Let r be a constant interest rate and the stock price the real world probability measure...

 

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Let r be a constant interest rate and the stock price the real world probability measure be given by S(t) under dS (t) = S (t)dt + oS (t)dW (t) where W (t) is a Brownian motion. Also, let (S(T) -K)+ be the payoff of a European call option at time T. Derive the Black-Scholes pricing formula of the option. Hint: Evaluate Ee (T-)(S(T) - K)+ | F(t), where the expectation is under the risk-neutral probability. measure. Let r be a constant interest rate and the stock price the real world probability measure be given by S(t) under dS (t) = S (t)dt + oS (t)dW (t) where W (t) is a Brownian motion. Also, let (S(T) -K)+ be the payoff of a European call option at time T. Derive the Black-Scholes pricing formula of the option. Hint: Evaluate Ee (T-)(S(T) - K)+ | F(t), where the expectation is under the risk-neutral probability. measure.

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