Question

This is a problem that has TWO questions. Therefore, please choose TWO answers (one choice for each question) to get full credit for this questions, otherwise you will only get partial points.

The price of a non-dividend paying stock is $75 and the price of a 9-month European put option on the stock with a strike price of $77 is $3.8. The risk-free rate is 7% per annum with continuous compounding.

1) What should be the price of a 9-month European call option with a strike price of $77, for no arbitrage?

2) If the European call option is currently trading at $5, what arbitrage strategy should be implemented to exploit the arbitrage opportunity?

		1) no-arbitrage-price = $4.78
		1) no-arbitrage-price = $3.74
		1) no-arbitrage-price = $5.74
		1) no-arbitrage-price = $2.78
		2) arbitrage strategy = buy the call, buy the put and short the stock
		2) arbitrage strategy = buy the call, buy the put and buy the stock
		2) arbitrage strategy = short the call, short the put and buy the stock
		2) arbitrage strategy = buy the call, short the put and short the stock

Answer 1

Ans 1) put call parity

call + present value of strike price = put + stock price

call = 3.8 + 75 - 77 * e^(-r*t)

= 78.8 - 77* e^(-.07*3/4)

= $5.74

thus the no arbitrage call price = $5.74

Ans 2) Since the call price is less than its intrinsic value one should buy the call and sell the put correct answer is last one i.e., arbitrage strategy = buy the call, short the put and short the stock