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
Simulation of Commodity Prices
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.
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.
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