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I would like to price a floating strike american lookback with a particular feature: I don't want to charge upfront the client, rather I would like to insert a "running fee", some sort of a dividend.

For a European case it is simple: the integral over the life of the running fee must equal the price. How to extend it in an American case? References are welcome, even if they don't refer to the lookback.

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  • $\begingroup$ You could do Monte Carlo Monte Carlo, or LSMC $\endgroup$
    – adam
    May 13, 2016 at 14:21

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What happens to the "running fee" when the American option is exercised? Do you stop paying it? If you do then the standard Blck-Scholes equation applies (as modified for a look-back but you need to add -f at the end as the option holder collects a negative dividend equal to the fee.

This assumes a continuous-fee.

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