Assume that you have just been hired as a financial analyst by Triple Play, a mid-sized California company that specializes in creating high-fashion clothing. Because no one at Triple Play is familiar with the basics of financial options, you have been asked to prepare a brief report that the firm’s executives can use to gain a cursory understanding of the topic.
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 binominal 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 the replicating portfolio? What is arbitrage?