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I have worked with generation of transition probabilities of mean reverting CEV type stochastic differential equations using Girsanov theorem. A variable grid is generated and Transition probabilities are calculated from the well known analytic distribution(CDF) of the CEV noise stochastic differential equation. Various conditional integrals representing noise and variance of the Girsanov exponential are calculated along the grid. The initial CEV transition probabilities are transformed by the conditional values of Girsanov exponential to give the transition probabilities of the CEV type mean reverting stochastic differential equations. These transition probabilities are used by the program to simulate the mean reverting SDE. Many times it will be difficult to numerically solve the problem on such a general grid using the partial differential equation techniques. The method is very general and can be used for precision simulation of other SDEs with more complex dynamics than mean reverting SDEs.

It is natural to use Girsanov on a grid that has no monte carlo like simulation noise that drastically affects the performance of measure related methods in a monte carlo setting.

The paper is not ready yet and will be posted on SSRN in a few days. The experimental code can be downloaded from http://www.infinitiderivatives.com. You have to go to New Technologies page and the link to code can be found at the bottom of the text.

The code only deals with generation of transition probabilities and simulation of the mean reverting SDE but the scope of the paper is wider and will cover other aspects of option pricing so it will take a bit more time.