_PROJECTION OF THE RISK FREE CURVE AND RECALIBRATION_v2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e4a19110",
   "metadata": {},
   "source": [
    "# PROJECTION OF THE RISK FREE CURVE AND RECALIBRATION_v2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6924f6fb",
   "metadata": {},
   "source": [
    "The purpose of this workbook is to showcase the calibration methodology inside OSEM. The key to the calibration is the Smith Wilson algorithm commonly used in insurance. This algorithm allows a continuous approximation of arbitrary maturities based on a subset of available maturities. This example is split onto 3 parts. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d4ea939",
   "metadata": {},
   "source": [
    " - The first part shows how the necessary parameters and curves are imported from input files. \n",
    " - Second part shows how the curves are generated and the Smith-Wilson calibrations derived. \n",
    " - The last part shows how the saved calibration can be used to derive an the discount rates for any maturity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "49ae88db",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.ticker as mtick"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "cae8e38e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from ImportData import import_SWEiopa\n",
    "from CurvesClass import Curves"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7936c21",
   "metadata": {},
   "source": [
    "## Importing files"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "489cc61f",
   "metadata": {},
   "source": [
    "The parameters and the current risk free curve are provided as input:\n",
    "\n",
    " - Parameters.csv; Parameters related to the run \n",
    " - EIOPA_param_file.csv; Assumed yield curve at modelling date and relevant maturities\n",
    " - EIOPA_curves_file.csv; Parameters related to the EIOPA time 0 calibration\n",
    " \n",
    " \n",
    " The exact location of the EIOPA files is encoded in the Parameters input file. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "76947335",
   "metadata": {},
   "outputs": [],
   "source": [
    "paramfile = pd.read_csv(\"Input\\Parameters.csv\", index_col=\"Parameter\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3df2f181",
   "metadata": {},
   "source": [
    "The location of the two EIOPA files are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "96ba2d05",
   "metadata": {},
   "outputs": [],
   "source": [
    "selected_param_file = paramfile[\"Value\"].loc[\"EIOPA_param_file\"]\n",
    "selected_curves_file = paramfile[\"Value\"].loc[\"EIOPA_curves_file\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e98d64b4",
   "metadata": {},
   "source": [
    "The risk free curve belongs to the following country:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9cf13695",
   "metadata": {},
   "outputs": [],
   "source": [
    "country = paramfile[\"Value\"].loc[\"country\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc1b15a1",
   "metadata": {},
   "source": [
    "Import all necessary parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "96d0a173",
   "metadata": {},
   "outputs": [],
   "source": [
    "[maturities_country, curve_country, extra_param, Qb] = import_SWEiopa(selected_param_file, selected_curves_file, country)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2358d29",
   "metadata": {},
   "source": [
    "## Preparation and treatment of the curves"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "703fedca",
   "metadata": {},
   "source": [
    "The OSEM does multiple steps in order to make it easier for OSEM to access discount curves at any point in time and for arbitrary maturities. All steps are performed and saved within the Curves class."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5eaaeb2e",
   "metadata": {},
   "source": [
    "### The curves class"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7b94b91",
   "metadata": {},
   "source": [
    "The curve class object contains all the data necessary to run the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "78b1b253",
   "metadata": {},
   "outputs": [],
   "source": [
    "# ultimate forward rate\n",
    "ufr = extra_param[\"UFR\"]/100\n",
    "\n",
    "# Numeric precision of the optimisation\n",
    "precision = float(paramfile[\"Value\"].loc[\"Precision\"])\n",
    "\n",
    "# Targeted distance between the extrapolated curve and the ultimate forward rate at the convergence point\n",
    "tau = float(paramfile[\"Value\"].loc[\"Tau\"])# 1 basis point\n",
    "\n",
    "modelling_date = paramfile.loc[\"Modelling_Date\"]\n",
    "\n",
    "# Number of projection years\n",
    "n_years = int(paramfile.loc[\"n_proj_years\"].values[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "68513113",
