= Homework 7. 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 Pa be the price of the put option at maturity if U or D occurs respectively. (a) Give explicit expressions for Pu and Pd. Moreover, express Pi in terms of the indicator random variables lu 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 Vi in terms of the indicator random variables lu and 1D, as well as other variables. a = > (c) Show that the replicating portfolio (a, b) for the put option is given by Pu - Pa So(u - d) uPa-dP b Blu d) Hence obtain Po, the price of the put option at time t = 0. = Homework 7. 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 Pa be the price of the put option at maturity if U or D occurs respectively. (a) Give explicit expressions for Pu and Pd. Moreover, express Pi in terms of the indicator random variables lu 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 Vi in terms of the indicator random variables lu and 1D, as well as other variables. a = > (c) Show that the replicating portfolio (a, b) for the put option is given by Pu - Pa So(u - d) uPa-dP b Blu d) Hence obtain Po, the price of the put option at time t = 0