Arbitrage between American and European put options on the same underlying asset

Question

Suppose there exist both American-style and European-style put options on the same underlying asset, at the same strike price, and with the same expiry date. Suppose the European put is selling below intrinsic value. Given that American put options are more valuable than European put options, it will be possible to get some cash now by simultaneously selling an American put option and buying a European put option. When these two options come closer to expiry, they will both be worth the same.

I have a feeling that this arbitrage is not feasible. My intuition tells me that even if there is a gain from this "arbitrage", it will always be less than one that could have been obtained at the risk-free rate.

Can you tell me why the arbitrage method mentioned above is not feasible?

Answer 1

In practice, you will not be able to find assets on which both types of options are written save for rare exceptions where there might have been a transition between one type to the other. For equity, options on individual titles tend to be American while options on indexes tend to be European... so, you can't really run a test of this idea.

In theory, if it was possible to do the sort of trade you have in mind, the arbitrage opportunities would eliminate themselves (up to market frictions).