   "metadata": {},
   "outputs": [],
   "source": [
    "curves = Curves(ufr, precision, tau, modelling_date, country)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27b97643",
   "metadata": {},
   "source": [
    "After the Curves class is initiated, there are a series if calibrations that needs to be performed.\n",
    "\n",
    " - Saving of the input term structure\n",
    " - Calculation of the forward rates\n",
    " - Projection of the forward spot rates\n",
    " - Calculation of the Smith-Wilson calibrations for each period"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31f91ad4",
   "metadata": {},
   "source": [
    "### Save the input term structure\n",
    "\n",
    "SetObservedTermStructure sets the liquid maturities and the corresponding yields to the m_obs and r_obs property of the Curves class. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "5ed1a4af",
   "metadata": {},
   "outputs": [],
   "source": [
    "curves.SetObservedTermStructure(maturity_vec=curve_country.index.tolist(), yield_vec=curve_country.values)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df97b77f",
   "metadata": {},
   "source": [
    "### Calculate 1 year forward rates\n",
    "\n",
    "Using the time 0 spot curve provided as input, the yearly forward rates can be calculated from the annually reported yield curve\n",
    "$$\n",
    "fw_{EIOPA,1} = y_1\n",
    "$$\n",
    "\n",
    "otherwise:\n",
    "\n",
    "$$\n",
    "fw_{EIOPA,i} = \\frac{(1 + y_i)^{-i}}{(1 + y_{i-1})^{-(i-1)}} \n",
    "$$\n",
    "\n",
    "Note that this implementation assumes that all forward rates are exactly 1 year apart as provided by EIOPA."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06cf272b",
   "metadata": {},
   "source": [
    "Where:\n",
    "\n",
    " - $i$ is the year (Ex. 1,2,3, $\\dots$)\n",
    " - $y_i$ is the yield for the year $i$\n",
    " - $fw_{EIOPA,i}$ is the 1-year forward rate between years $i-1$ and $i$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "aade7ad2",
   "metadata": {},
   "outputs": [],
   "source": [
    "curves.CalcFwdRates()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88cc544e",
   "metadata": {},
   "source": [
    "### Forward yield curve\n",
    "\n",
    "The forward yield curve can be calculated by using the 1-year forward rates from the suitable moment onwards. The spot yield curve is calculated for each projection period. For the projection period $i$, the yield curve can be calculated as:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb1997e6",
   "metadata": {},
   "source": [
    "$$\n",
    "y^j_{i-j} = \\prod_{k=j}^i\\big(1+fw_{EIOPA}(k)\\big)^{-(k-j)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcda63b7",
   "metadata": {},
   "source": [
    "Where:\n",
    " - $j$ is the modelling period at which the model is performing the calculations \n",
    " - $i-j$ is the time period within the modelling period\n",
    " - $y^j_{k}$ is the yield $k$ years after the modelling period $j$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "66b733c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "curves.ProjectForwardRate(n_years)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "017a8ee1",
   "metadata": {},
   "source": [
    "## Calibrate Smith-Wilson on each yield curve"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01756712",
   "metadata": {},
   "source": [
    "Each forward yield curve is used to calibrate the SW algorithm. This calibration can then be used to generate yield corves of arbitrary maturities. The calibration is split on two parts. First one calibrates the curve at time 0."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea489278",
   "metadata": {},
   "source": [
    "### Calibration of the interpolation/extrapolation algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68da0f63",
   "metadata": {},
   "source": [
    "Both at time 0 and in following projection years, the same calibration algorithm is performed. The algorithm looks to minimize the difference between the xxx and the ultimate forward rate as recommended by EIOPA:\n",
    "\n",
    "\n",
    "$$\n",
    "T = \\max(U+40,60)\n",
    "$$\n",
    "\n",
    "$$\n",
    "g(\\alpha) = |f(T) - \\omega| = \\frac{\\alpha}{|1-\\kappa e^{\\alpha T}|}\n",
    "$$\n",
    "\n",
    "The calibration consists of using a bisection algorithm to minimize the difference between the ultimate forward rate $\\omega$.\n",
    "\n",
    "The calibration is:\n",
    "\n",
    "$$\n",
    "\\min \\alpha \n",
    "$$\n",
    "\n",
    "subject to constraints:\n",
    "\n",
    "$$\n",
    "\\alpha \\geq \\alpha_{min}\n",
    "$$\n",
    "and\n",
    "\n",
    "$$\n",
    "g(\\alpha) \\leq \\tau\n",
    "$$\n",
    "\n",
