Question

19. A call option has X-$45 and expire in 115 days. The risk-free rate is 4.5%. The call is priced at $9.00. A put option has X=$45 and is priced at $3.75. The underlying asset is priced at $50. Which of the following statement is correct? A. There is no arbitrage opportunity B. There is arbitrage loss and whoever invest will lose a lot C. There is arbitrage profit and whoever invest will gain a lot D. It cannot be determined whether or not arbitrage opportunity exist E. None above 20. Which of the following statement is true? A. For any type of option strategy, the payoffs will never be negative B. For any type of option strategy, the profit will never be negative C. There is no option strategy that guarantees positive profit D. There is no option strategy that guarantees positive payoffs E. None above

Answer 1

19. This can be answered by examining whether put-call parity holds

i.e. put option value + current stock price = call option value (on the same stock, expiry & same strike price) + present value of strike price

Now, put option + current stock price = $3.75+$50 = $53.75

Call option value + present value of strike price

= $9 + 45 * e^{(- .045* 115/365})

=$9 + 45* 0.985922

= $9+$44.37 = $53.37

As put-call parity do not hold, there is an arbitrage profit to be made to earn a lot of profit, (option C)

20. For all option strategies, the payoffs or profits can always be negative sometimes, positive payoffs may also be guaranteed but not positve profits. (Payoff is what one gets after the expiry and does not include the investment cost of strategy, whereas profits do ). Hence , there is no option strategy that can guarantee positive profits (Option C)