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Stochastic Process Models in Finance

Michael Kelly
Organization: Wolfram Research, Inc.
Department: Wolfram Technology Group

Wolfram Technology Conference 2013
Conference location

Champaign, Illinois, USA

The Ito Stochastic Process forms the basis of all derivative pricing in finance. All options are special cases of the diffusion equation which is solved by the Black-Scholes partial differential equation (PDE) and because of the Feynman-Kac formula this can also be represented by a corresponding stochastic differential equation (SDE) which can now be described by the Mathematica function ItoProcess[]. For instance stocks and indices can be modeled as Geometric Brownian Motion, which is not only a stochastic process function in Mathematica but is also another example of an Ito process. In the same way the ItoProcess[] can be used to describe bonds with stochastic functions like the Brownian Bridge process and stochastic interest rate models can be described by the Ornstein-Uhlenbeck and the Cox-Ingersoll-Ross processes, all of which are now in the finance platform.

*Wolfram Technology

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StochasticProcessModelsInFinance2.nb (2.9 MB) - Mathematica Notebook