    " And $\\kappa$ is defined as:\n",
    "\n",
    " $$\n",
    "\\kappa = \\frac{1 + \\alpha u^T Qb}{sinh(\\alpha u^T)Qb}\n",
    " $$ \n",
    "\n",
    " $$\n",
    "Q = d I C\n",
    " $$\n",
    "\n",
    "$$\n",
    "d = e^{-\\omega u}\n",
    "$$\n",
    "\n",
    "\n",
    "\n",
    "Where:\n",
    " - $\\alpha$ is the free parameter to be calibrated\n",
    " - $\\alpha_{min}$ is the lower bound of the allowable values\n",
    " - $U$ is the last liquid point\n",
    " - $g(\\alpha)$ is the extrapolated\n",
    " - $C$ is a matrix of cash flows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "d4ce9ba0",
   "metadata": {},
   "outputs": [],
   "source": [
    "curves.CalibrateProjected(n_years, 0.05, 0.5, 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "061b1d6a-578c-4142-a5a7-53939d5b377d",
   "metadata": {},
   "source": [
    "### Spread treatment"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9904d259-636b-4eec-b6d7-4935b5b65e98",
   "metadata": {},
   "source": [
    "ToDo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4ca0bafc-792c-431c-8fb9-33c2ba163e54",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "d50fa78e",
   "metadata": {},
   "source": [
    "## Example 1\n",
    "\n",
    "One of the properties of the Smith-Wilson algorithm is that it retains the curve values at the liquid points provided in the calibration. This property is tested in the first example. A projection year is selected and the algorithm is asked to provide the values using the calibration vector. The original yield curve that was used to calibrate is then compared to the output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "cd2e3f2b-2925-41cd-a440-5a77db3cb94c",
   "metadata": {},
   "outputs": [],
   "source": [
    "spread = 0.00"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "a7589215",
   "metadata": {},
   "outputs": [],
   "source": [
    "p_year = 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "7e76257a",
   "metadata": {},
   "outputs": [],
   "source": [
    "interpolated_curve = curves.RetrieveRates(p_year, curves.m_obs[\"Maturities_year_\"+str(p_year)].values[:-p_year], \"Yield\",spread=spread)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "93e7db31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax1 = plt.subplots(1, 1)\n",
    "ax1.scatter(curves.m_obs[\"Maturities_year_\"+str(p_year)].values[:-p_year], interpolated_curve*100, label=\"Calculated\", marker=\"x\")\n",
    "ax1.plot(curves.m_obs[\"Maturities_year_\"+str(p_year)].values[:-p_year], curves.r_obs[\"Yield_year_\"+str(p_year)].values[:-p_year]*100)\n",
    "ax1.set_ylabel(\"yield\")\n",
    "ax1.set_title('Recalculated & provided yield curve')\n",
    "ax1.set_xlabel(\"time\")\n",
    "ax1.legend()\n",
    "ax1.yaxis.set_major_formatter(mtick.PercentFormatter())\n",
    "fig.set_figwidth(6)\n",
    "fig.set_figheight(3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a395933b",
   "metadata": {},
   "source": [
    "## Example 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f4a2902",
   "metadata": {},
   "source": [
    "The calibration will be used to provide OSAM with yields for arbitrary maturities. This example verifies if the calibration provides yields for maturities not provided as input into the calibration.\n",
    "Assuming the algorithm is processing the year 3. A hypothetical asset has a cash flow at year fractions:\n",
    "\n",
    "$$ \\{0.7, 1.2, 2.1, 3.543\\} $$\n",
    "\n",
    "To make it possible to calculate the present value, the corresponding discount rates are calculated:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "003c4e7e",
   "metadata": {},
   "source": [
    "With the calibrated vector $b$, the required yields can easily be obtained by applying the formula:\n",
    "\n",
    "$$\n",
    "p(v) = e^{-\\omega v} \\big(1 + H(v,u) b \\big)\n",
    "$$\n",
    "\n",
    "Where:\n",
    " - $v$ is the vector of desired maturities\n",
    " - $ \\omega $ is the ultimate forward intensity\n",
    " - $u$ is the vector of maturities that were used in the calibration\n",
    " - $H(v,u)$ is the Heart of the Wilson function\n",
    " - $b$ is the calibration vector\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "2eaf4b16",
   "metadata": {},
   "outputs": [],
   "source": [
    "desired_mat = np.array([0.7, 1.2, 1.3543])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6ec91c2",
   "metadata": {},
   "source": [
    "### Yield calculation\n",
    "\n",
    "\n",
    "The yield in each modelling period can be interpolated/extrapolated using the Smith-Wilson calibration vector calculated above. This allows OSEM to apply continuous yields."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "1aff0709-299d-410b-96be-4854c76fa277",
   "metadata": {},
   "outputs": [],
