Bergische Universität Wuppertal Fachbereich Mathematik und Naturwissenschaften Angewandte Mathematik - Numerische Analysis

People Research Publications Teaching

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An Exponentially Fitted Finite Volume Method for the Numerical Pricing of Options under Jump Diffusion Processes

Masterarbeit Wirtschaftsmathematik

Master's Thesis in Financial Mathematics, Halmstad University, Sweden

Supervision

• Prof. Dr. Matthias Ehrhardt

Description

In this thesis we investigate a new strategy of Zhang and Wang to construct exponentially fitted finite volume schemes. We apply this approach in the context of options under jump diffusion processes and certain nonlinear Black-Scholes equations, e.g. modeling transactions costs. The results are compared with the point-distributed finite volume scheme of Zvan, Vetzal and Forsyth.

Keywords

Option pricing, Finite volume method, Exponential Fitting, nonlinear partial integro differential equation

References:

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3. D.J. Duffy, Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach, John Wiley & Sons, Chichester, 2006.
4. C.-S. Huang, C.-H. Hung and S. Wang, A fitted finite volume method for the valuation of options on assets with stochastic volatilities, Computing 77 (2006), 297-320.
5. J.J.H. Miller and S. Wang, A new non-conforming Petrov-Galerkin method with triangular elements for a singularly perturbed advection-diffusion problem, IMA J. Numer. Anal. 14 (1994), 257-276.
6. J.J.H. Miller and S. Wang, An exponentially fitted finite element volume method for the numerical solution of 2D unsteady incompressible flow problems, J. Comput. Phys. 115 (1994), 56-64.
7. S. Wang, A novel fitted finite volume method for the Black-Scholes equation governing option pricing, IMA J. Numer. Anal. 24 (2004), 699-720.
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9. K. Zhang and S. Wang, A computational scheme for uncertain volatility model in option pricing, Appl. Numer. Math. 59 (2009), 1754-1767.
10. R. Zvan, K.R. Vetzal and P.A. Forsyth, PDE methods for pricing barrier options, J. Economic Dynamics & Control 24 (2000), 1563-1590.