6. An average strike call is similar to a standard call option, except that it uses the average asset price over a predetermined averaging period as the strike price. Consider a 3-month average strike call on a non-dividend-paying stock with a current price $60. Assume the stock price evolves according to a three-period binomial tree. Then the time length of each period is At = 1/12. In each period, the stock price at the end of period either goes up to 1.1 or goes down to 1/1.1 of the price at the beginning of the period. The strike price of this option is the average stock price over the first three periods, i.e., (S(0) + S(At) + S(2At)). In other words, the option pays off max {S(3At) (S(0) + S(At) + S(2At)), {)), 0} at the maturity date 3At. Suppose the interest rate is 5%. Try to use risk- neutral pricing to find the price of this average strike call.

6. An average strike call is similar to a standard call option, except that it uses the average asset price over a predetermined averaging period as the strike price. Consider a 3-month average strike call on a non-dividend-paying stock with a current price $60. Assume the stock price evolves according to a three-period binomial tree. Then the time length of each period is t=1/12. In each period, the stock price at the end of period either goes up to 1.1 or goes down to 1/1.1 of the price at the beginning of the period. The strike price of this option is the average stock price over the first three periods, i.e., 31(S(0)+S(t)+S(2t)). In other words, the option pays off max{S(3t)31(S(0)+S(t)+S(2t)),0} at the maturity date 3t. Suppose the interest rate is 5%. Try to use riskneutral pricing to find the price of this average strike call