Futures and Options market and arbitrage profits
Near market closing time on a given day, you lose access to stock prices, but some European call and put prices for a stock are available as follows:
| Strike Price | Call Price | Put Price |
| $40 | $11 | $3 |
| $50 | $6 | $8 |
| $55 | $3 | $11 |
All six options have the same expiration date. After reviewing the information above, X tells Y and Z that no arbitrage opportunities can arise from these prices.
Y disagrees with X. She argues that one could use the following portfolio to obtain arbitrage profit: Long one call option with strike price 40; short three call options with strike price 50; lend $1; and long some calls with strike price 55.
Z also disagrees with X. He claims that the following portfolio, which is different from Y’s, can produce arbitrage profit: Long 2 calls and short 2 puts with strike price 55; long 1 call and short 1 put with strike price 40; lend $2; and short some calls and long the same number of puts with strike price 50.
Which of the following statements is true?
(A) Only X is correct.
(B) Only Y is correct.
(C) Only Z is correct.
(D) Both Y and Z are correct.
(E) None of them is correct.
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1 solution
Answer to this question is (D). Both Y and Z are correct. Because Y's portfolio and Z's portfolio both yields arbitrage profits. Have a look at below tables to understand how does Y's portfolio and Z's portfolio yield arbitrage profits,