The current price of a stock is $55 per share. The price of a put option on

Fantastic news! We've Found the answer you've been seeking!

Question:

The current price of a stock is $55 per share. The price of a put option on this stock with a strike price of $60 and with two years to expiration is $7. The continuously compounded risk-free rate is 3% per year.

a. What is the fair price of a call option with a strike price of $60 and two years to maturity?

b. Suppose that calls with a strike of $60 and two years to maturity are trading at $5. Assume that it is possible to buy or short sell any amount of the stock or the options, and that you can borrow or lend at the risk-free rate (equivalently, buy or short sell any amount of risk-free zero-coupon bonds). Describe the trades you would need to make today to earn an arbitrage profit. How large is the profit in terms of today's dollars? Show that irrespective of whether the price of the stock in two years is less than or greater than the strike price, your arbitrage profit is unaffected.