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Stochastic Process Models in Finance
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| Organization: | Wolfram Research, Inc. |
| Department: | Wolfram Technology Group |
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Wolfram Technology Conference 2013
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Champaign, Illinois, USA
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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.
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http://www.wolfram.com/events/technology-conference/2013
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| StochasticProcessModelsInFinance2.nb (2.9 MB) - Mathematica Notebook |
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