Question: Question 3 ( 6 points) a) Show with explicit, step-by-step calculations that the solution to the Black-ScholesMerton SDE dSt=(rd)Stdt+StdBt,S0>0 is given by ST=S0e(rd212)T+BT Hint: Define

Question 3 ( 6 points) a) Show with explicit, step-by-step calculations

Question 3 ( 6 points) a) Show with explicit, step-by-step calculations that the solution to the Black-ScholesMerton SDE dSt=(rd)Stdt+StdBt,S0>0 is given by ST=S0e(rd212)T+BT Hint: Define Yt:=lnSt and apply It's formula. b) Let ST be given by (2). Calculate the price P of a European put option with strike K and maturity T, i.e. calculate the discounted expected payoff P=erTE[max(KST,0)]

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