Hi, Dear all, As for a simple European Call option, the price of the option should be: OptionPrice = exp(-rT)(max(P(t) - K, 0)),where K the the strike price, and P(t) is the price of the underlying stock at time T,and r is the risk-free rate. To price this option with Monte Carlo Simulation, under BS assumptions, we assume the underlying price follows log normal distribution, then we use Monte Carlo Simulation to simulate the stock price and calculate the expected payoff. However, I want to price the option price under the practical measure( I mean not in the risk-free / risk neutral measure), then in 'my' option, now, the expected return of the underlying stock is R, (which is not the risk-free rate), then I replace r with R in the log normal distribution to simulate the underlying price, finally, I calculate the option price with the same method discussed above. Now, I concern about the method I 'used' to price the option in practical measure is correct in theory? If it is not, please tell me why and are there some good ideas to price an option in practical measure?Thanks.

You can do this, but you need to change the rate at which you discount the option pay-off. If you have [$]P(T)=P(0)e^{(R-0.5 \sigma^2)T+\sigma W_T} [$], then you need to discount at the path wise return on the growth optimal portfolio, whose value can be written as (assuming that we normalize it to a time zero value of 1): [$]A(T)=e^{(r+0.5 \lambda^2)T+\lambda W_T} [$], where [$] \lambda = \frac{R-r}{\sigma} [$]. Thus you want to find the (P measure) expected value of [$] \frac{[P(T)-K]^+}{A(T)} [$]. And just as a point of convention, I have never heard the P measure referred to as "practical". More common usage is physical, real world, empirical or natural.

Thanks for your replying,Bearish.My English is not so good.