A stock price is currently trading at $40. Assume that the stock follows a one-period binomial model with one period lasting for half a year. The stock will either increase in value by 20% or fall in value by 10% in the binomial tree. The annual effective risk-free interest rate is 1.2%. The stock pays no dividends.

a. (6 MARKS) Find a fair (no-arbitrage) price of a European call option written on the stock with expiration in a half year and strike price of $35.

b. (6 MARKS) Assume that the actual price of the call from question a seen in the market is $6.52. Also assume that there are no put options written on the stock available for trading. Does the market allow arbitrage opportunities? What will be an arbitrage strategy and its profit if your answer to the previous question is Yes?

PROBLEM 4 CONTINUED

c. (6 MARKS) Suppose that the stock price can increase with probability of 60% and decrease with probability of 40%. Find the expected return on the stock and the standard deviation of the stock return

d. (6 MARKS) Suppose that the stock price can increase with probability of 60% and decrease with probability of 40%. Find the expected return on the call option from question a and the standard deviation of the return of this option