: (2 points) For any function f :R+ +R+ twice differentiable, and any 2, 20 > 0 we admit the following Carr-Madan formula 20 too $(x) = f(x0) + f'(o)(x vo) +6".s"(K)(K )+dK +. Ss"(K)(x K)+dK. + 20 . By setting 20 = SerT, compute the price po at time 0 of a product with the following payoff at time T: f(ST):= log(S) and an hedging strategy for this payoff, by using infinitely many calls and puts. Hint: remember (again) that po = e=T[F(ST)] and use Carr-Madan formula. : (2 points) For any function f :R+ +R+ twice differentiable, and any 2, 20 > 0 we admit the following Carr-Madan formula 20 too $(x) = f(x0) + f'(o)(x vo) +6".s"(K)(K )+dK +. Ss"(K)(x K)+dK. + 20 . By setting 20 = SerT, compute the price po at time 0 of a product with the following payoff at time T: f(ST):= log(S) and an hedging strategy for this payoff, by using infinitely many calls and puts. Hint: remember (again) that po = e=T[F(ST)] and use Carr-Madan formula