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
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
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