NoOfPaths</th>\n",
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       "      <th>11</th>\n",
       "      <td>HW</td>\n",
       "      <td>I</td>\n",
       "      <td>1000</td>\n",
       "      <td>600</td>\n",
       "      <td>50</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.01</td>\n",
       "      <td>Slovenia</td>\n",
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       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
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       "      <th>22</th>\n",
       "      <td>BS</td>\n",
       "      <td>D</td>\n",
       "      <td>1000</td>\n",
       "      <td>600</td>\n",
       "      <td>50</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.01</td>\n",
       "      <td>Slovenia</td>\n",
       "      <td>Param_no_VA.csv</td>\n",
       "      <td>Curves_no_VA.csv</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>V</td>\n",
       "      <td>D</td>\n",
       "      <td>1000</td>\n",
       "      <td>600</td>\n",
       "      <td>50</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.01</td>\n",
       "      <td>Slovenia</td>\n",
       "      <td>Param_no_VA.csv</td>\n",
       "      <td>Curves_no_VA.csv</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.3</td>\n",
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       "               model Type  NoOfPaths  NoOfSteps   T     a  sigma  epsilon  \\\n",
       "Calibration_ID                                                              \n",
       "11                HW    I       1000        600  50  0.02   0.02     0.01   \n",
       "22                BS    D       1000        600  50  0.00   0.02     0.01   \n",
       "33                 V    D       1000        600  50  0.00   0.02     0.01   \n",
       "\n",
       "                 Country selected_param_file selected_curves_file    mu  gamma  \n",
       "Calibration_ID                                                                  \n",
       "11              Slovenia     Param_no_VA.csv     Curves_no_VA.csv  0.00    0.0  \n",
       "22              Slovenia     Param_no_VA.csv     Curves_no_VA.csv  0.02    0.0  \n",
       "33              Slovenia     Param_no_VA.csv     Curves_no_VA.csv  0.02    0.3  "
      ]
     },
     "metadata": {},
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   ],
   "source": [
    "display(param_raw)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3474da3",
   "metadata": {},
   "source": [
    "This script will look at run with the callibration id that uses the Black-Sholes mode:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "7110f8d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "calibration_id = 22"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7378ce96",
   "metadata": {},
   "source": [
    "This example does not have a specific dataset in mind therefore, a set of dummy parameters is used for the Hull-White model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "738c22e8",
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   "source": [
    "NoOfPaths = 1000 # Number of stochastic scenarios\n",
    "NoOfSteps = 600  # Number of equidistand discrete modelling points (50*12 = 600)\n",
    "T = 50.0         # Time horizon in years (A time horizon of 50 years; T=50)\n",
    "mu = 0.02         # Hull-White mean reversion parameter a\n",
    "sigma = 0.02     # Hull-White volatility parameter sigma\n",
    "epsilon = 0.01   # Incremental distance used to calculate for numerical approximation\n",
    "                 # of for example the instantaneous spot rate (Ex. 0.01 will use an interval \n",
    "                 # of 0.01 as a discreete approximation for a derivative)"
   ]
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    "<a id=\"5\"></a> <br>\n",
    "         \n",
    "## External dependencies"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbeb172b",
   "metadata": {},
   "source": [
    "This script uses a set of well known Python packages that are commonly used in finance. Numpy for the mathematical operation and matrix multiplication, Pandas for its table manipulation functionality and Matplotlib for charts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "06f5daac",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "6a4bc7ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "param_raw = pd.read_csv(\"Parameters.csv\", sep=',', index_col=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "82f6efd6",
   "metadata": {},
   "outputs": [
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       "      <th>11</th>\n",
       "      <td>HW</td>\n",
       "      <td>I</td>\n",
       "      <td>1000</td>\n",
       "      <td>600</td>\n",
       "      <td>50</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.01</td>\n",
       "      <td>Slovenia</td>\n",
       "      <td>Param_no_VA.csv</td>\n",
       "      <td>Curves_no_VA.csv</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>BS</td>\n",
       "      <td>D</td>\n",
       "      <td>1000</td>\n",
       "      <td>600</td>\n",
       "      <td>50</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.01</td>\n",
       "      <td>Slovenia</td>\n",
       "      <td>Param_no_VA.csv</td>\n",
       "      <td>Curves_no_VA.csv</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>V</td>\n",
       "      <td>D</td>\n",
       "      <td>1000</td>\n",
       "      <td>600</td>\n",
       "      <td>50</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.01</td>\n",
       "      <td>Slovenia</td>\n",
       "      <td>Param_no_VA.csv</td>\n",
