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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

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  • $\begingroup$ You might want to look into "rollover rates", the money you make or lose daily for holding currency. Selling currency early could save you money if you're paying rollover, or even make you money if you're taking a short position in the currency. $\endgroup$ – barrycarter Nov 3 '14 at 18:46
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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.

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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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