15. The current price of a stock is 100. Suppose that the logarithm of the price of the stock changes according to a Brownian motion process with drift coefficient μ = 2 and variance parameter σ2 = 1. Give the Black-Scholes cost of an option to buy the stock at time 10 for a cost of

(a) 100 per unit.

(b) 120 per unit.

(c) 80 per unit.
Assume that the continuously compounded interest rate is 5 percent.
A stochastic process {Y(t), t  0} is said to be a Martingale process if, for s < t, E[Y(t)|Y(u), 0  u  s] = Y(s)