With the notation used in this chapter: (a) What is N0 (x)? 1 (b) Show that SN0 (d1) = Ker(T t)N0 (d2), where S is the stock price at time t and d1 = ln(S/K) + (r + 2/2)(T t) T t , d2 = ln(S/K) + (r 2/2)(T t) T t . (c) Calcualte d1/S and d2/S. (d) Show that when c = SN(d1) Ker(T t)N(d2), it follows that c t = rKer(T t)N(d2) SN0 (d1) 2 T t , where c is the price of a call option on a non-dividend-paying stock. (e) Show that c/S = N(d1). (f) Show that c satisfies the Black-Scholes-Merton differential equation. (g) Show that c satisfies the boundary condition for a European call option, i.e., that c = max(S K, 0) as t T.