Suppose that the price of a stock at time u in the future is a random variable Su = S0eαu+Wu, where S0 is the current price, α is a constant, and Wu is a random variable with known distribution. Suppose that you have available as many i.i.d. random variables as you wish with the distribution of Wu. Suppose that the m.g.f. ψ(t) of Wu is known and finite on an interval that contains t = 1.
a. What number should α equal in order that E(Su) = eruS0?
b. We wish to price an option to purchase one share of this stock at time u for the price q. Describe how you could use simulation to estimate the price of such an option.