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Validus-Risk-Management-Jun…/Validus Risk Management.ipynb
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2026-01-05 15:02:00 +00:00

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{
"cells": [
{
"cell_type": "markdown",
"id": "9162ed1c",
"metadata": {},
"source": [
"# Validus Risk Management Case Study"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "004f0ed6",
"metadata": {},
"outputs": [],
"source": [
"import math as m\n",
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt \n",
"import seaborn as sns\n",
"import numpy_financial as npf"
]
},
{
"cell_type": "markdown",
"id": "a9b3921a",
"metadata": {},
"source": [
"# Monte Carlo Simulation for GBPHUF FX Spot Rate\n",
"\n",
"The formula for Geometric Brownian Motion takes the following form:\n",
"\n",
"$$\n",
"dS_t = \\mu S_t \\, dt + \\sigma S_t \\, dW_t\n",
"$$\n",
"\n",
"where:\n",
"\n",
"- $ S_t $ is the asset price at time t \n",
"- $ \\mu $ is the drift \n",
"- $ \\sigma $ is the volatility \n",
"- $ W_t $ is a Wiener process\n",
"\n",
"\n",
"We can apply Ito's Lemma to $ f(t,S) = ln(S) $ to get the dynamic of $ ln(S_t) $. This yields:\n",
"\n",
"$$\n",
"S_t\n",
"=\n",
"S_0\n",
"\\exp\\!\\left(\n",
"\\left(\\mu - \\tfrac{1}{2}\\sigma^2\\right)(t - 0)\n",
"+ \\sigma (W_t - W_0)\n",
"\\right)\n",
"$$\n",
"\n",
"For our simulation we must discretize time with a time step $ \\delta t $. We also use properties of a Wiener process to get:\n",
"\n",
"$$\n",
"S_{t+\\delta t}\n",
"=\n",
"S_t \\exp\\!\\left[\n",
"\\left(\\mu - \\tfrac{1}{2}\\sigma^2\\right)\\delta t\n",
"+ \\sigma \\epsilon \\sqrt{\\delta t}\\, \n",
"\\right],\n",
"\\quad \\epsilon \\sim \\mathcal{N}(0,1)\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "adf3b3f2",
"metadata": {},
"outputs": [],
"source": [
"GBPHUF = 455.25 #start amount\n",
"sigma = 0.093 #this is the annual volatility \n",
"mu = 0 #drift\n",
"nr = 1000 #number of simulations\n",
"T = 5 #time to maturity \n",
"n = 5*252 #number of time steps\n",
"\n",
"nu = mu - 0.5 * sigma**2\n",
"dt = 1/252\n",
"\n",
"GBPHUF_val = np.zeros((nr,n+1))\n",
"epsilon = np.random.randn(nr,n)\n",
"\n",
"GBPHUF_val[:,0] = GBPHUF\n",
"for i in range(nr): \n",
" for j in range(1,n+1): \n",
" GBPHUF_val[i,j] = GBPHUF_val[i,j-1] * m.exp(nu*dt + sigma * dt**0.5 * epsilon[i,j-1])"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "1d6367c9",
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure()\n",
"for i in range(nr):\n",
" plt.plot(GBPHUF_val[i,:])\n",
"plt.title('Monte Carlo Method simulations - GBM Paths');"
]
},
{
"cell_type": "markdown",
"id": "1b78657a",
"metadata": {},
"source": [
"## Question (a)\n",
"\n",
"The GBPHUF FX Spot rate tells us the amount of HUF for 1 GBP. E.g. At t = 0, 455.25 HUF can be exchanged for 1 GBP. We can therefore convert HUF cashflows to GBP cashflows using the following:\n",
"\n",
"$$\n",
"GBP_{CF} = \\frac{HUF_{CF}}{S}\n",
"$$\n",
"\n",
"$GBP_{CF}$ is our required cashflow in GBP, $HUF_{CF}$ is our cashflow in HUF and $S$ is our GBPHUF FX spot rate.\n",
"\n",
"In order to do this calculation we will find the GBPHUF FX spot rate at the required time in our simulation and divide the HUF cashflows at that date by the rate. \n",
"\n",
"Then we calculate the IRR, which is a measure of an investments profatibility, in GBP terms using the formula below.\n",
"\n",
"$$0 = \\text{NPV} = \\sum_{t=1}^{T} \\frac{C_t}{(1 + \\text{IRR})^t} - C_0$$\n",
"\n",
"where:\n",
"\n",
"- $ C_{\\text{t}} $ is the net cash inflow during the period t \n",
"- $ C_{\\text{0}} $ is the total initial investment costs\n",
"- $ t $ is the number of time periods"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "6aef8790",
"metadata": {},
