Forums > Pricing & Modelling > Hermite polynomial Representation of the density of Stochastic Differential Equations

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Display using: amin Total Posts: 293 Joined: Aug 2005
 Posted: 2020-01-30 19:45 In this post, I want to describe how to convert an existing density that is in bessel coordinates into hermite polynomial representation. As we learnt earlier when we were expanding to find higher order terms in the expansion of SDEs, all the expansions have to be done in terms of the standard gaussian and hermite polynomials. The ideas I am going to present are extremely simple but could be quite far-reaching for the stochastics. We could represent an existing density and its drift and volatility each in its own hermite representation and add across orthogonal coordinates to find the evolution of the density. Similarly the ideas presented here would have very interesting implications when adding the two arbitrary SDE densities. Apart from so many other possible applications, we could use them in hybrid fX/equity/IR models where so many different SDEs are in action together.Read here in post 860: https://lnkd.in/dNNyc_p  amin Total Posts: 293 Joined: Aug 2005
 Posted: 2020-01-31 18:05 Download Matlab Program for Hermite polynomial Representation of the density of Stochastic Differential Equations.In this program, uploaded in post 861, we find hermite representation of the SDE variable w to Second Order as a function of two first hermite polynomials. In the previous post 860, I described how to convert an existing density that is in bessel coordinates into hermite polynomial representation. All the expansions are done in terms of the standard gaussian and their hermite polynomials. Read here in post 860: https://lnkd.in/dNNyc_p Page 1 of 1