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?