Question: Consider the case where an asset price,S(t), with initial price $120 is modeled by a geometric Brownian motion: S(t)=120e^(0.23125t+0.5B(t)),0t

Consider the case where an asset price,S(t), with initial price $120 is modeled by a geometric Brownian motion:

S(t)=120e^(0.23125t+0.5B(t)),0t<,

whereB(t) is a standard Brownian motion. Here the risk-free interest rate is 5% and the stock volatility is 75%. A discretely monitored Asian Arithmetic mean call option with strike price $120 monitored weekly (52 times per year) and expiring in one year has a discounted payoff of

52 52

payoff = max1S(j/52)120,0e0.05.j=1

With the same parameters and 104sample paths, estimate the price of the Asian Arithmetic mean call option.

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