Hi,I am interested in pricing exotic options such as Lookback, Asian, Barrier etc. Is there any article which is concernig about comparisons of prices of exotic options under different models (e.g. Rubistein - Implied tree, Duan's - Ngarch, Bates- stochastic volatility with jumps etc.). I was wondering if all of these models can be fit to the actual options prices do they give approximetly the same prices of exotic options and hedging parametrs? One more note, why everybody says that the geometric Brownian motions is a neccesary assumption of BSM formula, if this assumption can be left out and we can use forward measure with assumption that ending risk neutral distribution of asset is lognormal to obtain to obtain BSM formula (and the result is valid even in enviroment with the stochastic rates)? And I think it is also the reason why BSM formula yields approximatly correct vega parametr.Thanks Petr

I mean comparison under suitable set of parametrs given by market and of course the enviroment with stochstic interest rates.