Consider a non-dividend paying share with a current price of 550 pence and constant volatility (standard deviation) of 35%. Assume that the annual risk-free rate is constant at 6%.

The Black-Scholes option pricing formula for a European call option on a non-dividend paying share is given by

C = S.N(d1) - E.e-rt.N(d2), where

d1 ln(SE)(r2 2).tln(SE)rt. t . t . t 2

d2 d1 . t

S = share price, E = exercise price of the option, r = annual risk-free interest rate, t = time to maturity of the option, = standard deviation of share price, and N(d) = the Cumulative Standard Normal Distribution value of d.

1. a) Use the Black-Scholes formula, together with the put-call parity, to calculate fair theoretical prices for a European call option and a European put option on the above share assuming that these options have the same exercise price of 530 pence and time to maturity of six months.