Q2. (a) The price of a 40-strike European put option on a non-dividend paying stock is estimated using Monte Carlo method. The price of a 40-strike European call option on the same stock with the same expiry is used as a control variate. The price of call option is known to be 1.33. The following are the results of 5 trials: Price of call option 0.28 0.13 3.57 2.63 1.89 Price of put option 2.34 2.67 0.78 0.15 0.36 The Boyle modification of the control variate method is used with B estimated with above data. From the implemented simulation, calculate the resulting estimate of the price of the put option based on these 5 trials. (6 marks) (b) Suppose that you are given the following information for a stock: . The stock's price follows a lognormal process with y = 0.14 and 0 = 0.12. The stock's price is S, at time 7" (in years). The initial price is S. = 691. A 3-years European Call option on the stock has strike price of 645. . Find the 95" percentile payoff of the Call option. (7 marks) Q2. (a) The price of a 40-strike European put option on a non-dividend paying stock is estimated using Monte Carlo method. The price of a 40-strike European call option on the same stock with the same expiry is used as a control variate. The price of call option is known to be 1.33. The following are the results of 5 trials: Price of call option 0.28 0.13 3.57 2.63 1.89 Price of put option 2.34 2.67 0.78 0.15 0.36 The Boyle modification of the control variate method is used with B estimated with above data. From the implemented simulation, calculate the resulting estimate of the price of the put option based on these 5 trials. (6 marks) (b) Suppose that you are given the following information for a stock: . The stock's price follows a lognormal process with y = 0.14 and 0 = 0.12. The stock's price is S, at time 7" (in years). The initial price is S. = 691. A 3-years European Call option on the stock has strike price of 645. . Find the 95" percentile payoff of the Call option. (7 marks)