option pricing challenge zimin generalize initial comment process ds mu dt sigma dz delta hedging argument leads black scholes pde true arbitrary functions mu sigma includes gbm mean reversion others problem risk neutral world enter hedge drift actual process irrelevant believe concern would like see different option price mean reversion process happen asset hedgeable actual dynamics need factored option pricing assume underlying non traded factor pde reflect market price risk drift actual process reflected pde vasant zimin lu 10 17 2000 05 20 pm vince j kaminski hou ect ect stinson gibner hou ect ect vasant shanbhogue hou ect ect pinnamaneni krishnarao hou ect ect alex huang corp enron enron kevin kindall corp enron enron tanya tamarchenko hou ect ect cc subject option pricing challenge dear fundamental question back mind since 95 hope give convincing answer zimin deriving bs differential equation assume underlying follows gbm ds mu dt sigma dz mu drift sigma volatility function use delta hedging argument obtain bs differential equation option price regardless mu bs pde boundary condition derive bs formula fine problem question comes suppose underlying traded security follows say mean reverting process ds beta alpha dt sigma dz apparantly sde leads different probability distribution however using delta hedging argument still get bs differential equation boumdary condition get bs formula fair another angle derive distribution bs pde underlying lognormal distribution thinking drive distribution sde option pde answer yes got different pde rather bs pde delta hedging argument thanks