# 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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