{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5ff13587",
   "metadata": {},
   "source": [
    "## Section 3.5\n",
    "\n",
    "# Exercise 3.23"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "3d16730a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0.0744988074370093</li>\n",
       "\t<li>0.0839303017999433</li>\n",
       "\t<li>0.0939809434655701</li>\n",
       "\t<li>0.104636482894199</li>\n",
       "\t<li>0.115879676048752</li>\n",
       "\t<li>0.127690747804648</li>\n",
       "\t<li>0.14004785036307</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0.0744988074370093\n",
       "\\item 0.0839303017999433\n",
       "\\item 0.0939809434655701\n",
       "\\item 0.104636482894199\n",
       "\\item 0.115879676048752\n",
       "\\item 0.127690747804648\n",
       "\\item 0.14004785036307\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0.0744988074370093\n",
       "2. 0.0839303017999433\n",
       "3. 0.0939809434655701\n",
       "4. 0.104636482894199\n",
       "5. 0.115879676048752\n",
       "6. 0.127690747804648\n",
       "7. 0.14004785036307\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 0.07449881 0.08393030 0.09398094 0.10463648 0.11587968 0.12769075 0.14004785"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Inputs\n",
    "\n",
    "S0 <- 1\n",
    "sigma <- 0.25\n",
    "r <- 0.03\n",
    "T <- 1\n",
    "rg <- seq(-0.02,0.10,0.02)\n",
    "\n",
    "#Compute BS\n",
    "a <- (log(1+rg)-r*T+0.5*sigma^2*T)/(sigma*sqrt(T))\n",
    "V0 <- ((1+rg)*exp(-r*T)*pnorm(a)-pnorm(a-sigma*sqrt(T)))*S0\n",
    "\n",
    "#output\n",
    "V0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e70c68c",
   "metadata": {},
   "source": [
    "# Exercise 3.24"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "c5d07d86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0.103693512946142</li>\n",
       "\t<li>0.104956832473071</li>\n",
       "\t<li>0.104750903962892</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0.103693512946142\n",
       "\\item 0.104956832473071\n",
       "\\item 0.104750903962892\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0.103693512946142\n",
       "2. 0.104956832473071\n",
       "3. 0.104750903962892\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 0.1036935 0.1049568 0.1047509"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#inputs\n",
    "S0 <- 1\n",
    "sigma <- 0.25\n",
    "r <- 0.03\n",
    "T <- 1\n",
    "rg <- 0.04\n",
    "\n",
    "m1 <- 1e4\n",
    "m2 <- 1e5\n",
    "m3 <- 1e6\n",
    "\n",
    "#calculate returns\n",
    "eps_1 <- rnorm(m1) \n",
    "R_1 <- exp(r*T-0.5*sigma^2*T+sigma*sqrt(T)*eps_1)-1\n",
    "\n",
    "eps_2 <- rnorm(m2) \n",
    "R_2 <- exp(r*T-0.5*sigma^2*T+sigma*sqrt(T)*eps_2)-1\n",
    "\n",
    "eps_3 <- rnorm(m3) \n",
    "R_3 <- exp(r*T-0.5*sigma^2*T+sigma*sqrt(T)*eps_3)-1\n",
    "X1 <- pmax(rg-R_1[1:m1],0)\n",
    "X2 <- pmax(rg-R_2[1:m2],0)\n",
    "X3 <- pmax(rg-R_3[1:m3],0)\n",
    "\n",
    "#calculate BS\n",
    "v01 <- exp(-r*T)*mean(X1)*S0\n",
    "v02 <- exp(-r*T)*mean(X2)*S0\n",
    "v03 <- exp(-r*T)*mean(X3)*S0\n",
    "c(v01,v02,v03)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7f51493",
   "metadata": {},
   "source": [
    "# Excerise 3.25\n",
    "On the blackboard\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "80570db6",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "52a69b3f",
   "metadata": {},
   "source": [
    "# Exercise 3.27"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "904ffbe2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.10613003062603"
      ],
      "text/latex": [
       "0.10613003062603"
      ],
      "text/markdown": [
       "0.10613003062603"
      ],
      "text/plain": [
       "[1] 0.10613"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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/+ideD0aM4+2VafvzJvf87eOll3hUyb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\nx4KgNwAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “density.default(x = V_1)”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#inputs\n",
    "S0 <- 1\n",
    "sigma <- 0.25\n",
    "r <- 0.03\n",
    "T <- 1\n",
    "T_1<-0.5\n",
    "rg <- 0.04\n",
    "\n",
    "m <- 1e6\n",
    "\n",
    "#calculate returns\n",
    "eps <- rnorm(m) \n",
    "R_1<- exp(r*T_1-0.5*sigma^2*T_1+sigma*sqrt(T_1)*eps)-1\n",
    "S_1<-S0*(1+R_1)\n",
    "r_g1<-(1+rg)*S0/S_1-1\n",
    "\n",
    "#calculate BS\n",
    "a_1<- (log(1+r_g1)-r*(T-T_1)+0.5*sigma^2*(T-T_1))/(sigma*sqrt(T-T_1))\n",
    "V_1 <- ((1+r_g1)*exp(-r*(T-T_1))*pnorm(a_1)-pnorm(a_1-sigma*sqrt(T-T_1)))*S_1\n",
    "\n",
    "\n",
    "plot(density(V_1))\n",
    "\n",
