5. Let X and Y be the prices for two underlying stocks. Assume that they are...

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5. Let X and Y be the prices for two underlying stocks. Assume that they are both geometric Brownian motions under the risk neutral probability: = {(r = 1/10) T + 0) T + TZ } - 1 YT = Yoexp 0 {( r 10 2 ) T + TZ 2 } = Here (Z1, Z2) is assumed to be a jointly normal random vector with distribution N (10]. 1) The goal is to simulate the price of a basket call option with maturity T and payoff (CXTC2YT-K)+ We would like to compare the plain Monte Carlo with the method of conditioning. The latter method uses the tower property Price =E[er (CX + Y K)*] = E[E[eT (CX + 2 K)*|Z2]] (a) Given Z = z, what is the conditional distribution of Z? No need for any derivation. All you need to do is to state the result. (b) Given Z= z, what is the price of the option? [Hint: Be careful that cY K may be nonnegative.] (c) Write a MATLAB function to estimate the basket call price and compare plain Monte Carlo with the method of conditioning. The function should have input parameters , 01, 02, 0, X0, Yo, T, K, C, C and sample size n. Report your estimates and their standard errors for r = 0.1, = 0.2, = 0.3, X = 50, Y = 50, T = 1, K = 55, p = 0.7, c = 0.5, c = 0.5 with sample size n = 10000 5. Let X and Y be the prices for two underlying stocks. Assume that they are both geometric Brownian motions under the risk neutral probability: = {(r = 1/10) T + 0) T + TZ } - 1 YT = Yoexp 0 {( r 10 2 ) T + TZ 2 } = Here (Z1, Z2) is assumed to be a jointly normal random vector with distribution N (10]. 1) The goal is to simulate the price of a basket call option with maturity T and payoff (CXTC2YT-K)+ We would like to compare the plain Monte Carlo with the method of conditioning. The latter method uses the tower property Price =E[er (CX + Y K)*] = E[E[eT (CX + 2 K)*|Z2]] (a) Given Z = z, what is the conditional distribution of Z? No need for any derivation. All you need to do is to state the result. (b) Given Z= z, what is the price of the option? [Hint: Be careful that cY K may be nonnegative.] (c) Write a MATLAB function to estimate the basket call price and compare plain Monte Carlo with the method of conditioning. The function should have input parameters , 01, 02, 0, X0, Yo, T, K, C, C and sample size n. Report your estimates and their standard errors for r = 0.1, = 0.2, = 0.3, X = 50, Y = 50, T = 1, K = 55, p = 0.7, c = 0.5, c = 0.5 with sample size n = 10000