3. Recall that the price today of a derivative with pay off at expiry T being the function g(S) (of the stock price S) is Vo = e-TTE (g(ST)], where r > 0 is the continuously compounded interest rate and St is the random variable ST = S, exp[(r 02/2)T +OVTX], modeling the stock price at time T. Here X is a normal distribution random variable with mean zero, variance one, and So is the stock price today. Let K > 0. Recall that the payoffs 9C (S) and g(S) at expiry T for (respectively) a digital call V and a digital put VP are if S>K So if S > K 9(S) and g(S) otherwise, otherwise. { {I (a) Show that the price today of a digital call is VC = e-rT N(d), where In(S./K) + rT - (02T/2) d= NT and N(x) is the cumulative distribution function of a standard normal, i.e. N(x) = Via Lexp[-22 12) dt. (b) Use put-call parity to find the price today VP of a digital put with identical strike K and expiry T. 3. Recall that the price today of a derivative with pay off at expiry T being the function g(S) (of the stock price S) is Vo = e-TTE (g(ST)], where r > 0 is the continuously compounded interest rate and St is the random variable ST = S, exp[(r 02/2)T +OVTX], modeling the stock price at time T. Here X is a normal distribution random variable with mean zero, variance one, and So is the stock price today. Let K > 0. Recall that the payoffs 9C (S) and g(S) at expiry T for (respectively) a digital call V and a digital put VP are if S>K So if S > K 9(S) and g(S) otherwise, otherwise. { {I (a) Show that the price today of a digital call is VC = e-rT N(d), where In(S./K) + rT - (02T/2) d= NT and N(x) is the cumulative distribution function of a standard normal, i.e. N(x) = Via Lexp[-22 12) dt. (b) Use put-call parity to find the price today VP of a digital put with identical strike K and expiry T