Question

1a)

	Suppose a put option with a strike price of $65 has a premium of $11, while another put on the same underlying stock has a strike price of $70 and a premium of $9. Both options expire at the same time. In this situation, an arbitrageur would...
	Answers: a. do nothing because arbitrage is not possible. b. buy both put options. c. buy the 70-strike put and sell the 65-strike put. d. buy the 65-strike put and sell the 70-strike put. e. sell both put options. 1b)

Suppose a put option with a strike price of $30 has a premium of $7, while another put on the same underlying stock has a strike price of $35 and a premium of $11. Both options expire at the same time. In this situation, an arbitrageur would...

Answers: a. buy the 35-strike put and sell the 30-strike put. b. do nothing because arbitrage is not possible. c. buy both put options. d. buy the 30-strike put and sell the 35-strike put. e. sell both put options.

1c)

Suppose a stock’s price is $52, and the continuously compounded interest rate is 4%. The stock does not pay dividends. A 9-month $50-strike European call costs $7.12, and a 9-month $50-strike European put costs $4.33. In this situation, an arbitrageur would...

Answers: a. sell the stock, sell the call, and buy the put. b. buy the stock, sell the call, and buy the put. c. buy the stock, buy the call, and sell the put. d. sell the stock, buy the call, and sell the put.

Please explain the correct answers. Thank you.

Answer 1

1a) The correct answer is c) buy the 70-strike put and sell the 65-strike put.

So in this case outflow for buying will be 9 and inflow from selling will be 11. Thus the net effect will be positive cash flow of 2. Payout will be as below:

		Stock price
Particulars	Strike price	60	65	70	75
Buy Put	70	10	5	0	0
Sell Put	65	-5	0	0	0
Net Payoff		5	5	0	0

This will lead to maximum profit of 7 (5+2) with a minimum profit of 2 (0+2). $2 realised at the time of entering the strategy.

1 b) b. do nothing because arbitrage is not possible.

This is so becasue at one stage there could be loss in this strategy. The best possible option was to sell the 35 put and buy the 30 put. This will result in the net inflow of 11-7 = 4. But if the stock price closes on 30, then there would no profit no loss on the 30 strike put but there will be loss on the 35 strike put. Hence in this scenario, the arbitageur should not enter into any position.

1 c)