       "      <td>Curves_no_VA.csv</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.3</td>\n",
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       "               model Type  NoOfPaths  NoOfSteps   T     a  sigma  epsilon  \\\n",
       "Calibration_ID                                                              \n",
       "11                HW    I       1000        600  50  0.02   0.02     0.01   \n",
       "22                BS    D       1000        600  50  0.00   0.02     0.01   \n",
       "33                 V    D       1000        600  50  0.00   0.02     0.01   \n",
       "\n",
       "                 Country selected_param_file selected_curves_file    mu  gamma  \n",
       "Calibration_ID                                                                  \n",
       "11              Slovenia     Param_no_VA.csv     Curves_no_VA.csv  0.00    0.0  \n",
       "22              Slovenia     Param_no_VA.csv     Curves_no_VA.csv  0.02    0.0  \n",
       "33              Slovenia     Param_no_VA.csv     Curves_no_VA.csv  0.02    0.3  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "asset_id = 11\n",
    "display(param_raw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "5f0efb97",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Numpy version is 1.20.3.\n"
     ]
    }
   ],
   "source": [
    "print(f\"The Numpy version is {np.__version__}.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "15aa3e14",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pandas version is 1.3.4.\n"
     ]
    }
   ],
   "source": [
    "print(f\"The Pandas version is {pd.__version__}.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "87660d5f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Matplotlib version is 3.4.3.\n"
     ]
    }
   ],
   "source": [
    "print(f\"The Matplotlib version is {mpl.__version__}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e3d51a8",
   "metadata": {},
   "source": [
    "<a id=\"6\"></a> <br>\n",
    "## Importing data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60898959",
   "metadata": {},
   "source": [
    "This section specifies the names of external files with the information about the term structure. In particular, the Smith-Wilson calibration parameters and the term structure that is used to generate the stochastic paths."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "2183da18",
   "metadata": {},
   "outputs": [],
   "source": [
    "selected_param_file = 'Param_no_VA.csv'\n",
    "selected_curves_file = 'Curves_no_VA.csv'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "e435f175",
   "metadata": {},
   "outputs": [],
   "source": [
    "param_raw = pd.read_csv(selected_param_file, sep=',', index_col=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e899f27a",
   "metadata": {},
   "source": [
    "EIOPA provides curves for multiple countries. In this script, Slovenia is used as an example, but any other country can be substituted into the country variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "da95b722",
   "metadata": {},
   "outputs": [],
   "source": [
    "country = \"Slovenia\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "e6935c8d",
   "metadata": {},
   "outputs": [],
   "source": [
    "maturities_country_raw = param_raw.loc[:,country+\"_Maturities\"].iloc[6:]\n",
    "param_country_raw = param_raw.loc[:,country + \"_Values\"].iloc[6:]\n",
    "extra_param = param_raw.loc[:,country + \"_Values\"].iloc[:6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "3709531b",
   "metadata": {},
   "outputs": [],
   "source": [
    "relevant_positions = pd.notna(maturities_country_raw.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "647ef9b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "maturities_country = maturities_country_raw.iloc[relevant_positions]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "8b6822f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "Qb = param_country_raw.iloc[relevant_positions]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "2e549304",
   "metadata": {},
   "outputs": [],
   "source": [
    "curve_raw = pd.read_csv(selected_curves_file, sep=',',index_col=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "26793b8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "curve_country = curve_raw.loc[:,country]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b76f503a",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22910c29",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0249a8a3",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d62102a",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17b49387",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4019257",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9808a91e",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43b83c47",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1bd79cf",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca42bdc5",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b7433bb",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f2511f8",
   "metadata": {},
   "source": [
    "<a id=\"7\"></a> <br>\n",
    "## Smith & Wilson"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5db1d1d9",
   "metadata": {},
   "source": [
    "In this section, the EIOPA parameters and the EIOPA RFR curve are processed into the correct form that will be used for the rest of the script"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d90169a",
   "metadata": {},
   "source": [
    "### Smith & Wilson parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "0eadd369",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Maturity of observations:\n",
