3. Let {Wt>0} be a Brownian motion on a probability space (Q, F, P) with a...

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3. Let {Wt>0} be a Brownian motion on a probability space (Q, F, P) with a filtration {F: t>0}. Consider the Black-Scholes-Merton model with bank account and stock process dB = Brdt, dS = Stadt + SodWt, B = 1, So = So, where a, > 0 and r > 0 are constants. We denote by Co and by Po, 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 dS = Strdt + Stodt, where is a Brownian motion under P. (b) Show that ert St is a P-martingale. (c) Calculate Co and Po. (d) Find the prices for a call and a put if r So 100, K = 110, T = 0.5. = 0.05, a = 0.08, = 0.35 and 3. Let {Wt>0} be a Brownian motion on a probability space (Q, F, P) with a filtration {F: t>0}. Consider the Black-Scholes-Merton model with bank account and stock process dB = Brdt, dS = Stadt + SodWt, B = 1, So = So, where a, > 0 and r > 0 are constants. We denote by Co and by Po, 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 dS = Strdt + Stodt, where is a Brownian motion under P. (b) Show that ert St is a P-martingale. (c) Calculate Co and Po. (d) Find the prices for a call and a put if r So 100, K = 110, T = 0.5. = 0.05, a = 0.08, = 0.35 and

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a Find a probability measure P equivalent to P under which dSt SrdtWt where W is a Brownian motion u... View the full answer