   "source": [
    "spread = 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "02100def",
   "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>Yield</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.026187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.026155</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.026145</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Yield\n",
       "0  0.026187\n",
       "1  0.026155\n",
       "2  0.026145"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(curves.RetrieveRates(3, desired_mat, \"Yield\",spread))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "7c8441da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax1 = plt.subplots(1, 1)\n",
    "ax1.scatter(desired_mat, curves.RetrieveRates(3, desired_mat, \"Yield\", spread)*100, label=\"Yield\", marker=\"x\")\n",
    "ax1.set_ylabel(\"yield\")\n",
    "ax1.set_title('Selected yield curve')\n",
    "ax1.set_xlabel(\"time\")\n",
    "ax1.legend()\n",
    "ax1.yaxis.set_major_formatter(mtick.PercentFormatter())\n",
    "fig.set_figwidth(6)\n",
    "fig.set_figheight(3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4dff1424",
   "metadata": {},
   "source": [
    "### Capitalisation factor calculation\n",
    "\n",
    "\n",
    "The capitalisation factor can be calculated as:\n",
    "\n",
    "$$\n",
    "c_i(t) = \\big(1+ y_i(t)\\big)^{t} \n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "3ee30a54",
   "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>Capitalisation</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.018259</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.031468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.035572</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Capitalisation\n",
       "0        1.018259\n",
       "1        1.031468\n",
       "2        1.035572"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(curves.RetrieveRates(3, desired_mat, \"Capitalisation\", spread))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "5b0a6993",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax1 = plt.subplots(1, 1)\n",
    "ax1.scatter(desired_mat, curves.RetrieveRates(3, desired_mat, \"Capitalisation\", spread)*100, label=\"Capitalisation factor\", marker=\"x\")\n",
    "ax1.set_ylabel(\"Capitalisation factor\")\n",
    "ax1.set_title('Selected capitalisation curve')\n",
    "ax1.set_xlabel(\"time\")\n",
    "ax1.legend()\n",
    "ax1.yaxis.set_major_formatter(mtick.PercentFormatter())\n",
    "fig.set_figwidth(6)\n",
    "fig.set_figheight(3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9354da8c",
   "metadata": {},
   "source": [
    "### Discount factor calculation\n",
    "\n",
    "The discount factors can be calculated from the yield:\n",
    "\n",
    "$$\n",
    "d_i(t) = \\big(1+ y_i(t)\\big)^{-t} \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e89dcab",
   "metadata": {},
   "source": [
    "Where:\n",
    " - $t$ is time increment from the modelling period (Ex. 1.5 is 1 year and 6 months after the modelling period\n",
    " - $y_i(t)$ is the annualized yield for maturity t after the modelling period $i$\n",
    " - $c_i(t)$ is the capitalisation factor for 1 unit, until $t$ years after the modelling period $i$\n",
    "\n",
    " - $d_i(t)$ is the discount factor for a cash flow of value 1, occurring $t$ years after the modelling period $i$, discounted to the modelling period $i$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "7478eb1d",
   "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>Discount</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.982068</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.969492</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.965650</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Discount\n",
       "0  0.982068\n",
       "1  0.969492\n",
       "2  0.965650"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(curves.RetrieveRates(3, desired_mat, \"Discount\", spread))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "de82dbb8",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax1 = plt.subplots(1, 1)\n",
    "ax1.scatter(desired_mat, curves.RetrieveRates(3, desired_mat, \"Discount\", spread)*100, label=\"Discount factor\", marker=\"x\")\n",
    "ax1.set_ylabel(\"Discount factor\")\n",
    "ax1.set_title('Selected discount curve')\n",
    "ax1.set_xlabel(\"time\")\n",
    "ax1.legend()\n",
    "ax1.yaxis.set_major_formatter(mtick.PercentFormatter())\n",
    "fig.set_figwidth(6)\n",
    "fig.set_figheight(3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6b92dc4d-b746-4c13-b180-03094191c734",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ee852b03-e7ed-4723-8a7f-1b353b596562",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}