Throughout this question assume a standard Black and Scholes market. For p,K >- 0, let C(t,T,K,p) and P(t,T,K,p) denote the price at time t of the power options with payoffs (S; K)+ and (K 333?, respectively, at time T. 1. Derive an analytic expression for the price C(U, T, Km). 2. Show that P{t,T, Km) O'(t,T, K130) = er(TJK _ Sfenpagu where A1, = po 1)o'2 + (p 1):r'. 3. Consider a chooser power option, where at a xed time Td