Brigham, E. F., & Ehrhardt, M. C. (2017). Financial management: theory and practice. Australia: South-Western.

Chapter 8 Mini Case P. 370

d. Consider a stock with a current price of P = $27. Suppose that over the next 6 months the stock price will either go up by a factor of 1.41 or down by a factor of 0.71. Consider a call option on the stock with a strike price of $25 that expires in 6 months. The risk-free rate is 6%.

(1) Using the binomial model, what are the ending values of the stock price? What are the payoffs of the call option?

(2) Suppose you write one call option and buy Ns shares of stock. How many shares must you buy to create a portfolio with a riskless payoff (i.e., a hedge portfolio)? What is the payoff of the portfolio?

(3) What is the present value of the hedge portfolio? What is the value of the call option?

(4) What is a replicating portfolio? What is arbitrage?