Problem 4 - 02 In () + (r- (1 t) = - With the notation used in the lecture slides: (a) What is N'(x) ? (b) Show that SN'(d) = Ke =r(T-t)N'(d2), where S is the stock price at time t and 02 In () + (r + 2)(1 t) di d2 OVT-t OVT-t (c) Calculate adi/ as and ad2/ as. (d) Show that when c = SN(du) Ke=r(T-1) N(D2) it follows that ac = -rKe=r(T-t) N(D2) SN'(d1) at 2VT - t where c is the price of a call option on a non-dividend paying stock. (e) Show that ac/aS = N(d). (f) Show that c satisfies the Black-Scholes-Merton differential equation. 0 ) Problem 4 - 02 In () + (r- (1 t) = - With the notation used in the lecture slides: (a) What is N'(x) ? (b) Show that SN'(d) = Ke =r(T-t)N'(d2), where S is the stock price at time t and 02 In () + (r + 2)(1 t) di d2 OVT-t OVT-t (c) Calculate adi/ as and ad2/ as. (d) Show that when c = SN(du) Ke=r(T-1) N(D2) it follows that ac = -rKe=r(T-t) N(D2) SN'(d1) at 2VT - t where c is the price of a call option on a non-dividend paying stock. (e) Show that ac/aS = N(d). (f) Show that c satisfies the Black-Scholes-Merton differential equation. 0 )