A Mean-Reverting Jump Diffusion Process
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This Demonstration shows a path of a mean-reverting jump diffusion process (with mean 0) with normally distributed jumps. Such processes can be used for modelling the logarithm of the price of a commodity such as gas, oil, etc. that is subject to irregular disruptions but tends to revert to the mean (the production cost of the commodity).
Contributed by: Andrzej Kozlowski (June 2012)
Open content licensed under CC BY-NC-SA
Snapshots
Details
The stochastic process modelled here is described by the stochastic PDE:
,
where 
is the standard Wiener process, 
is normally distributed, and 
is a Poisson process. The coefficient 
is the volatility of the continuous random component of the process and the coefficient 
is the rate of mean reversion. In order to obtain rapid return to the mean after "spikes" that one observes in electric energy markets, has to be set to a high value.
Reference
[1] T. Kluge, "Pricing Swing Options and other Electricity Derivatives" [doctoral thesis], Oxford, 2006.
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