Early Exercise of American Puts on Foreign Currency
Summary
The document explains why early exercise can be optimal for an American put on foreign currency. It relates foreign exchange options to options on dividend-paying stocks: holding foreign currency earns the foreign risk-free rate, which acts like a dividend yield in the analogy. This lets familiar equity-option intuition help explain the FX case.
The replies emphasize that a put’s payoff is bounded, so waiting has less upside when the spot rate is very low, while exercising can release value that earns interest. One answer sketches an arbitrage comparison involving exercise proceeds, their present value, and a corresponding call price. These are conceptual explanations, not a full derivation of an exercise boundary. The precise decision depends on rates, spot, strike, remaining time, and option value; the document gives no numerical example or general threshold formula.
Key ideas
- Foreign currency options can be analyzed using the analogy to options on dividend-paying stocks.
- The foreign risk-free rate plays a role similar to a dividend yield on the underlying currency.
- A deeply in-the-money American put may favor early exercise because the put payoff is bounded.
- Exercise proceeds can be compared with the value of continuing to hold the option.
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Full text
# American put on a foreign currency # American put on a foreign currency I know that For an American-style put option, early exercise is a optimal for deep in-the-money options. In this case, it may make sense to exercise the option early in order to obtain the profit earlier so that it can start to earn interest immediately.\ but why it could be optimal to exercise prematurely an american put on Foreign currency? any tips are really appreciated thanks ## Answer by Mark Joshi (score 2) https://quant.stackexchange.com/a/15279 FX options are essentially the same mathematically as options on stocks that pay a continuous dividend. So the same arguments apply. If you are deeply in the money, it may be time to exercise a put. ## Answer by Amiro (score 0) https://quant.stackexchange.com/a/15305 Hi After searching Google I found some good reasons and I think that it might be useful for others also, So I post it here too. The put’s payoff is bounded: at maturity, the maximal gain is K (less the premium) if the underlying is worth 0 (It is not the same with the call where the potential gain is unlimited). In the case of an American put, this fact limits the benefit of waiting to exercise: an early exercise is optimal if the underlying spot price gets low enough (interest rate). The possible risk-free arbitrage takes place when the put is deep in-the-money. An early exercise provides X. If the difference between X and the present value of X is larger than the corresponding call price, one invests PV(X), buys the call and makes the risk-free profit. (notice: the foreign risk-free rate on the foreign currency can be viewed as a dividend yield)
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