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, fors < t, E[Y (t)|Y (u), 0 u s] = Y (s)