"outputs": [],
"source": [
"data = pd.read_excel(r\"C:\\Users\\roryx\\Downloads\\Junior_Quant_Case_Study_Aug_2025_-_Cashflow_Model.xlsx\")"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "4acdc665",
"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",
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"\n",
" .dataframe thead th {\n",
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>Fund</th>\n",
" <th>Cashflow Type</th>\n",
" <th>Cashflow Amount (in Local Asset Currecny)</th>\n",
" <th>Local Asset Currency</th>\n",
" <th>Fund Currency</th>\n",
" <th>Base Case IRR</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>2025-08-01</td>\n",
" <td>Validus V</td>\n",
" <td>Equity</td>\n",
" <td>-100000000</td>\n",
" <td>HUF</td>\n",
" <td>GBP</td>\n",
" <td>0.149914</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>2026-08-01</td>\n",
" <td>Validus V</td>\n",
" <td>Proceeds</td>\n",
" <td>15000000</td>\n",
" <td>HUF</td>\n",
" <td>GBP</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>2027-08-01</td>\n",
" <td>Validus V</td>\n",
" <td>Proceeds</td>\n",
" <td>15000000</td>\n",
" <td>HUF</td>\n",
" <td>GBP</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>2028-08-01</td>\n",
" <td>Validus V</td>\n",
" <td>Proceeds</td>\n",
" <td>15000000</td>\n",
" <td>HUF</td>\n",
" <td>GBP</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>2029-08-01</td>\n",
" <td>Validus V</td>\n",
" <td>Proceeds</td>\n",
" <td>15000000</td>\n",
" <td>HUF</td>\n",
" <td>GBP</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>2030-08-01</td>\n",
" <td>Validus V</td>\n",
" <td>Proceeds</td>\n",
" <td>115000000</td>\n",
" <td>HUF</td>\n",
" <td>GBP</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date Fund Cashflow Type \\\n",
"0 2025-08-01 Validus V Equity \n",
"1 2026-08-01 Validus V Proceeds \n",
"2 2027-08-01 Validus V Proceeds \n",
"3 2028-08-01 Validus V Proceeds \n",
"4 2029-08-01 Validus V Proceeds \n",
"5 2030-08-01 Validus V Proceeds \n",
"\n",
" Cashflow Amount (in Local Asset Currecny) Local Asset Currency \\\n",
"0 -100000000 HUF \n",
"1 15000000 HUF \n",
"2 15000000 HUF \n",
"3 15000000 HUF \n",
"4 15000000 HUF \n",
"5 115000000 HUF \n",
"\n",
" Fund Currency Base Case IRR \n",
"0 GBP 0.149914 \n",
"1 GBP NaN \n",
"2 GBP NaN \n",
"3 GBP NaN \n",
"4 GBP NaN \n",
"5 GBP NaN "
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "fd8da1f8",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Year 0 is after 0 Working Days\n",
"Year 1 is after 252 Working Days\n",
"Year 2 is after 504 Working Days\n",
"Year 3 is after 756 Working Days\n",
"Year 4 is after 1008 Working Days\n",
"Year 5 is after 1260 Working Days\n"
]
}
],
"source": [
"Years = []\n",
"for i in range(0,6):\n",
" Years.append(i*252)\n",
" print(f'Year {i} is after {i*252} Working Days')"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "a827c35e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[0, 252, 504, 756, 1008, 1260]"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Years"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "8955700b",
"metadata": {},
"outputs": [],
"source": [
"GBPHUF_val_aug = GBPHUF_val[:, Years] #These are the simulated spot rate values as at the date of the cashflow"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "06c632d4",
"metadata": {},
"outputs": [],
"source": [
"#Converting HUF Cashflows to GBP\n",
"GBP_CF = np.zeros_like(GBPHUF_val_aug)\n",
"for i in range(6):\n",
" GBP_CF[:, i] = data.iloc[i,3]/GBPHUF_val_aug[:,i]"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "7940bb90",
"metadata": {},
"outputs": [],
"source": [
"#IRR Calculation\n",
"irr = np.zeros(len(GBP_CF))\n",
"for i in range(len(GBP_CF)):\n",