    "m_obs = np.transpose(np.array(maturities_country.values))\n",
    "\n",
    "# Ultimate froward rate ufr represents the rate to which the rate curve will \n",
    "# converge as time increases:\n",
    "ufr = extra_param.iloc[3]/100\n",
    "\n",
    "# Convergence speed parameter alpha controls the speed at which the curve \n",
    "# converges towards the ufr from the last liquid point:\n",
    "alpha = extra_param.iloc[4]\n",
    "\n",
    "# For which maturities do we want the SW algorithm to calculate the rates. \n",
    "# In this case, for every year up to 150:\n",
    "m_target = np.transpose(np.arange(1,151)) \n",
    "\n",
    "# Qb calibration vector published by EIOPA for the curve calibration:\n",
    "Qb = np.transpose(np.array(Qb.values))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47dfc6f4",
   "metadata": {},
   "source": [
    "### Smith & Wilson calculation functions\n",
    "\n",
    "An independent version of the Smith&Wilson algorithm is implemented. To facilitate this, two functions are taken from the publicly available repository that already contains the complete implementation. It is then modified to accept the product of `Q*b` instead of the calibration vector `b`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "63883ebc",
   "metadata": {},
   "outputs": [],
   "source": [
    "from term_structure import smith_wilson_extrapolate_yield_curve"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "237056a4",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75add4e1",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66ebad3b",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bfb5b275",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57cb488b",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4db15038",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "732e8eef",
   "metadata": {},
   "source": [
    "<a id=\"8\"></a> <br>\n",
    "## Hull-White interest rate simulation functions\n",
    "\n",
    "In this step, the Hull-White simulation is implemented. The calculation of a discounted ZCB bond, calculation of a forward rate, the parameter $\\theta $ and finally the generation of multiple sample paths.\n",
    "\n",
    "The function P0t_f() calculates the price of a zero-coupon bond (ZCB) based on the given yield and maturity.\n",
    "\n",
    "$$ P0t = e^{-y0t *t} $$\n",
    "\n",
    "Where:\n",
    " - `t` is the time of interest expressed as a year fraction (Ex. for 18 months, `t` = 1.5).\n",
    " - `y0t` is the yield for single payoff at time `t`.\n",
    " -  `P0t` is the price of a zero-coupon bond issued in time `0` with a notional amount of 1 and maturity at time `t`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8134f90",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "500b3874",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61ad3ee1",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d2b4a2b",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ac6b55b",
   "metadata": {},
   "source": [
    "The function f0t() calculates the instantaneous forward rate at time `t` using a numerical approximation with a step size given by the parameter `epsilon`. The calculation of the instantaneous forward rate relies on the difference between two zero-coupon bond prices. One maturing at time $t +\\epsilon $ and another at time $t - \\epsilon $. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b03afae4",
   "metadata": {},
   "source": [
    "\n",
    "The centered finite difference method estimates the instantaneous forward rate using the following approximation:\n",
    "\n",
    "$$ f(0,t) \\approx -\\frac{\\log(P(0, t+\\epsilon)) - \\log(P(0, t-\\epsilon)) }{2 \\epsilon}  $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a47a8498",
   "metadata": {},
   "source": [
    "The function HW_theta calculates the time depened parameter $\\theta$. In this implementation, this parameter is calibrated to the term stucture obtained using the EIOPA RFR. The term structure is specified by the P0t function that is passed as argument.\n",
    "\n",
    "The parameter `theta` is calibrated using the following relation:\n",
    "\n",
    "$$ \\theta(t) =  \\frac{\\partial f(0,t)}{\\partial t} + a f(0,t) + \\frac{\\sigma^2}{2 a}\\big( 1 - e^{-2 a t} \\big)    $$\n",
    "\n",
    "Where:\n",
    " - `t` is the time at which we wish to calibrate $\\theta$ to the term structure. (Ex. 18 months means t = 1.5).\n",
    " - $a$ is the $ a$ parameter in the Hull-White model.\n",
    " - $\\sigma$ is the volatility parameter $ \\sigma$ of the Hull-White model.\n",
    " - $f(0,t)$ is the instantaneous forward rate at time `t` estimated at time 0.\n",
    " - $\\theta(t)$ is the time dependet parameter $\\theta$ of the Hull-White model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "ab97473b",
   "metadata": {},
   "outputs": [],
   "source": [
    "from term_structure import calculate_zero_coupon_price\n",
    "from read_input import read_model_input\n",
    "from black_sholes import calculate_black_sholes_paths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "ff8e5258",
   "metadata": {},
   "outputs": [],
   "source": [
    "[modeling_parameters, curve_parameters] = read_model_input(calibration_id)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "58e21fd2",
   "metadata": {},
   "outputs": [],
   "source": [
    "zero_coupon_price = lambda t: calculate_zero_coupon_price(t, curve_parameters[\"target_maturities\"], curve_parameters[\"calibration_vector\"], curve_parameters[\"ultimate_forward_rate\"], curve_parameters[\"convergence_speed\"] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "69681589",
