I am trying to price an option using the Monte Carlo method, and I have the price process simulations as an inputs. The underlying is a forward contract, so at all times the mean of the simulations is current forward price (also the starting point of the simulations). There is no drift.
However, these simulations are calibrated on market data and exhibit i.e. mean reversion and other best estimates of market behavior. So even though they have zero drift, I believe they are not risk neutral and cannot be used in Monte Carlo valuation.
Is there any way how to convert arbitrary market simulations (in market measure) to risk neutral measure? Without knowledge of the SDE that generated them, since it may have been SDE with some further arbitrary postprocessing.
The reason I believe I cannot use them directly, is that some simulations (particularly simulations of commodity spreads) exhibit mean reverting properties, just like in real market. This means, that the variance of terminal prices for larger times does not rise linearly, but slows down or even approaches a constant. This lowers the option price in comparison to standard GBM model. But for a process with similar properties, i.e. Ohrenstein-Uhlenbeck, the option price rises with the mean reversion speed (claimed by http://web.mit.edu/wangj/www/pap/LoWang95.pdf), which is just the opposite effect.
It seems that I am missing something obvious, because everywhere the Monte Carlo method is promoted as a best method for valuating the options on very complex price processes, but it seems that these cannot be completely arbitrary (have to be risk-neutral) and I haven't found any source on how to verify and/or ensure this.
Thanks for any help.