1. Consider a European put option with expiry T = 100 and strike price K = S0 = 1. Calculate the price at time 0 of such a put

(a) by exact methods, working backward from time T;

(b) by Monte Carlo simulation, quantifying your error. You may measure the error either in absolute or relative terms.

Consider a 100-step binomial model where the price of a non-dividend-paying asset at time n, Sn is modelled as Sn = SoZIZ2... Zn where Z, are i.i.d. random variables with Z u = 1.05 w. p. p d = 0.95 w. p. 1 p. Suppose So 1 and the continuously-compounded rate of interest per unit time step is r = 0.0001. Since r is expressed this way, you do not have to worry about the actual time unit each time step represents only the number of time steps.