" irr[i] = npf.irr(GBP_CF[i,:])"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "632f8b1f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"5th Percentile: 0.0801791930909101\n",
"50th Percentile: 0.15337294857214168\n",
"95th Percentile: 0.2351120011761991\n"
]
}
],
"source": [
"#Finding the percentiles\n",
"p5, p50, p95 = np.percentile(irr, [5, 50, 95])\n",
"\n",
"print(f\"5th Percentile: {p5}\")\n",
"print(f\"50th Percentile: {p50}\")\n",
"print(f\"95th Percentile: {p95}\")"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "ed00cf04",
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#Plotting the distribution\n",
"plt.hist(irr, bins=40, color='teal', edgecolor='black')\n",
"plt.axvline(p5, color='blue', linestyle='--', label='5th Pctl')\n",
"plt.axvline(p50, color='black', linestyle='-', label='50th Pctl')\n",
"plt.axvline(p95, color='red', linestyle='--', label='95th Pctl ')\n",
"plt.xlabel('Internal Rate of Return')\n",
"plt.ylabel('Frequency')\n",
"plt.title('Distribution Of IRR Values - Unhedged Portfolio')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "0a8f0245",
"metadata": {},
"source": [
"## Question (b)\n",
"\n",
"The payoff for a European Put Option is as such \n",
"$$\n",
"\\text{Payoff} = \\max(K - S_T,\\, 0)\n",
"$$\n",
"\n",
"This means the specified option will be in the money when the GBPHUF spot rate is less than the strike price of 455.25. Therefore we are protecting againt the HUF strenghtening vs the GBP.\n",
"\n",
"For our GBPHUF option we will use the following formula:\n",
"$$\n",
"\\text{Payoff}_{\\text{HUF}} = N_{\\text{GBP}} \\max(K - S_T,\\, 0)\n",
"$$\n",
"\n",
"where:\n",
"\n",
"- $ N_{\\text{GBP}} $ is the nominal amount in GBP \n",
"- $ K $ is the strike\n",
"- $ S_T $ is the GBPHUF Spot rate at 01/08/2029\n",
"\n",
"We then convert the payoff into GBP by dividing the payoffs calculated above by the spot rate at that time. \n",
"\n",
"Then to get the price of the option we use the Fundamental Theorm of Asset pricing. $f(S_T)$ is the option payoff in GBP.\n",
"\n",
"$$\n",
"f_0 = e^{-rT}\\mathbb{E}^{\\mathbb{Q}}[f(S_T)] \\approx e^{-rT}\\frac{1}{N}\\sum_{i=1}^N f(S_T^{(i)})\n",
"$$\n",
"\n",
"As the risk-free rates are 0%, Our discount factor ($e^{-rT}$) is 1. Therefore:\n",
"\n",
"$$\n",
"Option Price = \\mathbb{E}[Payoff_T]\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "742951e8",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The price of our Put Option in GBP is: 19065.094946892827\n"
]
}
],
"source": [
"S_T = GBPHUF_val_aug[:,4]\n",
"K = 455.25\n",
"N_HUF = 100000000\n",
"N_GBP = N_HUF/K\n",
"\n",
"FinPayOff_HUF = N_GBP * np.maximum(K-S_T, 0) #N_GBP*np.maximum((K-S_T), 0)\n",
"FinPayOff_GBP = FinPayOff_HUF/S_T\n",
"\n",
"price_gbp = FinPayOff_GBP.mean()\n",
"\n",
"print(f\"The price of our Put Option in GBP is: {price_gbp}\")"
]
},
{
"cell_type": "markdown",
"id": "096f1eb3",
"metadata": {},
"source": [
"## Question (c)\n",
"\n",
"The hedged portfolio cashflows consist of:\n",
"\n",
"-The original fund cashflows <br>\n",
"-The option premium paid at t = 0 <br>\n",
"-The option payoff received at expiry (t = 4) <br>\n",
"\n",
"The IRR will then be calculated similarly to above and the two portfolios will be compared"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "0515f794",
"metadata": {},
"outputs": [],
"source": [
"#New Cashflows of the Hedged Portfolio\n",
"H_GBP_CF = GBP_CF.copy()\n",
"H_GBP_CF[:,0] = GBP_CF[:,0] - price_gbp\n",
"H_GBP_CF[:,4] = GBP_CF[:,4] + FinPayOff_GBP "
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "d6ce7fc0",
"metadata": {},
"outputs": [],
"source": [
"#IRR Calculation\n",
"irr_hp = np.zeros(len(H_GBP_CF))\n",
"for i in range(len(H_GBP_CF)):\n",
