CDS and Synthetic CDO Tranche Pricing (Semi-Analytic One Factor Model).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 825,
   "id": "d36fa008",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy\n",
    "from scipy.stats import norm\n",
    "from scipy.integrate import quad\n",
    "import random\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from math import comb\n",
    "from scipy.stats import binom\n",
    "import sympy\n",
    "import math\n",
    "from scipy import integrate\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 826,
   "id": "48dd5088",
   "metadata": {
    "scrolled": true
   },
   "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability at least 3 defaults [0.0024287323219811426, 0.002711165136143723, 0.003011776695417391, 0.003330310976548595, 0.003666425885229224, 0.004019703171324586, 0.004389658359636513, 0.004775750445210315, 0.0051773911645398366, 0.0055939537088875516, 0.006024780792350824, 0.00646919202527077, 0.0069264905736663995, 0.007395969108425146, 0.007876915065040367, 0.00836861524672547, 0.008870359811727506, 0.009381445690438042, 0.009901179480195511, 0.010428879866106348, 0.010963879615270566, 0.011505527189908563, 0.012053188022348803, 0.012606245491904797, 0.013164101640545024, 0.013726177661059664, 0.01429191418826932, 0.014860771420771093, 0.015432229097823762, 0.016005786353260387, 0.01658096146580295, 0.017157291522861683, 0.017734332012786416, 0.01831165635864828, 0.018888855404913266, 0.019465536866835075, 0.020041324751022285, 0.020615858754418397, 0.02118879364784558, 0.021759798649304926, 0.02232855679138321, 0.022894764286359517, 0.023458129891953353, 0.02401837428006935, 0.02457522941039139, 0.025128437910207788, 0.02567775246148024, 0.026222935195783184, 0.02676375709745079, 0.027299997414972882, 0.0278314430804312, 0.02835788813653236, 0.0288791331705811, 0.029394984754530534, 0.029905254890052538, 0.03040976045738359, 0.030908322666504534, 0.031400766509017776, 0.03188692020889513, 0.032366614670017925, 0.03283968291823415, 0.0333059595353613, 0.03376528008228919, 0.03421748050798056, 0.0346623965408508, 0.03509986305846153, 0.035529713431063925, 0.03595177883387229, 0.036365887522272, 0.036771864063356204, 0.03716952851620466, 0.037558695552183344, 0.03793917350516869, 0.0383107633399548, 0.03867325752513388, 0.039026438794343116, 0.03937007877687172, 0.03970393647505026, 0.04002775656156494, 0.0403412674642853, 0.04064417919971336, 0.040936180907608526, 0.0412169380288815, 0.0414860890554236, 0.04174324176341436, 0.04198796881954261, 0.04221980262035166, 0.04243822919028943, 0.04264268090405329, 0.04283252774775921, 0.04300706672503045, 0.04316550889745531, 0.043306963368435064, 0.04343041726809149, 0.043534710432529294, 0.04361850293305671, 0.043680232800000676, 0.04371806003239706, 0.043729790993452575, 0.04371277402655019]\n"
     ]
    }
   ],
   "source": [
    "#1c for rho ranging from 0 to 0.9, calculate probabilities of at least n=3 before\n",
    "#plot dependence on rho\n",
    "#integrate over normal density to get rid of conditional m\n",
    "#use quad()for numerical integration\n",
    "\n",
    "t=5.0\n",
    "h=0.0075\n",
    "\n",
    "prob_list=[]\n",
    "i=0\n",
    "rho_list = np.linspace(0.00000001,0.9,100)\n",
    "\n",
    "\n",
    "\n",
    "for n in range(0,100):\n",
    "    \n",
    "    #prob(exactly 0)\n",
    "    def f(x):\n",
    "        tr=norm.ppf(np.exp(-t*h))\n",
    "        crit = (tr-x*np.sqrt(rho_list[n]))/(np.sqrt(1-rho_list[n]))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta= comb(8,0)*((1-gamma)**8)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "\n",
