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. Especially we discuss the numerical treatment of the case of small volatility, i.e. the convection dominated case. 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, Il'in scheme, Scharfetter-Gummer scheme, El-Mistikawy-Werle scheme, partial exponential fitting, complete exponential fitting

References:

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