   "metadata": {},
   "outputs": [],
   "source": [
    "out = calculate_black_sholes_paths(num_paths=modeling_parameters[\"num_paths\"], num_steps=modeling_parameters[\"num_steps\"], end_time=modeling_parameters[\"end_time\"], function_zero_coupon_price=zero_coupon_price, mean_drift=modeling_parameters[\"mu\"], volatility=modeling_parameters[\"sigma\"], tolerance=modeling_parameters[\"tolerance\"])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "e3989cbf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1)\n",
    "plt.grid()\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"P(0,t)\")\n",
    "plt.plot(out[\"time\"],np.transpose(out[\"R\"]))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "84899374",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_1 = out[\"R\"][0,0] + (mu-sigma**2 /2) * out[\"time\"] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "c29bcb75",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1)\n",
    "plt.grid()\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"P(0,t)\")\n",
    "plt.plot(out[\"time\"],np.mean(np.transpose(out[\"R\"]),axis=1))\n",
    "plt.plot(out[\"time\"], y_1,\"--r\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "150c615c",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_2 = np.sqrt(sigma**2 * out[\"time\"]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "d2ed7c41",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1)\n",
    "plt.grid()\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"P(0,t)\")\n",
    "plt.plot(out[\"time\"],np.std(np.transpose(out[\"R\"]),axis=1))\n",
    "plt.plot(out[\"time\"], y_2,\"--r\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "577414a1",
   "metadata": {},
   "source": [
    "<a id=\"9\"></a> <br>\n",
    "## Test 1; Comparison between ESG output and assumed term structure \n",
    "\n",
    "In this final section, the ESG output is generated and visualy compared to the assumed term structure. The Hull-White model belongs to the family of modells known as HJM. A well known property of this family of models is that the average rate over all simulations should be equal to the input term structure by construction. However in practice, this is often not exactly the case especially in the tails of the curve and if the number of paths is small. The visual check shows the average simulation compared to the input term structure (interpolated/extrapolated by the Smith-Willson algorithm)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2e3527e",
   "metadata": {},
   "source": [
    "***\n",
    "<span style=color:black>\n",
    "    <b>Implied and simulated price of a ZCB</b>\n",
    "</span>\n",
    "<br>\n",
    "<span style=color:black>   \n",
    "    Visual comparison\n",
    "</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "510bfd54",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'ZCBs from Hull-White model')"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1)\n",
    "plt.grid()\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"P(0,t)\")\n",
    "plt.plot(t, implied_term_structure)\n",
    "plt.plot(t, P,\"--r\")\n",
    "plt.legend([\"P(0,t) market\", \"P(0,t) Monte Carlo\"])\n",
    "plt.title(\"ZCBs from Hull-White model\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b99378df",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "9d769ef7",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_statistics_bdp_1 = pd.DataFrame(abs(P- implied_term_structure)*10000, columns=[\"Abs diff in bps\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c19bcd0",
   "metadata": {},
   "source": [
    "***\n",
    "<span style=color:black>\n",
    "    <b>Implied and simulated term structure</b>\n",
    "</span>\n",
    "<br>\n",
    "<span style=color:black>   \n",
    "    Absolute difference in bps\n",
    "</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "c878316d",
   "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>Abs diff in bps</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.220446e-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6.884390e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.758009e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6.214429e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.106268e+01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Abs diff in bps\n",
       "0     2.220446e-12\n",
       "1     6.884390e-01\n",
       "2     2.758009e+00\n",
       "3     6.214429e+00\n",
       "4     1.106268e+01"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_statistics_bdp_1.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ba10cde",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9727e479",
   "metadata": {},
   "source": [
    "### Test 1; Success criteria\n",
    "\n",
    "The successful application of the success criteria marks the completion/failiure of the test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "86c6cb63",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test failed\n",
      "Test failed\n"
     ]
    }
   ],
   "source": [
    "result1 = SuccessTest(test_statistics_bdp_1.values, statistics_mean_max_diff_in_bps, statistics_mean_average_diff_in_bps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "e0fc7cf8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax1 = plt.subplots(1,1)\n",
    "ax1.plot(t, test_statistics_bdp_1, label= \"Absolute difference\")\n",
    "ax1.axhline(y = statistics_mean_max_diff_in_bps, color = 'r', linestyle = '-',label=\"Max allowed diff\")\n",
    "\n",
    "ax1.set_xlabel(\"time\")\n",
