Finite Volume Schemes for Solving Nonlinear Partial Differential Equations in Financial Mathematics

Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 4)

Abstract

In order to estimate a fair value of financial derivatives, various generalizations of the classical linear Black–Scholes parabolic equation have been made by adjusting the constant volatility to be a function of the option price itself. We present a second order numerical scheme, based on the finite volume method discretization, for solving the so–called Gamma equation of the Risk Adjusted Pricing Methodology (RAPM) model. Our new approach is based on combination of the fully implicit and explicit schemes where we solve the system of nonlinear equations by iterative application of the semi–implicit approach. Presented numerical experiments show its second order accuracy for the RAPM model as well as for the test with exact Barenblatt solution of the porous–medium equation which has a similar character as the Gamma equation.

Keywords

finite volume method second-order scheme financial mathematics 

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Notes

Acknowledgements

This work was supported by grants APVV–0351–07 and VEGA 1/0733/10.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of MathematicsSlovak University of TechnologyBratislavaSlovak Republic

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