Thx for helping!

+ Problem 8. Consider an Asian option written on a stock index that expires in 4 years. At expiration, the option holder may choose to receive a payment equal to the geometric average of the stock price index sampled at the ends of years 1, 2, 3, 4 in return for the payment of a strike price K. Therefore, we can write the payoff of this option at expiration as Payoff = ((Sz x Sz x Sz x S1)1/4 K) Suppose the stock price follows a lognormal distribution: In(St/S) ~ N(ut, ot) where =r-8-02 (1) (5 points) Suppose we sample {z", z.?), 2) , ("}. Then what is the Monte Carlo estimator for the stock price? Write the result as a function of parameters So, K,7,8,0, N and samples {Zi}. (2) (5 points) Suppose So = K = 100, r = 0.05, 8 = 0.01,0 = 0.30 and one sample is Z(1) = 0.8, 2(2) = -0.1, Z(3) = -0.5, Z(1) = 1.2. What is the option payoff for this sample? T- i=1 = = - = + Problem 8. Consider an Asian option written on a stock index that expires in 4 years. At expiration, the option holder may choose to receive a payment equal to the geometric average of the stock price index sampled at the ends of years 1, 2, 3, 4 in return for the payment of a strike price K. Therefore, we can write the payoff of this option at expiration as Payoff = ((Sz x Sz x Sz x S1)1/4 K) Suppose the stock price follows a lognormal distribution: In(St/S) ~ N(ut, ot) where =r-8-02 (1) (5 points) Suppose we sample {z", z.?), 2) , ("}. Then what is the Monte Carlo estimator for the stock price? Write the result as a function of parameters So, K,7,8,0, N and samples {Zi}. (2) (5 points) Suppose So = K = 100, r = 0.05, 8 = 0.01,0 = 0.30 and one sample is Z(1) = 0.8, 2(2) = -0.1, Z(3) = -0.5, Z(1) = 1.2. What is the option payoff for this sample? T- i=1 = = - =