Pricing a Floating-Strike American Lookback with a Continuous Running Fee

Summary

The document asks how to price a floating-strike American lookback option when the client pays a running fee over the option’s life instead of an upfront premium. It contrasts this with a European option, where the questioner views the total fee over the term as matching the option price, and asks how early exercise changes the treatment.

The answer says the key modeling choice is whether fee payments stop when the option is exercised. If they stop, it suggests using the Black–Scholes equation adapted for a lookback payoff, with an adjustment for the fee as a continuous negative dividend received by the option holder. The response is brief and does not derive the equation, specify boundary conditions, or show a numerical example. The fee convention and exercise timing therefore need to be made explicit in any implementation.

Key ideas

• A running fee changes the pricing problem for an American lookback option.
• Whether fees stop at exercise affects how the fee enters the model.
• For a continuous fee that ends at exercise, the answer proposes a negative-dividend adjustment to the pricing equation.
• The document gives no derivation or numerical procedure for implementing the adjustment.

Tags

# How to price lookback american option when its payment is distributed during its life


# How to price lookback american option when its payment is distributed during its life












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.

## Answer by Jon Ingersoll (score 2)

https://quant.stackexchange.com/a/75873

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