With the notation used in this chapter:

(a) What is N'(x)?

d =

(b) Show that SN'

(d) = Ke'(-)N'(d), where S is the stock price at time t and In(S/K)+(+02/2)(T-t) oT-1 In(S/K)+(-2/2)(T-t) d = oT-t

(c) Calculate ads and ada

(d) Show that when c=SN

(d) - Ke(-1) N

(d) it follows that = -Ke-)N

(d) SN'(d)- - at 2T-t where c is the price of a call option on a non-dividend-paying stock.

(e) Show that ac/a = N(d).

(f) Show that c satisfies the Black-Scholes differential equation. (g) Show that c satisfies the boundary condition for a European call option, i.e., that c=max(SK, 0) as tT.AppendixLO1