I have two rather elemenentary questions:1. The Black-Scholes model does not involve mean reversion at all. Presumably this is because mean-reversion of the asset would be irrelevant for option pricing in the same way the mean or expected return is irrelevant (the dynamic hedging argument). Is this correct? 2. If 1 is true, then why is mean reversion an important parameter in certain interest rate models (I know the Black formula for vanilla options does not involve mean-reversion at all). Also in general when would we need to worry about mean-reversion while pricing an optionThanks in advance

Correct on 1. Which interest rates model is mean reversion important for?

I thought the mean-reversion was an important parameter used in any model used to price exotic interest rate options like bermudans e.g. HJM, BGM, etc. Am I on the wrong track here?Thanks

1. According to the Black & Scholes framework the expected return is a parameter of the dynamics of the asset. When you create the risk free portfolio this term disappears. On the contrary the mean reversion is not a parameter of the model. If you assumed it you would obtain a different formula. Therefore while the expected return is irrilevant in the determination of the final price, the mean reversion should be relevant if taken in consideration.2. The mean reversion is an important parameter in interest rate models because the assumption of a pure geometric motion is not realistic. The price of a stock can move from 0 to + infinite while an interest rate tends to be attracted toward a long term average value. Infact the most important short rate models (HW, CIR, BK,...) incorporate in their dynamics one (or more) parameter that can be interpreted as "mean reversion"P.

2. It's mean reversion in the risk-neutral random walk for interest rates that matters. The real drift of rates doesn't matter* just like the real drift of the stock doesn't matter.P*Some simple technical requirements here.

I'm been trying to find any papers related to implementing MR in a BGM/J model - as yet, no luck. Would any of you know of any you could recommend?Many thanks, J.