" irr_hp[i] = npf.irr(H_GBP_CF[i,:])"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "1c534a68",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"5th Percentile of Hedged Portfolio: 0.06. 5th Percentile of Unhedged Portfolio: 0.08.\n",
"50th Percentile of Hedged Portfolio: 0.13. 50th Percentile of Unhedged Portfolio: 0.15.\n",
"95th Percentile of Hedged Portfolio: 0.25. 95th Percentile of Unhedged Portfolio: 0.24.\n"
]
}
],
"source": [
"hp5, hp50, hp95 = np.percentile(irr_hp, [5, 50, 95])\n",
"\n",
"print(f\"5th Percentile of Hedged Portfolio: {hp5:.2f}. 5th Percentile of Unhedged Portfolio: {p5:.2f}.\")\n",
"print(f\"50th Percentile of Hedged Portfolio: {hp50:.2f}. 50th Percentile of Unhedged Portfolio: {p50:.2f}.\")\n",
"print(f\"95th Percentile of Hedged Portfolio: {hp95:.2f}. 95th Percentile of Unhedged Portfolio: {p95:.2f}.\")"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "8a91b56e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The standard deviation of the Hedged Portfolio is: 0.05901\n",
"The standard deviation of the Unhedged Portfolio is: 0.04617\n"
]
}
],
"source": [
"std_dev_hp = np.std(irr_hp)\n",
"std_dev_p = np.std(irr)\n",
"print(f\"The standard deviation of the Hedged Portfolio is: {std_dev_hp:.5f}\")\n",
"print(f\"The standard deviation of the Unhedged Portfolio is: {std_dev_p:.5f}\")"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "fc6d45ee",
"metadata": {},
"outputs": [
{
"data": {
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arG48mFZ5795cf9VVaZ/TrVs31q9f3zR91113sXDhQn7/+99nvJ3GH8n26NH2O/UmxpM4f8WKFRx88MEcdNBBNDQ0UFlZyR133EFZWRlz585l5MiR7L///nzxxReceuqp3HRTPm8T0jpKDJIzLZ00MjkJSGmrrq2lYtSonJW3YtasnJVVSg444ACqqqrYsmULJ554IjNnzuR73/seAMceeyxPPPEEX3zxBYcffjhnnHEGxxxzTJEjjqfEIDnT0kljez0JSPGsWbOGiy66iOrqagCmTJnCMcccw9q1aznnnHNYs2YNgwcPJnYU6V/96lfcd999fOlLX6JHjx4cccQRXH755SxfvpxLLrmENWvW0KVLF2677TYGDBjAu+++y7nnnsvmzZsZMWJEVvF17NiRwYMH88EHzW+x3LlzZwYOHJh0WbHl7RpDuIdsVczfp2Y2zsz2NLOnzGxZ+L9HvmIQkfbviy++YODAgU1/EyZsu9X4pZdeymWXXcbLL7/MQw89xI9//GMArrvuOoYMGcKiRYs4/fTTmxLHwoULeeihh1i0aBEPP/xw3BhsY8eO5b//+7955ZVXuOmmm/jJT37StI2LL76Yl19+mb333jur2Ovr63nppZeSJpR169axbNkyhg4dmvU+ybe81Rjc/U2i+9RiZh2J7pX8CNG9Yue4+2QzGx+mr8xXHCLSvnXu3Jmqqqqm6cZrDABPP/00S5YsaVr26aef8tlnn/Hss8/y8MPR7aBPOeUU9tgj+v45b948Ro4cSefOnQE47bTTAFi/fj3PP/88Z599dlNZGzduBGD+/Pk89NBDAPzgBz/gyitbPl0tX76cgQMHsmzZMs466ywOPXTbrdGfe+45Dj30UN58803Gjx+fdbIphEI1JQ0Hlrv7e2Y2EhgW5k8D5qLEICKtsHXrVl544YWmE32sZF04U92YbOvWrXTv3j0uAbVUVjqN1xhqamoYNmwYjz32GKeffjqw7RrDW2+9xZAhQzjjjDMYOHBgVuXnW6G6q34XeCA87u3uNQDhf69kK5jZWDNbaGYL16xZU6AwRaQ9Oemkk+J6JzWe2IcOHcp9990HwF/+8hfWrVsHwJAhQ3j88cepr69n/fr1/O///i8Au+22G/369ePPf/4zECWQ1157DYBjjjmG6dOnAzSVmak+ffowefJkbrjhhmbLDjzwQK666ir+8z//M6syCyHvNQYz2xk4HciqO4q7TwWmAlRWVur+oyIloLx375x2Iijv3btN6//ud7/jkksu4dBDD2Xz5s0MHTqUW2+9lWuvvZZzzjmHQYMGcdxxx1FeXg7AkUceyemnn85hhx3GfvvtR2VlJbvvvjsQnfQvvvhiJk2axKZNm/jud7/LYYcdxi233MK5557LLbfcwre+9a2sYxw1ahQTJ07kueeea7bsoosu4qabbuLdd9/N2XAWuZD3ez6HpqNL3P2kMP0mMMzda8ysDzDX3Q9KV0ZlZaXrRj2lb8y4cS32SrprypSCxSNt98Ybb3DwwQcXO4ycWr9+Pd26dePzzz9n6NChTJ06lUGDBhU7rDZL9l6Z2SvuXpltWYW4xnAO25qRAB4DRgOTw/9HCxCDlIBFVVWMGTcu5XL9zkEKYezYsSxZsoT6+npGjx69XSSFXMtrYjCzLsCJwIUxsycDM83sfKAaODvZurL92dDQoN85SNHdf//9xQ6h5OU1Mbj758BeCfPWEvVSEhGREqRB9EREJI4Sg4iIxFFiEBGROBpET+JohFRJZ8KEKVRX1+WsvPLy7lx//biUy1esWMGpp57KP/7xj6Z5EydOpFu3blx++eUp12vN0Nyx5s6dy0033cQTTzzRqvUziSV2/sSJE7ntttvo2bMnDQ0N/PKXv+Scc84BYMyYMfz9739n9913x925+eabGT48v5dplRgkjkZIlXSqq+uoqJiYs/JWrMhdWe3dZZddxuWXX86yZcs44ogjOOussygrKwPgxhtv5KyzzuKZZ55h7NixLFu2LK+xqClJRNqtYcOGceWVVzJ48GAOPPDAuF8Xf/jhh4wYMYL+/ftzxRVXNM3/61//ytFHH82gQYM4++yzm266M3v2bAYMGMCQIUOaBuCDaGjvE088kUGDBnHhhRey33778dFHHwFw7733MnjwYAYOHMiFF17Ili1bALjzzjs58MADOe6445g/f35Wr6l///506dKlaRiPWEcffXRBhulWYhCRdm3z5s0sWLCAKVOmcN111zXNr6qqYsaMGbz++uvMmDGD999/n48++ohJkybx9NNP8+qrr1JZWcnNN99MfX