Question 2 Assume the risk-free asset B, and the (non-dividend paying) stock S, follow the dynamics of the Black Scholes model (with interest rate r> 0, stock drift ER, volatility > 0 and So > 0). (a) Find the price at time 0 of a European option that pays ST1(n(Sr)2K) at maturity T. (b) Find the price at time 0 of a European option that pays Sr(In(ST)-K)+ at maturity T. Hint: It could be useful to use that for the density function f of a standard normal distribution it holds f'(x)=-xf(x) for all x E R.