particularly need explanation of put-call parity for part (b)

3. Recall that the price today of a derivative with pay off at expiry T being the function (S) (of the stock price S) is Vo = e-PTE (g(Sr)], where r >0 is the continuously compounded interest rate and Sr is the random variable Sr = S, exp[(r - 02/2)T +0VTX], 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 g (S) and g(S) at expiry T for (respectively) a digital call V and a digital put VP are 1 if S>K 9(S) = and g(S) = So if S >K 11 otherwise. (a) Show that the price today of a digital call is V. = e-PT N(d), where d= In(S./K) + rT - (o?T/2) NT and N(r) is the cumulative distribution function of a standard normal, i.e. N(z) = 2 L expl-t* /2}dt. (b) Use put-call parity to find the price today V. 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 (S) (of the stock price S) is Vo = e-PTE (g(Sr)], where r >0 is the continuously compounded interest rate and Sr is the random variable Sr = S, exp[(r - 02/2)T +0VTX], 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 g (S) and g(S) at expiry T for (respectively) a digital call V and a digital put VP are 1 if S>K 9(S) = and g(S) = So if S >K 11 otherwise. (a) Show that the price today of a digital call is V. = e-PT N(d), where d= In(S./K) + rT - (o?T/2) NT and N(r) is the cumulative distribution function of a standard normal, i.e. N(z) = 2 L expl-t* /2}dt. (b) Use put-call parity to find the price today V. of a digital put with identical strike K and expiry T