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.

2 Answers

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!

The original framework for lookback options was devolped by Goldman, Sosin & Satto in Path Dependent Options: "Buy at the Low, Sell at the High".

You can probably find some additional details there.

• Thanks for your reference although this is not exactly I was looking for, I am really looking for a straightforward calculation to reach the price for the lookback option or path dependent option as stated in the paper. – Alexander Jan 22 '14 at 19:55