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If the stock price S follows the geometric Brownian motion process as below, what is the process followed by dS = u Sdt + o

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If the stock price S follows the geometric Brownian motion process as below, what is the process followed by dS = u Sdt + o Sdz w 1. y= 5 2. y = e In each case express the coefficients of dt and dz in terms of y rather than S. 3. Now assume the current stock price is 50. Its expected return and volatility are u= 12% and o= 30%, respectively. What is the probability that the stock price will be greater than 80 in 2 years? (Hint: S,> 80 when In S, > In80)

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