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Sep 3

Finite Element package

Posted by abiao at 14:39 | Code » C++ | Comments(0) | Reads(11045)
Recently I have been working on pricing a high dimensional (4 dimension, actually) derivative via partial differencial equation (PDE), which can be solved numerically by Finite Element or Finite Difference method. Indeed Matlab has a PDE toolbox to use, however, as I know, this PDE toolbox can only calculate two dimensional problem, for instance, stock and time dimension as Black Scholes model does.

For your attention, I found an excellent Finite Element package named Getfem++ written in C++, as its webpage says, "The Getfem++ project focuses on the development of a generic and efficient C++ library for finite element methods. The goal is to provide a library allowing the computation of any elementary matrix (even for mixed finite element methods) on the largest class of methods and elements, and for arbitrary dimension (i.e. not only 2D and 3D problems). " what's more interesting is this library can be linked easily to Matlab.

We know Finite Element method is an alternative to Finite Difference discretization of the BS and other equations in the price resp. the log-price space variable. The advantage of FE is that it gives convergent deterministic approximations of the option price under realistic, low smoothness assumptions on the payoff function, as e.g. for binary contracts and in particular allow a higher rate of convergence that that achievable with Monte Carlo simulations.

To get a deeper insight on and download open source Getfem++ please be at http://home.gna.org/getfem/
wiki(Finite element)

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