An Asian call option pays off max(Ave - k, o) at the maturity data where Ave is the arithmetic average of the stock price over a given period of time. We consider a three-step binomial tree to price a 1-year Asian call where the average is defined by Ave = (S4m + S8m + S12m)/3, where the S4m. S8m, and S12m are stock price in 4 months, 8 months, and 1 year respectively. We assume that the spot stock price is 90, its volatility is 36%, and there is no dividend. The strike price K is 90, and the risk-free interest rate is 4%.
a) calculate the tree parameter u, d, a, p
b what are possible averages after 1 year
c) price the Asian call using a 3-step binomial tree
d) without pricing the corresponding at-the-money 1 year European standard call option, how would its price compare to the Asian call price computed in part c above.