# Lookback option explicit formula using Black Scholes

I would like to compute the time-0-price for a lookback option using Black Scholes formula, the explicit formula is given by

$$S_0[(\frac{2r+\sigma^2}{2r})\Phi((\frac{2r+\sigma^2}{2\sigma/\sqrt{T}}))-e^{-rT}((\frac{2r-\sigma^2}{2\sigma/\sqrt{T}}))-\frac{\sigma^2}{2r}]$$

I know how to get to this price in theory, I looked into the book "Methods in Financial Modelling" by Musiela which is cited by wikipedia for a derivation but I am not very happy in the way he is doing all the calculations, do you have any reference for a nice clear derivation of this formula? It would be very helpful.

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The derivation on page 238 in Martingale Methods in Financial Modelling by Marek Musiela, Marek Rutkowski is very detailed and you won't find anything better.

Don't hesitate to ask about details here if there are something that you do not understand!

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