    "\n",
    "    I0= quad(f,-6,6)\n",
    "\n",
    "\n",
    "    #prob(exactly 1)\n",
    "    def f(x):\n",
    "        tr=norm.ppf(np.exp(-t*h))\n",
    "        crit = (tr-x*np.sqrt(rho_list[n]))/(np.sqrt(1-rho_list[n]))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta= comb(8,1)*(gamma)*((1-gamma)**7)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I1= quad(f,-6,6)\n",
    "\n",
    "\n",
    "    #prob(exactly 2)\n",
    "    def f(x):\n",
    "        tr=norm.ppf(np.exp(-t*h))\n",
    "        crit = (tr-x*np.sqrt(rho_list[n]))/(np.sqrt(1-rho_list[n]))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta= comb(8,2)*((gamma)**2)*((1-gamma)**6)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "\n",
    "    I2=quad(f,-10,10)\n",
    "\n",
    "    prob= 1-I0[0]-I1[0]-I2[0]\n",
    "    prob_list.append(prob)\n",
    "    \n",
    "\n",
    "\n",
    "plt.plot(rho_list,prob_list)\n",
    "plt.ylabel('Probability at least 3 defaults')\n",
    "plt.xlabel('rho')\n",
    "plt.title('Probability of at least 3 defaults before t=5 vs. rho')\n",
    "plt.show()\n",
    "\n",
    "print('Probability at least 3 defaults', prob_list)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 827,
   "id": "3db4589f",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Vfee 3rd to default CDS\n",
    "\n",
    "def vfee():\n",
    "    t_list = np.linspace(0.25,5,20)\n",
    "    survival_list=[]\n",
    "\n",
    "    \n",
    "    h=0.0075\n",
    "    rho=0.7\n",
    "    recovery=0.4\n",
    "\n",
    "    for j in range(0,len(t_list)):\n",
    "\n",
    "        def f(x):\n",
    "            tr=norm.ppf(np.exp(-(t_list[j])*h))\n",
    "            crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "            gamma=(1-norm.cdf(crit))\n",
    "            beta= comb(8,0)*(gamma**0)*((1-gamma)**8)\n",
    "            func = beta*norm.pdf(x)\n",
    "            return(func)\n",
    "\n",
    "        I0= quad(f,-6,6)\n",
    "\n",
    "\n",
    "        def f(x):\n",
    "            tr=norm.ppf(np.exp(-(t_list[j])*h))\n",
    "            crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "            gamma=(1-norm.cdf(crit))\n",
    "            beta= comb(8,1)*(gamma**1)*((1-gamma)**7)\n",
    "            func = beta*norm.pdf(x)\n",
    "            return(func)\n",
    "\n",
    "        I1= quad(f,-6,6)\n",
    "\n",
    "        def f(x):\n",
    "            tr=norm.ppf(np.exp(-(t_list[j])*h))\n",
    "            crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "            gamma=(1-norm.cdf(crit))\n",
    "            beta= comb(8,2)*(gamma**2)*((1-gamma)**6)\n",
    "            func = beta*norm.pdf(x)\n",
    "            return(func)\n",
    "\n",
    "        I2= quad(f,-6,6)\n",
    "        prob = 1-I0[0]-I1[0]-I2[0]\n",
    "\n",
    "        survival_list.append(1-prob)\n",
    "\n",
    "\n",
    "    vfee=0.25*sum(survival_list)\n",
    "    print('vfee=',vfee)\n",
    "    return vfee\n",
    "\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 828,
   "id": "be8e98f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Vcon 3rd to default CDS\n",
    "#assume interest is 0\n",
    "\n",
    "def vcon():\n",
    "\n",
    "    t_list = np.linspace(0,5,21)\n",
    "    survival_list=[]\n",
    "\n",
    "    s_diff_list=[]\n",
    "    # def vfee():\n",
    "    h=0.0075\n",
    "    rho=0.7\n",
    "    recovery=0.4\n",
    "\n",
    "    for j in range(0,len(t_list)):\n",
    "\n",
    "        def f(x):\n",
    "            tr=norm.ppf(np.exp(-(t_list[j])*h))\n",
