# 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, IEÃ¢â‚¬Â) with aÃ¯Â¬Âltration {It : t 2 0}. Consider the BlackÃ¢â‚¬â€ScholesÃ¢â‚¬â€Merton model with bank accountand stock process dB; = Byrdt, Bo = 1,(Ã‚Â£83 = Stadt Ã¢â‚¬ËœlÃ¢â‚¬â„¢ StUth, 80 = 80, where (1,0 &gt; 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&quot;, equivalent to P, under whichas; = Strdt + 3mm, where W is a Brownian motion under IfÃ¢â‚¬Â(b) Show that eÃ¢â‚¬ËœTÃ¢â‚¬ËœSt is a PÃ¢â‚¬â€martingale.(c) Calculate C(SO,K, T) and P090, K, T). ((1) Using ItoÃ¢â‚¬â„¢s formula, write the Stochastic Differential Equation veriÃ¯Â¬Âed 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.

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