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Suppose that the price of an asset obeys geometric Brownian motion (GBM) with an annual drift and an annual volatility of . Suppose that these
Suppose that the price of an asset obeys geometric Brownian motion (GBM) with an annual drift and an annual volatility of . Suppose that these parameters are equal to calibrated values from Question 19. If todays price is $100, what is the probability that the price two years from now will drop below $80? Note that under GBM, the future price at T, i.e. ST , given todays spot price, St, is ST = St exp [ ( 2 2 ) + ] with = T t and N(0,1). (a) 21% (b) 35% (c) 51% (d) 30%
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