    "            crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "            gamma=(1-norm.cdf(crit))\n",
    "            beta= comb(8,0)*(gamma**0)*((1-gamma)**8)\n",
    "            func = beta*norm.pdf(x)\n",
    "            return(func)\n",
    "\n",
    "        I0= quad(f,-6,6)\n",
    "\n",
    "\n",
    "        def f(x):\n",
    "            tr=norm.ppf(np.exp(-(t_list[j])*h))\n",
    "            crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "            gamma=(1-norm.cdf(crit))\n",
    "            beta= comb(8,1)*(gamma**1)*((1-gamma)**7)\n",
    "            func = beta*norm.pdf(x)\n",
    "            return(func)\n",
    "\n",
    "        I1= quad(f,-6,6)\n",
    "\n",
    "        def f(x):\n",
    "            tr=norm.ppf(np.exp(-(t_list[j])*h))\n",
    "            crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "            gamma=(1-norm.cdf(crit))\n",
    "            beta= comb(8,2)*(gamma**2)*((1-gamma)**6)\n",
    "            func = beta*norm.pdf(x)\n",
    "            return(func)\n",
    "\n",
    "        I2= quad(f,-6,6)\n",
    "        prob = 1-I0[0]-I1[0]-I2[0]\n",
    "\n",
    "        survival_list.append(1-prob)\n",
    "\n",
    "\n",
    "    for i in range (1,len(survival_list)):\n",
    "        s_diff= survival_list[i-1]-survival_list[i]\n",
    "        s_diff_list.append(s_diff)\n",
    "\n",
    "\n",
    "    vcon=sum(s_diff_list)\n",
    "    print('vcon =',vcon)\n",
    "    return vcon\n",
    "\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 829,
   "id": "a4eaff2c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "vcon = 0.039703934421481346\n",
      "vfee= 4.901695504667828\n",
      "The par spread is: 81.00040972286375\n"
     ]
    }
   ],
   "source": [
    "print(\"The par spread is:\",10000*vcon()/vfee())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 830,
   "id": "034609f2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        0-3       3-6       6-9          9-12         12-22\n",
      "0  0.748085  0.067655  0.000482  4.559073e-07  4.559073e-07\n",
      "1  0.514318  0.196991  0.073685  2.782784e-02  2.782784e-02\n",
      "2  0.418614  0.204986  0.109567  6.159116e-02  6.159116e-02\n",
      "3  0.351637  0.195713  0.121858  8.024278e-02  8.024278e-02\n",
      "4  0.296865  0.180547  0.123358  8.902611e-02  8.902611e-02\n",
      "5  0.248379  0.162296  0.118683  9.133792e-02  9.133792e-02\n",
      "6  0.203091  0.141658  0.109628  8.883214e-02  8.883214e-02\n",
      "7  0.158657  0.118303  0.096582  8.201008e-02  8.201008e-02\n",
      "8  0.111886  0.090417  0.078354  6.995304e-02  6.995304e-02\n",
      "9  0.041872  0.040918  0.040313  3.985337e-02  3.985337e-02\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": [
    "#2a graph of fraction of paths generating loss for various tranches\n",
    "\n",
    "t=5.0\n",
    "h=0.0075\n",
    "rho_list = np.linspace(0.00000001,0.999,10)\n",
    "prob_loss_list03=[]\n",
    "prob_loss_list36=[]\n",
    "prob_loss_list69=[]\n",
    "prob_loss_list912=[]\n",
    "prob_loss_list1222=[]\n",
    "\n",
    "for i in range(0,10):\n",
    "\n",
    "#0-3 tranche\n",
    "    def f(x):\n",
    "        tr=norm.ppf(np.exp(-t*h))\n",
    "        crit = (tr-x*np.sqrt(rho_list[i]))/(np.sqrt(1-rho_list[i]))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta1=binom.cdf(5,200,gamma)\n",
    "        func = beta1*norm.pdf(x)\n",
    "        return(func)\n",
    "    \n",
    "    I_special=quad(f,-6,6)[0]\n",
    "\n",
    "    prob_loss =1-I_special\n",
    "    prob_loss_list03.append(prob_loss)\n",