    "mean(V_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "368f8725",
   "metadata": {},
   "source": [
    "# Exercise 3.28\n",
    "\n",
    "On the blackboard"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e737bec9",
   "metadata": {},
   "source": [
    "# Exercise 3.29"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "bc724e23",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0.0286196350331757</li>\n",
       "\t<li>0.0386079743292686</li>\n",
       "\t<li>0.0474763097846211</li>\n",
       "\t<li>0.0958837610084006</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0.0286196350331757\n",
       "\\item 0.0386079743292686\n",
       "\\item 0.0474763097846211\n",
       "\\item 0.0958837610084006\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0.0286196350331757\n",
       "2. 0.0386079743292686\n",
       "3. 0.0474763097846211\n",
       "4. 0.0958837610084006\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 0.02861964 0.03860797 0.04747631 0.09588376"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#inputs\n",
    "S0 <- 1\n",
    "sigma <- 0.25\n",
    "r <- 0.03\n",
    "T <- 1\n",
    "rg <- 0.04\n",
    "rc <- c(0.09,0.12,0.15,0.5)\n",
    "\n",
    "#calc BS\n",
    "ag <- (log(1+rg)-r*T+0.5*sigma^2*T)/(sigma*sqrt(T))\n",
    "ac <- (log(1+rc)-r*T+0.5*sigma^2*T)/(sigma*sqrt(T))\n",
    "v_0 <- ((1+rg)*exp(-r*T)*pnorm(ag)-pnorm(ag-sigma*sqrt(T)))*S0-\n",
    "    ((1+rc)*exp(-r*T)*pnorm(ac)-pnorm(ac-sigma*sqrt(T)))*S0-(1-exp(-r*T)*(1+rc))*S0\n",
    "v_0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b8f6d14",
   "metadata": {},
   "source": [
    "## Exercise - Greeks\n",
    "\n",
    "Greeks are derivatives of the value of an option with respect to the parameters of the B-S-model. Assume a put option with strike K=1.04, r=0.03, T=1 and sigma=0.25. Approximate the derivative of $V_0$ with respect to $S_0$, r, $\\sigma$ and T."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "8aaca7b7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"V0 is 0.104636482894199\"\n",
      "[1] \"New V0 is 0.100066677682884\"\n",
      "[1] \"Delta is -0.456980521131506\"\n"
     ]
    }
   ],
   "source": [
    "#inputs\n",
    "S0 <- 1\n",
    "sigma <- 0.25\n",
    "r <- 0.03\n",
    "T <- 1\n",
    "K <- 1.04\n",
    "\n",
    "S0_h <- 1.01\n",
    "sigma_h <- 0.26\n",
    "r_h <- 0.04\n",
    "T_h <- 1.01\n",
    "\n",
    "#Compute BS\n",
    "a <- (log(K/S0)-r*T+0.5*sigma^2*T)/(sigma*sqrt(T))\n",
    "V0 <- K*exp(-r*T)*pnorm(a)-S0*pnorm(a-sigma*sqrt(T))\n",
    "print(paste(\"V0 is\",V0))\n",
    "\n",
    "#Compute BS for S0_h\n",
    "a_h <- (log(K/S0_h)-r*T+0.5*sigma^2*T)/(sigma*sqrt(T))\n",
    "V0_h <- K*exp(-r*T)*pnorm(a_h)-S0_h*pnorm(a_h-sigma*sqrt(T))\n",
    "print(paste(\"New V0 is\",V0_h))\n",
    "print(paste(\"Delta is\",(V0_h-V0)/0.01))\n",
    "\n",
    "\n",
    "      "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "0fd5adbf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"V0 is 0.104636482894199\"\n",
      "[1] \"New V0 is 0.0990486933611043\"\n",
      "[1] \"Rho is -0.55877895330948\"\n"
     ]
    }
   ],
   "source": [
    "print(paste(\"V0 is\",V0))\n",
    "\n",
    "#Compute BS for r_h\n",
    "a_h <- (log(K/S0)-r_h*T+0.5*sigma^2*T)/(sigma*sqrt(T))\n",
    "V0_h <- K*exp(-r_h*T)*pnorm(a_h)-S0*pnorm(a_h-sigma*sqrt(T))\n",
    "print(paste(\"New V0 is\",V0_h))\n",
    "print(paste(\"Rho is\",(V0_h-V0)/0.01))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "a84849ec",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"V0 is 0.104636482894199\"\n",
      "[1] \"New V0 is 0.107186461712859\"\n",
      "[1] \"Vega is 0.254997881866009\"\n"
     ]
    }
   ],
   "source": [
    "print(paste(\"V0 is\",V0))\n",
    "\n",
    "#Compute BS for sigma\n",
    "a_h <- (log(K/S0)-r*T+0.5*sigma_h^2*T)/(sigma_h*sqrt(T))\n",
    "V0_h <- K*exp(-r*T)*pnorm(a)-S0*pnorm(a_h-sigma_h*sqrt(T))\n",
    "print(paste(\"New V0 is\",V0_h))\n",
    "print(paste(\"Vega is\",(V0_h-V0)/0.01))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "6ac84703",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"V0 is 0.104636482894199\"\n",
      "[1] \"New V0 is 0.105260583971674\"\n",
      "[1] \"Theta is 0.0624101077475181\"\n"
     ]
    }
   ],
   "source": [
    "print(paste(\"V0 is\",V0))\n",
    "\n",
    "#Compute BS for T\n",
    "a_h <- (log(K/S0)-r*T_h+0.5*sigma^2*T_h)/(sigma*sqrt(T_h))\n",
    "V0_h <- K*exp(-r*T_h)*pnorm(a)-S0*pnorm(a_h-sigma*sqrt(T_h))\n",
    "print(paste(\"New V0 is\",V0_h))\n",
    "print(paste(\"Theta is\",(V0_h-V0)/0.01))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "73d6ea84",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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