    "ax1.set_ylabel(\"Difference (in bps)\")\n",
    "ax1.set_title('Absolute difference in term structure')\n",
    "ax1.legend()\n",
    "fig.set_figwidth(6)\n",
    "fig.set_figheight(3)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "982edefa",
   "metadata": {},
   "source": [
    "<a id=\"10\"></a> <br>\n",
    "\n",
    "## Test 2; Comparison between simulated an calculated volatility\n",
    "\n",
    "The Hull-White model is one of the few widely used short rate models that has a closed-form formula for the calculation of the volatility. The formula is:\n",
    "\n",
    "$$ V[r(t)｜F_0] = \\frac{\\sigma^2}{2a}\\big( 1-e^{-2at} \\big) $$\n",
    "\n",
    "This fact makes it possible to compare the volatility calculated from the parameters with the simulated volatility. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "2b97115c",
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'Paths' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_20168/3386586715.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mpaths\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mPaths\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mNoOfPaths\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mNoOfSteps\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mT\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mP0t\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msigma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mepsilon\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[0mR\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpaths\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m\"R\"\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0mt\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpaths\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m\"time\"\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'Paths' is not defined"
     ]
    }
   ],
   "source": [
    "paths = Paths(NoOfPaths, NoOfSteps, T, P0t, a, sigma, epsilon)\n",
    "R = paths[\"R\"]\n",
    "t = paths[\"time\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5aa1e3f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "time = np.linspace(start=0,stop=T,num=NoOfSteps+1, endpoint=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "21b4c1b2",
   "metadata": {},
   "outputs": [],
   "source": [
    "var_series = np.var(R, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "81f48648",
   "metadata": {},
   "outputs": [],
   "source": [
    "vol = sigma**2/(2*a)*(1-np.exp(-2*a*time))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "23a0caa8",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure(1)\n",
    "plt.grid()\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"V(0,t)\")\n",
    "plt.plot(t,var_series)\n",
    "plt.plot(t,vol,\"--r\")\n",
    "plt.legend([\"V(0,t) simulated\", \"V(0,T) closed formula\"])\n",
    "plt.title(\"Variance function from Hull-White model\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d1c5d37f",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_statistics_bdp_2 = pd.DataFrame(abs(var_series-vol)*10000, columns=[\"Abs diff in bps\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5345b610",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46a1be21",
   "metadata": {},
   "source": [
    "***\n",
    "<span style=color:black>\n",
    "    <b>Theoretical and simulated volatility</b>\n",
    "</span>\n",
    "<br>\n",
    "<span style=color:black>   \n",
    "    Absolute difference in bps\n",
    "</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0eb1eaa8",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_statistics_bdp_2.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61a213c5",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8536ad3",
   "metadata": {},
   "source": [
    "### Test 2; Success criteria\n",
    "\n",
    "The successful application of the success criteria marks the completion/failiure of the test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1c26a1b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "result2 = SuccessTest(test_statistics_bdp_2.values, statistics_vol_max_diff_in_bps, statistics_vol_average_diff_in_bps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7051448d",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax1 = plt.subplots(1,1)\n",
    "ax1.plot(t, test_statistics_bdp_2, label= \"Absolute difference\")\n",
    "ax1.axhline(y = statistics_vol_max_diff_in_bps, color = 'r', linestyle = '-',label=\"Max allowed diff\")\n",
    "\n",
    "ax1.set_xlabel(\"time\")\n",
    "ax1.set_ylabel(\"Difference (in bps)\")\n",
    "ax1.set_title('Absolute difference in volatility')\n",
    "ax1.legend()\n",
    "fig.set_figwidth(6)\n",
    "fig.set_figheight(3)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9a21900",
   "metadata": {},
   "source": [
    "<a id=\"11\"></a> <br>\n",
    "## Conclusion\n",
    "\n",
    "The tests are successfull if the Hull-White curve generator calibrated using the March 2023 EIOPA curve, passes the success criteria. Based on the preformed tests, if all the tests pass, it is likely that the implementation was generated using a correct methodology and ran using the correct parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "043dbe75",
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   "outputs": [],
   "source": [
    "pd.DataFrame(data = [result1, result2], columns = [\"Mean test\",\"Max test\"],  \\\n",
    "             index= [\"Average term structure\",\"Theoretical vs empirical volatility\"])"
   ]
  }
 ],
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