    "#3-6 tranche\n",
    "    \n",
    "    def f(x):\n",
    "        tr=norm.ppf(np.exp(-t*h))\n",
    "        crit = (tr-x*np.sqrt(rho_list[i]))/(np.sqrt(1-rho_list[i]))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.cdf(11,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    \n",
    "    I_special=quad(f,-6,6)[0]\n",
    "\n",
    "    prob_loss =1-I_special\n",
    "    prob_loss_list36.append(prob_loss)\n",
    "\n",
    "#6-9 tranche\n",
    "\n",
    "    def f(x):\n",
    "        tr=norm.ppf(np.exp(-t*h))\n",
    "        crit = (tr-x*np.sqrt(rho_list[i]))/(np.sqrt(1-rho_list[i]))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.cdf(17,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I_special=quad(f,-6,6)[0]\n",
    "\n",
    "    prob_loss =1-I_special\n",
    "    prob_loss_list69.append(prob_loss)\n",
    "    \n",
    "#9-12 tranche    \n",
    "    def f(x):\n",
    "        tr=norm.ppf(np.exp(-t*h))\n",
    "        crit = (tr-x*np.sqrt(rho_list[i]))/(np.sqrt(1-rho_list[i]))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.cdf(23,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    \n",
    "    I_special=quad(f,-6,6)[0]\n",
    "\n",
    "    prob_loss =1-I_special\n",
    "    prob_loss_list912.append(prob_loss)\n",
    "\n",
    "#12-22 tranche    \n",
    "    def f(x):\n",
    "        tr=norm.ppf(np.exp(-t*h))\n",
    "        crit = (tr-x*np.sqrt(rho_list[i]))/(np.sqrt(1-rho_list[i]))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.cdf(43,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    \n",
    "    I_special=quad(f,-6,6)[0]\n",
    "\n",
    "    prob =1-I_special\n",
    "    prob_loss_list1222.append(prob_loss)\n",
    "    \n",
    "\n",
    "\n",
    "df = pd.DataFrame(list(zip(prob_loss_list03, prob_loss_list36,prob_loss_list69,prob_loss_list912,prob_loss_list1222)),\n",
    "               columns =['0-3', '3-6','6-9','9-12','12-22'])\n",
    "print(df)\n",
    "\n",
    "plt.plot(rho_list, prob_loss_list69,prob_loss_list912)\n",
    "plt.xlim(xmin=0,xmax=1)\n",
    "plt.ylim(ymin=0,ymax=0.5)\n",
    "\n",
    "plt.ylabel('fraction of paths generating tranche loss')\n",
    "plt.xlabel('rho')\n",
    "plt.title('Tranches 6-9% and 9-12%')\n",
    "plt.show() \n",
    "    \n",
    "plt.plot(rho_list, prob_loss_list03)\n",
    "plt.xlim(xmin=0,xmax=1)\n",
    "\n",
    "plt.ylabel('fraction of paths generating tranche loss')\n",
    "plt.xlabel('rho')\n",
    "plt.title('0-3%')\n",
    "plt.show()\n",
    "\n",
    "plt.plot(rho_list, prob_loss_list36)\n",
    "plt.xlim(xmin=0,xmax=1)\n",
    "\n",
    "plt.ylabel('fraction of paths generating tranche loss')\n",
    "plt.xlabel('rho')\n",
    "plt.title('3-6%')\n",
    "plt.show()\n",
    "\n",
    "plt.plot(rho_list, prob_loss_list69)\n",
    "plt.xlim(xmin=0,xmax=1)\n",
    "\n",
    "plt.ylabel('fraction of paths generating tranche loss')\n",
    "plt.xlabel('rho')\n",
    "plt.title('6-9%')\n",
    "plt.show()\n",
    "\n",
    "plt.plot(rho_list, prob_loss_list912)\n",
    "plt.xlim(xmin=0,xmax=1)\n",
    "\n",
    "plt.ylabel('fraction of paths generating tranche loss')\n",
    "plt.xlabel('rho')\n",
    "plt.title('9-12%')\n",
    "plt.show()\n",
    "    \n",
    "    \n",
    "plt.plot(rho_list, prob_loss_list1222)\n",
    "plt.xlim(xmin=0,xmax=1)\n",
    "\n",
    "plt.ylabel('fraction of paths generating tranche loss')\n",
    "plt.xlabel('rho')\n",
    "plt.title('12-22%')\n",
    "plt.show() \n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 834,
   "id": "56216f23",
