3. Consider the BlackScholes model for the price of stock 3:, 1 1 d8; = EStdt + 5.5}ch Sn 2 1, and savings anemmt {it = eit. {a} Show that the discounted stock price Stfc is not a martingale. {b} Change the probability measure so that the discounted stock priee is a martingale under the new measure, use Girsanov theorem. Derive the expression for S} lmder the new measure. {c} Denote by C: the price at time t, of the call option on this stock with exercise prioe K = 1 and expiration date T = 1, t :1 1. By quoting an appropriate result, give the expression for On, the price of this option at ti1ne zero, and show that it is equal to 3'31 [Terri Meme. _3 32 where Mar) = 1 5?. Using the BlackScholars formula, or otherwise, show that Cg = {ME} e'iti'll), where @{e} = Em ex. {d} Write down the condition for a portfolio in this model to be self-nancing. Find all possible selfnancing portfolios at, h; with a; = 1 for all t Consider the portfolio given by at : 1 {stock} and b1; [savings account). Find all possible bf, ll :11 t if. 1, so that this portfolio is self-nancing