We will derive a two-state call option value in this problem. Data: S₀ = $120; X = $100; 1 + r = 1.10. The two possibilities for S_T are $140 and $90. The portfolio consists of 4 shares of stock and 5 calls short.

Required:

a. The range of S is $50 while that of C is $40 across the two states. What is the hedge ratio of the call? (Round your answer to 2 decimal places.)

b. Calculate the value of a call option on the stock with an exercise price of $100. (Do not use continuous compounding to calculate the present value of X in this example, because the interest rate is quoted as an effective per-period rate.) (Do not round intermediate calculations. Round your answer to 2 decimal places.)