Question

A European call with strike X and maturity T is trading at c. The underlying stock does not pay any dividend. The annual interest rate is r_f. Suppose c > S – X/(1+r_f)^T and one call is on one share for simplicity. Then you can_____ one call, ____one share of the stock and ____ X/(1+r_f)^T to form an arbitrage portfolio.

		buy, sell, borrow
		sell, buy, lend
		sell, buy, borrow
		buy, sell, lend

Answer 1

The correct answer is "sell, buy, borrow"

The call price should be equal to S – X/(1+r_f)^T to avoid arbitrage. Here "S" is the stock price and X/(1+r_f)^T is the present value of strike price. So as c > S – X/(1+r_f)^T, so Call price is overvalued, it means it will go down. So you need to sell call.

If the call price doesn't increase then stock should increase to tally the equation. So the stock is under-priced now, buy it. You need to have money to enter the strategy, so borrow X/(1+r_f)^T.