Homework 8. Consider the one-step Binomial model. Let Pt for t = 0,1 be the price of a put option with strike K and maturity T = 1. Define the events U = {up movement} and D = {down movement}. Let Pu and Pd be the price of the put option at maturity if U or D occurs respectively. (a) Give explicit expressions for P, and Pd. Moreover, express Pi in terms of the indicator random variables ly and 1D, as well as other variables. (b) Let V = aSt + bt, t = 0,1, be the value of a replicating portfolio (a,b). Express V1 in terms of the indicator random variables ly and 1p, as well as other variables. (c) Show that the replicating portfolio (a, b) for the put option is given by Pu-Pa Sou-d)' uPa-dP b= Blu-d) Hence obtain Po, the price of the put option at time t = 0. a Homework 8. Consider the one-step Binomial model. Let Pt for t = 0,1 be the price of a put option with strike K and maturity T = 1. Define the events U = {up movement} and D = {down movement}. Let Pu and Pd be the price of the put option at maturity if U or D occurs respectively. (a) Give explicit expressions for P, and Pd. Moreover, express Pi in terms of the indicator random variables ly and 1D, as well as other variables. (b) Let V = aSt + bt, t = 0,1, be the value of a replicating portfolio (a,b). Express V1 in terms of the indicator random variables ly and 1p, as well as other variables. (c) Show that the replicating portfolio (a, b) for the put option is given by Pu-Pa Sou-d)' uPa-dP b= Blu-d) Hence obtain Po, the price of the put option at time t = 0. a