Suppose that there are two European put options on the same underlying asset with the same time to matu

rity, i.e., investors can buy or write those two put options. Put X has a strike price of $30 and Put Y has a

strike price of $40. Put Xs premium is $3.25 and Put Ys premium is $2.50.

What opportunities are there for an arbitrageur? Please write down all the steps on how to fifind arbitrage

opportunity, how to arbitrage, and demonstrate that this is an arbitrage strategy?

Hint:

Step 1: identify the arbitrage opportunity with reasoning/calculation.

Step 2: to demonstrate that this is an arbitrage opportunity, you want to show that you will have a positive

payoff today and non-negative payoff at the expiration, no matter what the state of nature (i.e., the rage

of ST ) will be at T. You do not need to assume additional specifific numbers except for those given in the

question.