esther19930730 发表于 2014-7-5 23:00
i want to know using monte carlo method to estimate the option price (or sotck price at time t) why ...
You use alpha for expected payoff (at maturity), and r for expected price (at time 0).
The reason is that it's difficult to find the suitable discount rate to "bring back" the payoff to time 0 that goes with alpha, so risk-neutral pricing is used where you use r for both "projection" and discount.
Hope it clarifies things for you.