Question

If you observed a European call option trading at a price below its theoretical lower bound, what transactions must be made today to capture the arbitrage profit on offer?

Select one:

Long the call option, short a corresponding put option, short sell the underlying stock and invest the proceeds in the bank.

Long the call option, short sell the underlying stock and invest the proceeds.

Long the call option, long a corresponding put option, and borrow enough money to buy the underlying stock.

Long the call option, and borrow enough money to buy the underlying stock.

Answer 1

B) Long the call option, short sell the underlying stock and invest the proceeds.

explanation:

For instance, a call option with a strike price of $30 on a stock that is currently trading at $40 should never sell for less than $10. If it did, you could make an immediate profit by buying the call for less than $10 and exercising right away to make $10.

Assume that you have one year to expiration and that the riskless interest rate is 10%.

Present value of Strike Price = $ 30/1.10 = $27.27

Lower Bound on call value = $ 40 - $27.27 = $12.73

The call has to trade for more than $12.73. if it traded for less than $12, You would buy the call for $12, sell short a share of stock for $40 and invest the net proceeds of $28 at the riskless rate of 10%.

If the stock price > 30: You first collect the proceeds from the riskless investment ($28(1.10) =$30.80), exercise the option (buy the share at $ 30) and cover your short sale. You will then get to keep the difference of $0.80.