### An Asian call option pays off max (Ave - K, 0) at the maturity date where Ave is the arithmetic average of the stock price over a given period of...

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An Asian call option pays off max (Ave - K, 0) at the maturity date 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 = (S 4m + S 8m + S 12m)/3, where the S 4m, S 8m, and S 12m are stock prices in 4 months, 8 months, and 1 year respectively. We assume that the spot stock price is $90, its volatility is 36%, and that there is no dividend. The strike price K is $90 and the risk-free interest rate is 4%. (a) Calculate the tree parameters u, d, a, and p. (5 marks) (b) What are the possible averages after 1 year? (6 marks) (c) Price the Asian call using a 3-step binomial tree. Please show all the details. (6 marks) (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? Please explain intuitively. (5 marks)

#### Question

An Asian call option pays off max (Ave - K, 0) at the maturity date where Ave is the arithmetic average of the stock price over a given period of...

- Written in: 17-Oct-2019
- Paper ID: 11497336

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DATE ANSWEREDOct 17, 2019

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