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Pseudospectral Symbolic Computation for Financial Models

F.O. Bunnin
Y. Ren
Y. Guo
J. Darlington

1999 International Mathematica Symposium

The modelling of financial markets as continuous stochastic processes provides the means to analyse the implications of models and to compute prices for a host of financial instruments. We code as a symbolic computing program the analysis, initiated by Black, Scholes and Merton, of the formation of a partial differential equation whose solution is the value of a derivative security, from the specifcation of an undelying security's process. The Pseudospectral method is a high order solution method for partial differential equations that approximates the solution by global basis functions. We apply symbolic transformations and approximating rewrite rules to extract essential information for the Pseudospectral Chebyshev solution. We write these programs in Mathematica. Our C++ template implementing general solver code is parameterised with this information to create instrument and model specific pricing code. The Black-Scholes model and the Cox Ingersoll Ross term structure model are used as examples.

*Business and Economics

financial markets, stochastic processes, Black, Scholes, Merton, Pseudospectral method, global basis functions, Pseudospectral Chebyshev solution, Black-Scholes model, Cox Ingersoll Ross term structure model