09F1xwAY8//jjPPfccq1atairnuuuu44QTTuDVV1/ljDPOaBrC+4033mDGjBnMnz+fqqoqOnbsyH333UdNTQ3XXnst8+fP56mnnoob/TUTr776Kv3796dXr+bDyM2ePZtRObxRUipqShKRkpVqVNPY+WeeeSYARxxxBCtWrGiaP3z48KZxkA455BDee+896urqWLJkSdMd0xoaGjj66KNZunQp/fr1o3///gB8//vfZ+rUqUA0VPcjjzwCwIgRI5qG8J4zZw6vvPIKRx55JBDdN6JXr1689NJLDBs2jJ49ewLwne98h7feeqvF1/rb3/6W2267jXfeeYfZs2fHLfvFL37BFVdcwerVq3nxxRdbLKutVGMQkZK11157NWtS+fjjj+Pu3bzLLrsA0d3SNm/e3Gx+7DJ358QTT6SqqoqqqiqWLFnCHXfcAaROQqnGk3N3Ro8e3VTWm2++ycSJE9OWlc5ll13Gm2++yYwZM/jhD39IfX1907Ibb7yRt99+m0mTJjF69Oisy86WEoNsFyZMmMKYMROb/U2YMKXYoUkbdOvWjT59+jBnzhwgSgqzZ89myJAhrSrvqKOOYv78+bz99tsAfP7557z11ltNt/Bcvnw5AA88sG14tyFDhjBz5kwguj7RmKiGDx/Ogw8+yOrVq5tie++99/jqV7/K3LlzWbt2LZs2bWoayjtTZ555JpWVlUybNi1ufocOHbj00kvZunUrTz75ZKtef6bUlCTbhVS9ZdTrJbfKy7vndJ+Wl3dv8Tl33303l1xyCT//+c8BuPbaaznggANatb2ePXty1113cc455zTdoW3SpEkceOCBTJ06lVNOOYUePXowZMiQpi6yjUN4z5gxg+OOO44+ffqw66670qNHDyZNmsRJJ53E1q1bKSsr4w9/+ANHHXUUEydO5Oijj6ZPnz4MGjSo6aJ0piZMmMC5557LBRdcEDffzLjmmmv4zW9+wze+8Y1W7YNM5H3Y7VzQsNuF05ahs1ta996rr+b7v/51q8puyZgxE1Mmhrvuaj5fMrM9DrudrY0bN9KxY0d22mknXnjhBS6++OKUd3orpvY27LaISLtVXV3Nt7/9bbZu3crOO+/MbbfdVuyQ8k6JQUQkjf79+7No0aJih1FQuvgsImm1h+bmHV2u3yMlBhFJqVOnTqxdu1bJoYS5O2vXrqVTp045K1NNSSKSUt++fVm5ciVr1qwpdiiSRqdOnejbt2/OylNiEJGUysrK6NevX7HDkAJTU5KIiMRRYhARkTh5bUoys+7A7cBXAAfOA94EZgAVwArg2+7efHxZKUmLqqoYM25c8mWLF6f9gZuItA/5vsZwCzDb3c8ys52BLsDVwBx3n2xm44HxwJV5jkNyZENDQ8qT/7wFCwobjIjkRd6aksxsN2AocAeAuze4ex0wEmgcHWoaMCpfMYiISPbyWWPYH1gD3GlmhwGvAJcCvd29BsDda8ys+d0oADMbC4wFKC8vz2OYsj1btOg1xoyZ2Gx+S/caFtmR5TMx7AQMAn7q7i+Z2S1EzUYZcfepwFSIBtHLT4iyvduwwTXqqkiW8tkraSWw0t1fCtMPEiWKWjPrAxD+r85jDCIikqW81RjcfZWZvW9mB7n7m8BwYEn4Gw1MDv8fzVcM0n5NmDCF6uq6ZvPVBCSSf/nulfRT4L7QI+kd4EdEtZSZZnY+UA2cnecYpB3SjXdEiievicHdq4BkN4kYns/tiohI6+mXzyIiEkeJQURE4igxiIhIHA27Le1Kqh+sLVq0hIqKgoej3lOyXVJikHYl1Q/W5s0bVfBYQL2nZPukpiQREYmjGoO0C8889xyfbNhA7Zo1zJo9u9nytR9/XISoRLZPSgzSLnyyYQPdBwyg7P1udB8woNny5W9sKUJUItsnNSWJiEgcJQYREYmjxCAiInF0jWEHNOGGG6iurU26LF/3bX7mT7OoXbaJWZOnx83fvVcnjj8v99sTkdZTYtgBVdfWFvy+zZ+srqes00V03zt+/MS6VZPzsj0RaT01JYmISBwlBhERiaPEICIicZQYREQkji4+i+RBqlFgNeqqtAdKDCJ5kGoUWI26Ku2BmpJERCROXmsMZrYC+AzYAmx290oz2xOYAVQAK4Bvu/u6fMYhIiKZK0SN4Xh3H+julWF6PDDH3fsDc8K0iIiUiGI0JY0EpoXH04BRRYhBRERSyPfFZwf+amYO/NHdpwK93b0GwN1rzKxXshXNbCwwFqC8vDzPYUopWFRVxZhx4wCYt+AtqpZuuyFPTW1t0vswNNrY0JD0Bj6NN/bZvWtXjj/22KTrphs7CqC8d2+uv+qqDF+FSPuX78RwjLt/GE7+T5nZ0kxXDElkKkBlZaXnK0ApHRsaGprGcKpaOp3ue29LBNUffJB23a1btyZNHI039qlbmvrQSzd2FMCKWbPSbltke5PXpiR3/zD8Xw08AgwGas2sD0D4vzqfMYiISHbyVmMws65AB3f/LDw+CbgeeAwYDUwO/x/NVwwiqcT+AC1qtoqGA081DPiECVOorq5LUs4SKiryF6dIMeSzKak38IiZNW7nfnefbWYvAzPN7HygGjg7jzGIJBX7A7SqpbObmq1SDQNeXV2X9Adr8+aNylOEIsWTt8Tg7u8AhyWZvxYY3nwNEREpBRoSQ4pq1bLlTXd1i73DW82yarrvXczIRHZcSgxSVA31Hei+d/Qbx7JOc5ru8Fb9+oXFDEtkh6axkkREJI4Sg4iIxFFiEBGROEoMIiISJ6PEYGZfyXcgIiJSGjKtMdxqZgvM7Cdm1j2fAYmISHFl1F3V3YeYWX/gPGChmS0A7nT3p/Ianch2RveClvYg498xuPsyM7sGWAj8DjjcovEurnb3h/MVoMj2RPeClvYg02sMh5rZb4E3gBOA09z94PD4t3mMT0RECizTGsPvgduIagdfNM4M91q4Ji+RiYhIUWSaGE4GvnD3LQBm1gHo5O6fu/s9eYtOREQKLtNeSU8DnWOmu4R5IiKynck0MXRy9/WNE+Fxl/yEJCIixZRpYthgZoMaJ8zsCOCLNM8XEZF2KtNrDOOAP5vZh2G6D/CdvEQkIiJFlekP3F42swHAQYABS919U14jEymC2BsHNVpfXU3Xsm66t7PsMLK5Uc+RQEVY53Azw93vzktUIkUSe+OgJnVLWf/RrcUJSKQIMkoMZnYPcABQBWwJsx1QYhAR2c5kWmOoBA5xd892A2bWkWgYjQ/c/VQz2xOYQVT7WAF8293XZVuuiIjkR6a9kv4BtPbW7JcSDaXRaDwwx937A3PCtIiIlIhME0MPYImZPWlmjzX+tbSSmfUFTgFuj5k9EpgWHk8DRmURr4iI5FmmTUkTW1n+FOAKYNeYeb3dvQbA3WvMrFeyFc1sLDAWoLy8vJWbl0J75k+z+GR1fbP5NcuqifoviEipy7S76t/NbD+gv7s/bWZdgI7p1jGzU4HV7v6KmQ3LNjB3nwpMBaisrMz62oYUxyer65v36gGqX79QN5IVaScy7ZV0AdG39z2JeiftC9wKDE+z2jHA6WZ2MtAJ2M3M7gVqzaxPqC30AVa35QWIiEhuZdqUdAkwGHgJmm7ak7QJqJG7XwVcBRBqDJe7+/fN7EZgNDA5/H+0VZFL0aRqLqpdtonPdqume2u7KeRRzapVzJo9u2m6ds2apuma2lq6DxjQqnLXfvxxXLmJ5e/etSvHH3ts64IWKZJME8NGd2+IbtgGZrYT0e8YWmMyMNPMzgeqgbNbWY4USarmorJOc9hUP7MIEbVs05YtcSf/sve7NU1Xf/BBq8vdnFBuYvl1S5e2umyRYsk0MfzdzK4GOpvZicBPgMcz3Yi7zwXmhsdrSd8EJSIiRZRpYhgPnA+8DlwI/D/iu6CKSBLpmrAANTVJScq0V9JWolt73pbfcES2L+masAA1NUlJyrRX0rskuabg7vvnPCIRESmqbMZKatSJ6ILxnrkPR0REii2jnxy5+9qYvw/cfQpwQn5DExGRYsi0KWlQzGQHohrErimeLiIi7VimTUn/FfN4M2G47JxHIyIiRZdpr6Tj8x2IiIiUhkybkv4t3XJ3vzk34YiISLFl0yvpSKDxHgynAc8C7+cjKBERKZ5ME0MPYJC7fwZgZhOBP7v7j/MVmIiIFEemiaEcaIiZbiC6Z7OUoAk33EB1bW3K5YsWL6Zi1KjCBSQpNQ6Zsf7TBYwZNy5uWXnv3lx/1VXFCUx2aJkmhnuABWb2CNEvoM8A7s5bVNIm1bW1aU/88xYsKFwwklbTkBmrypu9ZytmzSpKTCKZ9kr6DzP7C9A42teP3H1R/sISEZFiybTGANAF+NTd7zSznmbWz93fzVdgIgITJkyhurqu2fzy8u5cf/24gscjO4ZMu6teS9Qz6SDgTqAMuJfo9p0ikifV1XVUVExsNn/FiubzRHIl09uznwGcDmwAcPcP0ZAYIiLbpUybkhrc3c3MAcysax5jEikpNatW8fm6NUnv7byxoSHJGtlbtWw5syZPj5u3vrqarmXdqKjIySZEMpZpYphpZn8EupvZBcB56KY9soPYtGULZd26Jb2389ZFW3OyjYb6Ds3vo123lPUf3ZqT8kWy0WJiMDMDZgADgE+JrjNMcPenWlivE9Gvo3cJ23nQ3a81sz1DeRWEwfjcfV0bXoOIiORQi4khNCHNcvcjgLTJIMFG4AR3X29mZcC80OX1TGCOu082s/FE95O+sjXBi4hI7mV68flFMzsym4I9sj5MloU/B0YC08L8acCobMoVEZH8yjQxHE+UHJab2WIze93MFre0kpl1NLMqYDXwlLu/BPR29xqA8L9XK2MXEZE8SNuUZGbl7l4NfLM1hbv7FmCgmXUHHjGzr2S6rpmNBcYClJeXt2bzIiLSCi3VGGYBuPt7wM3u/l7sX6Ybcfc6YC4wAqg1sz4A4f/qFOtMdfdKd6/s2bNnppsSEZE2aikxWMzj/bMpOAyb0T087gx8HVhKdE+H0eFpo4FHsylXRETyq6VeSZ7icSb6ANPMrCNRAprp7k+Y2QtEv4s4H6gGzs6yXBERyaOWEsNhZvYpUc2hc3hMmHZ33y3Viu6+GDg8yfy1wPBWxisiInmWNjG4e8dCBSIi8dINxbH+0wVMuOEG3chH8iKbYbdFpIDSDcXBqvK0d+kTaYtMf8cgIiI7CCUGERGJo8QgIiJxlBhERCSOEoOIiMRRYhARkThKDCIiEke/YyhRE264IWU/9fLevfXDJhHJGyWGElVdW0vFqFFJl62YNaugsYjIjkVNSSIiEkeJQURE4igxiIhIHCUGERGJo4vP7dCiqirGjBuXevnixSkvXMv2YdWy5Txa9Rlf/uvJcfO77uocfvRBvLNsGfv3759yffVsk3SUGNqhDQ0NaU/88xYsKFwwUhQN9R2wsgvoOzj+nld1qyZTMWoU866+mhPSHCPq2SbpqClJRETiKDGIiEgcJQYREYmTt8RgZl8ys2fM7A0z+6eZXRrm72lmT5nZsvB/j3zFICIi2ctnjWEz8HN3Pxg4CrjEzA4BxgNz3L0/MCdMi4hIichbYnD3Gnd/NTz+DHgD2BcYCUwLT5sGjMpXDCIikr2CdFc1swrgcOAloLe710CUPMysV4p1xgJjAcrLywsRpiR45k+z+GR1fdy82mWb+Gy3arrvXaSgRCTv8p4YzKwb8BAwzt0/NbOM1nP3qcBUgMrKSs9fhJLKJ6vr6b53fEtfWac5bKqfWaSIRKQQ8toryczKiJLCfe7+cJhda2Z9wvI+wOp8xiAiItnJW43BoqrBHcAb7n5zzKLHgNHA5PD/0XzFUMrS3YgH2jasxdrq9cyaPL3Z/N17deL481pXpmyfJkyYQnV1XbP55eXduf76cQWPR0pDPpuSjgF+ALxuZlVh3tVECWGmmZ0PVANn5zGGkpXuRjzQtmEtNm/cpVkTEETDJYjEqq6uo6JiYrP5K1Y0nyc7jrwlBnefB6S6oDA8xXwRESkyDaIncb2PapdtamqGqlmm3kfSXEvNoBq5tf1TYpC43kdlnebQfe+oQlf9+oXFDEtKVEvNoBq5tf3TWEkiIhJHNYYdyKply5k1eXpccxGoyWhHkPhjxfXV1YwZM5FFi5ZQUVG8uKQ0KTHsQBrqO9B97/FxzUWgJqMdQbMfK9YtpaJiBPPmjSpaTFK61JQkIiJxlBhERCSOEoOIiMRRYhARkTi6+CyyA6pZtYpZs2dTu2YNs2bPbr585dOMGVeXdN22jOMl7YMSg8gOaNOWLXQfMICy97vRfcCAZsuXL9+Y8uTflnG8pH1QU5KIiMRRjSGP0o0pk4vqeLI7rAFs3LC5TeVK+6UfMUouKDHkUboxZXJRHU92hzWArVu+1eaypX3SjxglF9SUJCIicZQYREQkjhKDiIjEUWIQEZE4SgwiIhJHiUFEROLkLTGY2Z/MbLWZ/SNm3p5m9pSZLQv/98jX9kVEpHXyWWO4CxiRMG88MMfd+wNzwrSIiJSQvCUGd38W+Dhh9khgWng8DRiVr+2LiEjrFPqXz73dvQbA3WvMrFeqJ5rZWGAsQHl5eYHCK02JQ180DnegYQ5EJB9KdkgMd58KTAWorKz0IodTVIlDXzQOd6BhDkQkHwrdK6nWzPoAhP+rC7x9ERFpQaFrDI8Bo4HJ4f+jBd6+iLTBM3+a1WzkVoDde3Xi+PNGFScoybm8JQYzewAYBvQws5XAtUQJYaaZnQ9UA2fna/siknufrK6nrNNFcSO3AtStmlykiCQf8pYY3P2cFIuGp5gvIiIloGQvPotI+zdhwhSqq+uaphctXsyG+nq67uocfvRBzZ5f3rs31191VQEjlGSUGEQkb6qr66iomNg0XbV0Nn0PHUDdqslJb2K1YtasgsUmqWmsJBERiaMag4jk1KKqKsaMGwfAvAVvUbV0dtOymtpaug8Y0Oqy091HXc1QuaPEICI5taGhoamZqGrpdLrvvS0RVH/wQZvKTncfdTVD5Y6akkREJI5qDG2QrloLUQ+MVN9uRErZxg1fNPsRG0DNsmrgyMIHJAWlxNAG6aq1APMWLChcMCI5tHXLLnHjczWqfv1CtTPsAJQYRKTNVi1b3lTDiB0yo5RGANaF68wpMYhImzXUd2iqYTSO/guU1AjAunCdOVUKRUQkjmoMaeTr4nKqESrXffgee+yzH1C61XGRfIr9DUTS5Wk+c21ZV+IpMaSRr4vLqUaorH79QvoNKu3quEg+xf4GIpl0n7m2rCvx1JQkIiJxtvsaQ0vNQdn0Rkh172XdpEQkO7G9mGKtfP3jpPP1GSus7T4xtNQclE1vhFT3XtZNSkSyE9uLKdbmhpeTztdnrLDUlCQiInG2+xpDS9L1ZGhrL4a11es1rICItDs7fGJI15Ohrb0YNm/UsAIi0v7o9CQiInGKUmMwsxHALUBH4HZ315UlEcmZxB6EEPUifOZPs5L2bmrpx3H5HEsplz0nc6XgicHMOgJ/AE4EVgIvm9lj7r6k0LGIyPYpsQchRL0IP1n9ctLnt/TjuHyOpZTLnpO5UoympMHA2+7+jrs3ANOBkUWIQ0REkjB3L+wGzc4CRrj7j8P0D4Cvuvu/JjxvLDA2TB4EvJnFZnoAH+Ug3EJoT7FC+4pXseZPe4p3R451P3fvme1KxbjGYEnmNctO7j4VmNqqDZgtdPfK1qxbaO0pVmhf8SrW/GlP8SrW7BWjKWkl8KWY6b7Ah0WIQ0REkihGYngZ6G9m/cxsZ+C7wGNFiENERJIoeFOSu282s38FniTqrvond/9njjfTqiaoImlPsUL7ilex5k97ilexZqngF59FRKS06ZfPIiISR4lBRETitKvEYGYjzOxNM3vbzJqNTmeR34Xli81sUKbrlmC8K8zsdTOrMrOFJRDrADN7wcw2mtnl2axbYrEWdL9mGO/3wvu/2MyeN7PDMl23xGIttWN2ZIizyswWmtmQTNctwXgLe9y6e7v4I7pQvRzYH9gZeA04JOE5JwN/IfqtxFHAS5muW0rxhmUrgB4ltG97EY0V/h/A5dmsWyqxFnq/ZhHv14A9wuNvFuu4bUusJXrMdmPbddRDgaXF2K9tjbcYx217qjFkMpTGSOBuj7wIdDezPhmuW0rxFlqLsbr7and/GdiU7bolFGsxZBLv8+6+Lky+SPTbnozWLaFYCy2TWNd7OKsCXdn2Q9qSPB+kibfg2lNi2Bd4P2Z6ZZiXyXMyWTfX2hIvRAfFX83slTA8SD61Zf8Uet+2dXuF3K+QfbznE9UiW7NuW7UlVijBY9bMzjCzpcD/Audls26OtSVeKPBx255u1JPJUBqpnpPRMBw51pZ4AY5x9w/NrBfwlJktdfdncxphZnHkc93WaOv2CrlfIYt4zex4opNtY9tyye7bJLFCCR6z7v4I8IiZDQV+BXw903VzrC3xQoGP2/ZUY8hkKI1UzynGMBxtiRd3b/y/GniEqCqaL23ZP4Xet23aXoH3K2QYr5kdCtwOjHT3tdmsm0NtibWkj9lwEj3AzHpku26OtCXewh+3hbqY0dY/otrNO0A/tl28+ZeE55xC/MXcBZmuW2LxdgV2jXn8PNGItEWLNea5E4m/+FzQfdvGWAu6X7M4DsqBt4Gvtfa1lkCsJXfMAl9m28XcQcAH4bNWqueDVPEW/rjNZ+F52LknA28RXd3/9zDvIuCi8NiIbgK0HHgdqEy3bqnGS9Rz4bXw989CxJtBrHsTfev5FKgLj3crxr5tbazF2K8Zxns7sA6oCn8Li3XctjbWEj1mrwyxVAEvAEOKtV/bEm8x9q2GxBARkTjt6RqDiIgUgBKDiIjEUWIQEZE4SgwiIhJHiUFEROIoMUjemdn6DJ4zzsy6FCCWYWb2RIr5n5jZIjNbamY3ZVDWKDM7JEdx7WJmT4fRM7+TsOwuM3s3LHvNzIa3UFaFmZ2bi7hkx6TEIKViHJBVYjCzjjmO4Tl3Pxw4HDjVzI5p4fmjgJwkhrDNMncf6O4zkiz/hbsPJNpPt7ZQVgWQdWLIw/6UdkqJQQomfCufa2YPhm/l91nkZ8A+wDNm9kx47kkW3VPhVTP7s5l1C/NXmNkEM5sHnB2mrwvPe93MBoTnDQ73C1gU/h+UaZzu/gXRj4z2DWVdYGYvh2/rD5lZFzP7GnA6cGP4Jn9A+JsdBjp7rjGWhH2wp5nNCuPuv2hmh4bxb+4FBjaWlSa8F2Li6mhmN4bYFpvZheE5k4FjQ1mXmdkYM/t9TAxPmNmw8Hi9mV1vZi8BR4fp/wiv9UUz653pfpPthxKDFNrhRN96DyH6Recx7v47onFjjnf348P4MNcAX3f3QcBC4N9iyqh39yHuPj1MfxSe93+BxhvzLAWGhhrABODXmQZoZnsA/YHGQcoedvcj3f0w4A3gfHd/HniM8E3e3ZcT3cj9p+5+RIjjf5IUfx2wyN0PBa4mGnZ9NfBjohpLY1mpjABmhcfnA5+4+5FE95+4wMz6AeNjyvptCy+3K/APd/+qu88L0y+G1/oscEEL68t2qD2NrirbhwXuvhLAzKqImj3mJTznKKLEMd/MIBpb5oWY5YlNLQ+H/68AZ4bHuwPTzKw/0SiWZRnEdqyZLQYOAia7+6ow/ytmNgnoTnQzlScTVww1mq8Bfw4xA+ySZBtDgG8BuPvfzGwvM9s9g9huNLPfEN2E6Kgw7yTgUDM7K0zvTpTQGjIor9EW4KGY6Qag8RrMK8CJWZQl2wklBim0jTGPt5D8GDTgKXc/J0UZG1KUGVver4Bn3P0MM6sA5mYQ23PufqqZHQjMM7NH3L0KuAsY5e6vmdkYYFiSdTsAdeE6QDqtHfL5F0QJ8GfANOCIUNZP3T0uUTU2E8XYTHzrQKeYx/XuviVmepNvGycn1fsj2zk1JUmp+AzYNTx+ETjGzL4MENr0D8yyvN2JRqcEGJPNiu7+FnAD0aBmhLhqzKwM+F6ymN39U+BdMzs7xGwWcz/kGM82lhFO4B+FdTOJaytwC9DBzL5BVHO5OMSFmR1oZl2J35cQ3RZyoJl1MLMvkf+hxqWdU2KQUjEV+IuZPePua4hO5g+Epp0XgWYXclvwG+AGM5tPdL/dbN0KDA1t9r8EXgKeIrp20Wg68ItwgfsAohP++WbWOApmsttFTgQqw+uaDIzOJqjwbX4ScAXRSKdLgFfN7B/AH4m+4S8GNocLyJcB84F3iUbwvQl4NZttyo5Ho6uKiEgc1RhERCSOEoOIiMRRYhARkThKDCIiEkeJQURE4igxiIhIHCUGERGJ8/8Byl74tzgqqAMAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.hist(irr_hp, bins=40, color='teal',alpha=0.5, label='Hedged IRR', edgecolor='black')\n",
"plt.hist(irr, bins=40, color='blue',alpha=0.5, label='Unhedged IRR', edgecolor='black')\n",
"plt.xlabel('Internal Rate of Return')\n",
"plt.ylabel('Frequency')\n",
"plt.title('Distribution Of IRR Values - Hedged vs Unhedged Portfolio')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "229fb326",
"metadata": {},
"source": [
"We can see from these results that the choice of a European Put Option as a hedge is incorrect. It doesnt protect against a weakening HUF, which leads to a decrease in our GBP Cashflows. <br> \n",
"It instead pays out when $S_t < K$ which means the HUF has strengthened and our cashflows have increased in GBP i.e. we are getting a payout in an already favourable situation. This is why the 95th percentile of the Hedged Portfolio is greater than that of the Unhedged Portfolio. <br> \n",
