Let {Wt : t 2 0} be a Brownian motion on a probability space (ELF, IE") with a ltration {It : t 2 0}. Consider the BlackScholesMerton model with bank...

Problem B i can solve but for other problem i do not know how to solve it

Let {Wt : t 2 0} be a Brownian motion on a probability space (ELF, IE”) with afiltration {It : t 2 0}. Consider the Black—Scholes—Merton model with bank accountand stock process dB; = Byrdt, Bo = 1,(£83 = Stadt ‘l’ StUth, 80 = 80, where (1,0 > 0 and r 2 0 are constants. We denote by C(SO,K, T) and byP(So, K, T), the price at time 0 of a Call and respectively Put option on the stock St with strike K and maturity T. (a) Find a probability measure If", equivalent to P, under whichas; = Strdt + 3mm, where W is a Brownian motion under If”(b) Show that e‘T‘St is a P—martingale.(c) Calculate C(SO,K, T) and P090, K, T). ((1) Using Ito’s formula, write the Stochastic Differential Equation verified by theprocess S: (i.e. St raised at the power 7) for a parameter 7 E (0, 1). (e) Give now the price of a call option and put option on the process 8: withmaturity T and strike K.