Section D - Valuation principles [16 marks in total] Question 1 [6 marks] Assume you know the pricing formula for a call option. Explain how you can retrieve the formula for a put option using the notion of put-call parity. [Assume the options are written on the same underlying stock and have the same strike price and maturity.] Question 2 [10 marks] Consider an underlying following a (risk-neutral) geometric Brownian motion (GBM) of the form x = x and dx = u X ds toxdZs, 0 >0, where Z is a (standard) Brownian motion. At time te [0,1], if the underlying reaches a price x, the fair price of a European option written on this underlying and with a payout function G()) at maturity T > 0 is given by f(x, t) = Eje-r(T t) G(X)). Elaborate on the connection between this term f(x, t) and the solution 9:[0,00) [0,1] (-00,00) to the problem of (x, t) + ur (x, t) + 02x2304 (x, t) r(x, t) = t fort e (0,), Q(x, T) = g(x). ax ar2