where r is the constant, instantaneous interest rate, W, () and W,() are independent Wiener processes, and of and o, are constant parameters. a) Express the values of S,() (as a function, in particular, of S,(0)) and of S, (1)/5,(1) (as a function, in particular, of S, (0)/5,(0); use Ito's Lemma). Then show that these two processes are independent. b) Compute, under the risk-neutral probability, E(S,(7)) and E(S, (D)/S,(D)) at date t = 0. (Hint. think of the Laplace transform of a Gaussian variable.) c) Write the payoff at date 7 of option B as a portfolio of 2 risky assets, one of which is a European call exchange option, denoted by CE. CE is the right, but not the obligation, to buy, at date 7, one unit of asset #1 at the price of one unit of asset #2. d) Rewrite CE's payoff at date T so that a product of two terms appears. e) Compute the value of option CE at date t = 0. (Hint: use b) and a) for f = T and try to recover a Black-Scholes-like formula). f) Give the value of the "Best of' option B at date f = 0