Question: Consider stock X that follows a single-step binomial tree. The current price of stock X is 100$ and it can increase to 108$ with probability

Consider stock X that follows a single-step binomial tree. The current price of stock X is 100$ and it can increase to 108$ with probability p = 55% or decrease to 92$ with probability 1 p = 45% over next 6 months. The effective annual interest rate is 3%. Suppose that investor Michael writes the call option on stock X with expiration in 6 months and strike price of 98$.

a. Design a portfolio with stock X and T-bills that Michael has to buy to hedge his risk (that is, to remove the aggregate risk from the short position in the call and a long position in the portfolio).

b. Assume that the markets are efficient. What is the expected rate return from stock X and the call option over 6 months?

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