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W t is a Brownian motion under the actual measure and W t is a Brownian motion under the equivalent risk-neutral measure. With risk-free rate
Wtis a Brownian motion under the actual measure andWtis a Brownian motion under the equivalent risk-neutral measure.
With risk-free rate of interest r,
1. evaluate EQ[ST] where STis the stock price at time T.
2. derive the Black-Scholes equation for an European Call Option C(t,St) from the dynamics of the stock price St,
dSt= Stdt + StdWtand a portfolio = St C(t, St) where is the number of shares of the stock.
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