   "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": [
    "#2b expected loss as a function of time for 6-9% tranche\n",
    "\n",
    "t=5.0\n",
    "h=0.0075\n",
    "t_list = np.linspace(0,5,21)\n",
    "rho=0.25\n",
    "N=10**7\n",
    "\n",
    "exp_loss_listrho25=[]\n",
    "\n",
    "for i in range(0,21):\n",
    "\n",
    "\n",
    "#default 13,14,15,16,17,18\n",
    "    \n",
    "    def f13(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(13,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I13=1-quad(f,-6,6)[0]\n",
    "    \n",
    "    def f14(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(14,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I14=1-quad(f,-6,6)[0]\n",
    "    \n",
    "    def f15(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(15,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I15=1-quad(f,-6,6)[0]\n",
    "    \n",
    "    def f16(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(16,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I16=1-quad(f,-6,6)[0]\n",
    "    \n",
    "    def f17(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(17,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I17=1-quad(f,-6,6)[0]\n",
    "    \n",
    "\n",
    "#binom cdf 1-binom.cdf(17...)\n",
    "    def f(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.cdf(17,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I_special=1-quad(f,-6,6)[0]\n",
    "\n",
    "    expected_loss = I13+2*I14+3*I15+4*I16+5*I17+6*I_special\n",
    "    exp_loss_listrho25.append(N*expected_loss)\n",
    "    \n",
    "t=5.0\n",
    "h=0.0075\n",
    "t_list = np.linspace(0,5,21)\n",
    "rho=0.5\n",
    "N=10**7\n",
    "\n",
    "exp_loss_listrho50=[]\n",
    "\n",
    "for i in range(0,21):\n",
    "\n",
    "\n",
    "#default 13,14,15,16,17,18\n",
    "    \n",
    "    def f13(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(13,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I13=1-quad(f,-6,6)[0]\n",
    "    \n",
    "    def f14(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(14,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I14=1-quad(f,-6,6)[0]\n",
    "    \n",
    "    def f15(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(15,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I15=1-quad(f,-6,6)[0]\n",
    "    \n",
    "    def f16(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(16,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I16=1-quad(f,-6,6)[0]\n",
    "    \n",
    "    def f17(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(17,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I17=1-quad(f,-6,6)[0]\n",
    "\n",
    "#binom cdf 1-binom.cdf(17...)\n",
    "    def f(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.cdf(17,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I_special=1-quad(f,-6,6)[0]\n",
    "\n",
    "    expected_loss = I13+2*I14+3*I15+4*I16+5*I17+6*I_special\n",
    "    exp_loss_listrho50.append(N*expected_loss)\n",
    "    \n",
    "\n",
    "t=5.0\n",
    "h=0.0075\n",
    "t_list = np.linspace(0,5,21)\n",
    "rho=0.75\n",
    "N=10**7\n",
    "\n",
    "exp_loss_listrho75=[]\n",
    "\n",
    "for i in range(0,21):\n",
    "\n",
    "\n",
    "#default 13,14,15,16,17,18\n",
    "    \n",
    "    def f13(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(13,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I13=1-quad(f,-6,6)[0]\n",
    "    \n",
    "    def f14(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(14,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I14=1-quad(f,-6,6)[0]\n",
    "    \n",
