Suppose that the European options with the same maturity and the same underlying assets have the following prices:
(1) a 50-strike call costs $9;
(2) a 50-strike put costs $7;
(3) a 55-strike call costs $10;
(4) a 55-strike put costs $6.
(i) Some of the monotonicity conditions for no-arbitrage is violated by the above premiums.
Which ones?
(ii) Which spread position would you use the create an arbitrage?
(iii) Substantiate your answer to part (ii) by demonstrating that using that particular spread one obtains a non-negative profit in all states of the world and strictly positive profit with positive probability.