The Java applet below is a simulation of the behavior of commodity prices according to a geometric brownian motion model where the transition of the price from one point in time to the next is a continuous-time stochastic process satisfying the following stochastic differential equation:
For an arbitrary initial price So the equation has the solution:
which is a random variable with value
and variance
where mu is the drift, sigma is the volatility. This solution can be verified according to Ito's Lemma.
Wednesday, September 24, 2008
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