This question explores the links between the implied volatility skew and the shape of the risk-neutral density. Consider calls and puts as well as digitals. Current time is t. Fix a maturity T>t. The implied volatility curve for that maturity is giv(K,T; S, t). Assume that r is a constant and that there are no dividends paid between now and T included. In this question, we are going to compare the Black-Scholes world to a world with a skew, keeping F(T) constant. a. [4 marks] Imposing No Arbitrage (NA), show via the FTAP that the forward price on the stock at t for delivery of one unit of the stock at T must satisfy F: (T) = e(T-) St b. [4 marks] Argue by contradiction that if the IV curve has a skew, then the Black- Scholes-Merton (BSM) model cannot be true. c. [4 marks] Show that the risk-neutral density of log excess returns R = In (ST) is sidi (R,r)