1. Suppose that the current price of a stock is $80 per share. The price of a put option on this stock with a strike price of $90andwith 1.5yearsto expiration (maturity)is $15. The continuously compounded risk-free rate is 1% per year. a. What is the fair price of a call option with a strike price of $90and 1.5yearsto maturity?(Hint: recall the put-call parity from class.) b. Suppose that calls with a strike of $90and 1.5yearsto maturity are trading at $7. 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(or equivalently, buy or short sell any amount of risk-free 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 regardless of whether the price of the stock in 1.5years is less than or greater than the strike price, your arbitrage profit is unaffected.(Hint: This question is about options but is similar to what we did in class 2, i.e., according to the law of one price, a portfolio of strips that hast he same cash flows as a coupon bond must have the same price as the coupon bond. Start by comparing the actual$7call price to the price you computed in part a)