Want to know the detail of those question how to use Brownian and probability space to solve the black scholes model

2. Let {Wt : t > 0} be a Brownian motion on a probability space (0, F, P) with a filtration {Ft : t 2 0}. Consider the Black-Scholes-Merton model with bank account and stock process dBt = Birdt, Bo = 1, dSt = Stadt + StodWt, So = So, where a, o > 0 and r 2 0 are constants. We denote by C(So, K, T) and by P(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 P, equivalent to P, under which dSt = Strat + StodWt, where W is a Brownian motion under P. (b) Show that e rtSt is a P-martingale. (c) Calculate C(So, K, T) and P(So, K, T). (d) Using Ito's formula, write the Stochastic Differential Equation verified by the process St (i.e. St raised at the power y) for a parameter y E (0, 1). (e) Give now the price of a call option and put option on the process St with maturity T and strike K