This homework is intended to make sure you all understand how to get the implied volatility (IV) from an option price. General: We will extract IV from put options on a stock index (XXX). The XXX index level at the opening of Friday November 11 was equal to 158.69. Assume an annualized risk free rate of 0.40% (zero point four per cent), and an annualized dividend yield of 2.3%. Objective: we want to extract the IV for the put options with expiration December 27. The time to maturity is equal to 35 (trading) days. Platform: you can use any software package you know how to use. You will be able to do this exercise in Excel, just be careful in constructing your spreadsheet. If you use MATLAB, you CANNOT use the matlab function blsimpv! Data: the data is in a companion Excel spreadsheet called homework4.xls 1. Lets compute the Implied volatilities Set up the Black and Scholes formula. Put in one column the volatility parameter. A good starting value could be 1. Use solver to minimize the difference between the market price and the Black and Scholes price. Plot the IV against the strike prices. What do you observe?

STRIKE PUT price 0.05 0.07 139 140 141 0.09 142 0.11 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 0.13 0.15 0.18 0.21 0.25 0.29 0.34 0.41 0.49 0.59 0.71 0.86 1.06 1.28 1.54 1.89 2.29 2.78 158 159 160 161 162 163 3.35 4.02 4.77 164 165 166 167 168 169 170 5.61 6.51 7.46 8.42 9.7 11.1 12.6 STRIKE PUT price 0.05 0.07 139 140 141 0.09 142 0.11 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 0.13 0.15 0.18 0.21 0.25 0.29 0.34 0.41 0.49 0.59 0.71 0.86 1.06 1.28 1.54 1.89 2.29 2.78 158 159 160 161 162 163 3.35 4.02 4.77 164 165 166 167 168 169 170 5.61 6.51 7.46 8.42 9.7 11.1 12.6