3. We presented in class that the Black-Scholes-Merton pricing formula for a European put option, with payoff function $(x) = (K - x)+ at time T > 0, is given by p(t, x) = Ke-r(Tt)/(-d_) XV(-d+), where r > 0 is the risk-free interest rate, V is the cumulative distribution function of a standard normal random variable, and dt = d+(t, x) are given by 1 X / log 7 tr 1 d+(t, x) = - OVT -t OK L (a) Derive the pricing formula (3). (b) Suppose you are the seller of this put option, and would like to replicate it by trading in stock and money market. Show that the corresponding trading strategy process A is given by A(t) = V(d+(t, S(t))) 1, where S is the stock price process. 3. We presented in class that the Black-Scholes-Merton pricing formula for a European put option, with payoff function $(x) = (K - x)+ at time T > 0, is given by p(t, x) = Ke-r(Tt)/(-d_) XV(-d+), where r > 0 is the risk-free interest rate, V is the cumulative distribution function of a standard normal random variable, and dt = d+(t, x) are given by 1 X / log 7 tr 1 d+(t, x) = - OVT -t OK L (a) Derive the pricing formula (3). (b) Suppose you are the seller of this put option, and would like to replicate it by trading in stock and money market. Show that the corresponding trading strategy process A is given by A(t) = V(d+(t, S(t))) 1, where S is the stock price process