"We also see the 5th percentile and 50th percentile of the Hedged Portfolio is lower than the Unhedged Portfolio due to the option price. This means that our Hedged Portfolio performs worse in adverse scenarios.<br> \n",
"The standard deviation of the Hedged Portfolio is also higher, meaning IRR results are more volatile with the purchase of the Put option. These are not things we want from a hedge.\n",
"\n",
"The correct hedging option would be a GBPHUF European Call. We will quickely compare the distributions below."
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "05186de4",
"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": [
"FinPayOffCall_HUF = N_GBP * np.maximum(S_T-K, 0) \n",
"FinPayOffCall_GBP = FinPayOffCall_HUF/S_T\n",
"\n",
"pricecall_gbp = FinPayOffCall_GBP.mean()\n",
"\n",
"Call_GBP_CF = GBP_CF.copy()\n",
"Call_GBP_CF[:,0] = GBP_CF[:,0] - pricecall_gbp\n",
"Call_GBP_CF[:,4] = GBP_CF[:,4] + FinPayOffCall_GBP \n",
"\n",
"irr_call = np.zeros(len(Call_GBP_CF))\n",
"for i in range(len(Call_GBP_CF)):\n",
" irr_call[i] = npf.irr(Call_GBP_CF[i,:])\n",
" \n",
"plt.hist(irr, bins=40, color='teal',alpha=0.5, label='Unhedged IRR', edgecolor='black')\n",
"plt.hist(irr_call, bins=40, color='blue',alpha=0.5, label='Call Hedged IRR', edgecolor='black')\n",
"plt.xlabel('Internal Rate of Return')\n",
"plt.ylabel('Frequency')\n",
"plt.title('Distribution Of IRR Values- Hedged vs Unhedged Portfolio')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "22dfd26d",
"metadata": {},
"source": [
"We can see from the comparison of the distributions that we are much better protected against adverse scenarios with a GBPHUF Call option. This is because a Call Option pays out when $S_t > K$, which corresponds to a weakening HUF and a decrease in our projects cashflow in GBP.\n",
"\n",
"We will also notice a lower standard deviation. This means our portfolio is less risky."
]
},
{
"cell_type": "markdown",
"id": "0219ab38",
"metadata": {},
"source": [
"## Question (d)\n",
"\n",
"This forward contract will allow us to exchange 115,000,000 HUF for GBP at a fixed rate of K = 455.25. Again as the risk-free rates are 0%, our discount factor is 1.\n",
"\n",
"Mark-to-Market is the current market value of the forward contract.\n",
"\n",
"We agree to Pay N HUF and receive $\\frac{N}{K}$ GBP. At time t The market may give us $\\frac{N}{S_t}$ GBP. The difference between these to values is the MTM:\n",
"\n",
"$$\n",
"MTM_t^{GBP} = N (\\frac{1}{S_t} - \\frac{1}{K})\n",
"$$\n",
"\n",
"A margin call is triggered whenever the absolute value of the MTM exceeds the GBP 70,000 threshold."
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "3533aa3b",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The probability of at least one margin call over the life of the trade is 25.60%\n"
]
}
],
"source": [
"GBPHUF_val_2029 = GBPHUF_val[:, 0:1009] \n",
"sim, time = GBPHUF_val_2029.shape\n",
"N = 115000000\n",
"threshold = 70000\n",
"\n",
"margin_call = np.zeros(sim, dtype=bool)\n",
"\n",
"for i in range(sim):\n",
" for j in range(time):\n",
" mtm = N * (1/GBPHUF_val_2029[i, j] - 1/K)\n",
" if abs(mtm) > threshold:\n",
" margin_call[i] = True \n",
" break\n",
"\n",
"prob_margin_call = margin_call.mean()*100 \n",
"\n",
"print(f\"The probability of at least one margin call over the life of the trade is {prob_margin_call:.2f}%\")"
]
},
{
"cell_type": "markdown",
"id": "308f60aa",
"metadata": {},
"source": [
"### Notes\n",
"\n",
"Approximate time spent: 6 hours. <br>\n",
"Use of AI: Latex syntax for formulas, Reference for MTM theory, Improving graphs, Introduction to numpy_financial IRR method."
]
}
],
"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": "3.8.8"
}
},
"nbformat": 4,
"nbformat_minor": 5
}