Practical Limits on Arbitrage Between American and European Puts

Summary

The document examines a proposed trade involving American and European put options on the same asset, strike, and expiry. The idea is to sell the American put and buy a cheaper European put, potentially collecting cash if the European contract is priced below intrinsic value. The question asks whether the apparent arbitrage is viable and whether financing returns affect its value.

The response emphasizes a practical obstacle: the two exercise styles are rarely listed on the same underlying, so the required matched contracts are generally unavailable. It notes that individual equity options are commonly American-style, while index options are commonly European-style. In theory, if comparable contracts did exist and a true arbitrage were available, trading pressure would tend to remove it, subject to market frictions. The source gives no payoff proof, pricing bounds, or worked example, so it does not fully analyze the proposed position’s risks or cash flows.

Key ideas

• The proposed position sells an American put and buys a European put with matching terms.
• The trade depends on finding both exercise styles on the same underlying, strike, and expiry.
• Such matched contracts are generally scarce in practice.
• Equity options and index options commonly differ in exercise style.
• A theoretical arbitrage would tend to disappear through trading, subject to market frictions.

Tags

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


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












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 by Stéphane (score 1)

https://quant.stackexchange.com/a/53705

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).

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.