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In this problem, you are asked to price an Asian option using the simulation method we talked about in class. Suppose that the stock price
In this problem, you are asked to price an Asian option using the simulation method we talked about in class. Suppose that the stock price follows Geometric Brownian Motion dSt = uStdt + oS dB. The initial stock price So is $10. The drift u = 15% and the volatility o = 40%. The continuously-compounded riskfree rate r is 5%. These are exactly the same parameters you have for Problem 5 of Homework 1. Consider an Asian put option on the stock with maturity T = 1 and strike price K = $10. The average stock price is calculated using the closing stock price of each trading day. That is, letting N = 252 and At =T/N, the average stock price is defined as Savg = Sat + S2At +...+ Snat N To ensure the reproducibility of your results, you can set random seed in Matlab using mng('default'). (a) (8 points) Simulate 100,000 independent paths of the pseudo-price process So, at, aat, ... , Nat under d = rdt+odB, So = So. Compute the pseudo-price average as at + aat + ... + Nat N (b) (8 points) Calculate the current price of this Asian option using the risk-neutral pricing formula ETTE (max(K avg,0)] In this problem, you are asked to price an Asian option using the simulation method we talked about in class. Suppose that the stock price follows Geometric Brownian Motion dSt = uStdt + oS dB. The initial stock price So is $10. The drift u = 15% and the volatility o = 40%. The continuously-compounded riskfree rate r is 5%. These are exactly the same parameters you have for Problem 5 of Homework 1. Consider an Asian put option on the stock with maturity T = 1 and strike price K = $10. The average stock price is calculated using the closing stock price of each trading day. That is, letting N = 252 and At =T/N, the average stock price is defined as Savg = Sat + S2At +...+ Snat N To ensure the reproducibility of your results, you can set random seed in Matlab using mng('default'). (a) (8 points) Simulate 100,000 independent paths of the pseudo-price process So, at, aat, ... , Nat under d = rdt+odB, So = So. Compute the pseudo-price average as at + aat + ... + Nat N (b) (8 points) Calculate the current price of this Asian option using the risk-neutral pricing formula ETTE (max(K avg,0)]
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