A stock is currently selling for $60 per share. In a year the price will be either $70 or $40. The risk-free rate is 5%. You are interested in valuing the at-the-money call option that matures in a year. 1) For obtaining the price of the at-the-money call option, you use the replicating strategy with the stock and a borrowed fund (i.e., a zero-coupon bond). (a) (2 pts) How many shares or what fraction of a share should you buy in order to replicate the call option? (b) (2 pts) How much should you borrow (short position of a risk-free zero-coupon bond) in order to replicate the call option? (c) (1 pts) What is the price of the at-the-money call option? 2) For obtaining the price of the at-the-money call option, you use the risk-neutral valuation strategy. (a) (2 pts) What is the risk-neutral (or pseudo) probability that the stock price will increase to $70? (b) (2 pts) Given the probability, what is the price of the at-the-money call option? 3) Now assume that the price of the above call option is $10. You buy one unit of the call option and also buy one unit of the (at-the-money) put option (on the same stock). The Item#4b/4 7 price of the put option is also $10. Draw a profit/loss (not payoff) diagram for your combined position on the expiration date, and answer the following questions. (a) (1 pts) What is the profit/loss from your long position of the call option if the stock price is 50 on the expiration date? (b) (1 pts) What is the profit/loss from your long position of the put option if the stock price is 50 on the expiration date? (c) (3 pts) What is the profit/loss from your combined (call & put) position if the stock price is 90 on the expiration date?