Question: 6. (a) [5 marks) Derive the Black-Scholes formula for the price co at time 0 of a European call option on a zero dividend stock

6. (a) [5 marks) Derive the Black-Scholes formula for the price co at time 0 of a European call option on a zero dividend stock with price So using put-call parity and the formula for the price of a European put option with the same strike price X and expiry date T > 0: Po = ev"X (-d2 + OVT) - S0(-di) (12) where: log(So/X) + (y + o2/2)T di OVT (13) (b) (4 marks] Show that the delta of this put is: (di) - 1. (c) (4 marks) Show that the value of a long position in a forward on a this stock with contract price F = X and expiry T is: V = So - Xeyr. (d) (4 marks] Show that this forward has the same value as the long call and the short put (-)po. (e) (4 marks) What is the delta of this forward? () (4 marks] Use the results at (6) and (d) to find the delta of Co. Co 7. $ 3 4 5 RO 6 & 7 8 g 0 6. (a) [5 marks) Derive the Black-Scholes formula for the price co at time 0 of a European call option on a zero dividend stock with price So using put-call parity and the formula for the price of a European put option with the same strike price X and expiry date T > 0: Po = ev"X (-d2 + OVT) - S0(-di) (12) where: log(So/X) + (y + o2/2)T di OVT (13) (b) (4 marks] Show that the delta of this put is: (di) - 1. (c) (4 marks) Show that the value of a long position in a forward on a this stock with contract price F = X and expiry T is: V = So - Xeyr. (d) (4 marks] Show that this forward has the same value as the long call and the short put (-)po. (e) (4 marks) What is the delta of this forward? () (4 marks] Use the results at (6) and (d) to find the delta of Co. Co 7. $ 3 4 5 RO 6 & 7 8 g 0

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