    "    def f15(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(15,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I15=1-quad(f,-6,6)[0]\n",
    "    \n",
    "    def f16(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(16,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I16=1-quad(f,-6,6)[0]\n",
    "    \n",
    "    def f17(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(17,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I17=1-quad(f,-6,6)[0]\n",
    "\n",
    "#binom cdf 1-binom.cdf(17...)\n",
    "    def f(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.cdf(17,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I_special=1-quad(f,-6,6)[0]\n",
    "\n",
    "    expected_loss = I13+2*I14+3*I15+4*I16+5*I17+6*I_special\n",
    "    exp_loss_listrho75.append(N*expected_loss)\n",
    "    \n",
    "plt.plot(t_list, exp_loss_listrho25, label = \"rho=0.25\")\n",
    "plt.plot(t_list, exp_loss_listrho50, label = \"rho - 0.5\")\n",
    "plt.plot(t_list, exp_loss_listrho75, label = \"rho - 0.75\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "    \n",
    "    \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 832,
   "id": "055ad868",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Par spread: 1016.8208973868819\n"
     ]
    }
   ],
   "source": [
    "#2c par spread\n",
    "\n",
    "t=5.0\n",
    "h=0.0075\n",
    "t_list = np.linspace(0,5,21)\n",
    "rho=0.5\n",
    "N=10**7\n",
    "\n",
    "exp_loss_listrho50=[]\n",
    "\n",
    "for i in range(0,21):\n",
    "\n",
    "\n",
    "#default 13,14,15,16,17,18\n",
    "    \n",
    "    def f13(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(13,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I13=1-quad(f,-6,6)[0]\n",
    "    \n",
    "    def f14(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(14,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I14=1-quad(f,-6,6)[0]\n",
    "    \n",
    "    def f15(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(15,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I15=1-quad(f,-6,6)[0]\n",
    "    \n",
    "    def f16(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(16,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I16=1-quad(f,-6,6)[0]\n",
    "    \n",
    "    def f17(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.pmf(17,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I17=1-quad(f,-6,6)[0]\n",
    "\n",
    "#binom cdf 1-binom.cdf(17...)\n",
    "    def f(x):\n",
    "        tr=norm.ppf(np.exp(-1*t_list[i]*h))\n",
    "        crit = (tr-x*np.sqrt(rho))/(np.sqrt(1-rho))\n",
    "        gamma=(1-norm.cdf(crit))\n",
    "        beta=binom.cdf(17,200,gamma)\n",
    "        func = beta*norm.pdf(x)\n",
    "        return(func)\n",
    "    I_special=1-quad(f,-6,6)[0]\n",
    "\n",
    "    expected_loss = I13+2*I14+3*I15+4*I16+5*I17+6*I_special\n",
    "    exp_loss_listrho50.append(expected_loss)\n",
    "\n",
    "KL = 0.06*200   \n",
    "KU = 0.09*200\n",
    "deltat = 0.25\n",
    "\n",
    "vfee=[]\n",
    "for j in range(0,len(t_list)):\n",
    "    v = 0.25*((KU-KL)-(exp_loss_listrho50[j]))\n",
    "    vfee.append(v)\n",
    "VFee= N*sum(vfee)\n",
    "\n",
    "\n",
    "diff_list=[]\n",
    "for i in range (1,len(exp_loss_listrho50)):\n",
    "    diff = exp_loss_listrho50[i]-exp_loss_listrho50[i-1]\n",
    "    diff_list.append(diff)\n",
    "VCon=N*sum(diff_list)\n",
    "    \n",
    "\n",
    "    \n",
    "print('Par spread:', 10000*VCon/VFee)    \n",
    "\n",
    "\n"
   ]
  }
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