monotonic_smooth.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "bb26ad03-dc2a-437a-9065-8f33c4a41207",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import math\n",
    "import numpy \n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "28a9ac51-34eb-452c-bf82-e4400b2a4ee9",
   "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>Fitch_grade</th>\n",
       "      <th>Fitch_observed_DR</th>\n",
       "      <th>Moodys_grade</th>\n",
       "      <th>Moodys_observed_DR</th>\n",
       "      <th>SnP_grade</th>\n",
       "      <th>SnP_observed_DR</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>AAA</td>\n",
       "      <td>0.0012</td>\n",
       "      <td>Aaa</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>AAA</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>AA+</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>Aa1</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>AA+</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>AA</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>Aa2</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>AA</td>\n",
       "      <td>0.0002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>AA-</td>\n",
       "      <td>0.0008</td>\n",
       "      <td>Aa3</td>\n",
       "      <td>0.0004</td>\n",
       "      <td>AA-</td>\n",
       "      <td>0.0003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>A+</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>A1</td>\n",
       "      <td>0.0006</td>\n",
       "      <td>A+</td>\n",
       "      <td>0.0005</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Fitch_grade  Fitch_observed_DR Moodys_grade  Moodys_observed_DR SnP_grade  \\\n",
       "0         AAA             0.0012          Aaa              0.0000       AAA   \n",
       "1         AA+             0.0000          Aa1              0.0000       AA+   \n",
       "2          AA             0.0000          Aa2              0.0000        AA   \n",
       "3         AA-             0.0008          Aa3              0.0004       AA-   \n",
       "4          A+             0.0000           A1              0.0006        A+   \n",
       "\n",
       "   SnP_observed_DR  \n",
       "0           0.0000  \n",
       "1           0.0000  \n",
       "2           0.0002  \n",
       "3           0.0003  \n",
       "4           0.0005  "
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_excel(\"cr.xls\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "f33fba98-1f40-4e59-8fd3-25d04ed7b9df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x243418e1e50>]"
      ]
     },
     "execution_count": 35,
     "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.plot(df.Fitch_observed_DR)\n",
    "plt.plot(df.Moodys_observed_DR)\n",
    "plt.plot(df.SnP_observed_DR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "9cb241c3-84d6-4853-927d-3ffbe9c0617c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mono_smooth(y):\n",
    "    y = y.dropna().to_numpy()\n",
    "    x = numpy.arange(len(y))\n",
    "    N = len(y)\n",
    "\n",
    "    # Prepare bases (Imat) and penalty\n",
    "    dd = 3\n",
    "    E  = numpy.eye(N)\n",
    "    D3 = numpy.diff(E, n = dd, axis=0)\n",
    "    D1 = numpy.diff(E, n = 1, axis=0)\n",
    "    la = 100\n",
    "    kp = 10000000\n",
    "\n",
    "    # Monotone smoothing\n",
    "    ws = numpy.zeros(N - 1)\n",
    "\n",
    "    for it in range(30):\n",
    "        Ws      = numpy.diag(ws * kp)\n",
    "        mon_cof = numpy.linalg.solve(E + la * D3.T @ D3 + D1.T @ Ws @ D1, y)\n",
    "        ws_new  = (D1 @ mon_cof < 0.0) * 1\n",
    "        dw      = numpy.sum(ws != ws_new)\n",
    "        ws      = ws_new\n",
    "        if(dw == 0): break  \n",
    "\n",
    "    # Monotonic and non monotonic fits\n",
    "    return mon_cof"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "71db061e-a1ef-4212-947f-89259aa77a11",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-42-333765bc0fff>:3: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  df['SnP_observed_DR'][:-1] = mono_smooth(df.SnP_observed_DR)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x24341c5f9d0>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 2000x1500 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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": [
    "df['Fitch_observed_DR'] = mono_smooth(df.Fitch_observed_DR)\n",
    "df['Moodys_observed_DR'] = mono_smooth(df.Moodys_observed_DR)\n",
    "df['SnP_observed_DR'][:-1] = mono_smooth(df.SnP_observed_DR)\n",
    "df.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "16cbc4c7-2e2a-40f4-a95d-4fc015e867a4",
   "metadata": {},
   "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": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}