Rapid
Numerical Solution of Jump Diffusion Models
Masterarbeit Wirtschaftsmathematik
Master's Thesis in Financial Mathematics, Halmstad University, Sweden
Supervision
Description
In this thesis we discuss the proper numerical treatment of
partial integro differential equations (PIDE) that appear as
pricing equations for options on assets that follow jump-diffusion processes.
Usually these PIDEs need a high computational effort due to the involved
integrals.
Although Fast Fourier Transform (FFT) methods (pioneered by Andersen and Andreasen [1])
can be applied to evaluate these jump-integrals, the usage of the FFT induces
additional errors such that the jump integral must be discretized on a much finer grid
than the one for the differential operators (cf. Y. d'Halluin et al.).
Moreover, usually implicit time stepping methods are considered and hence
the FFT is inside some iterative solution procedure (i.e. a micro-iteration)
which makes the benefits using the FFT relatively small.
Consequently, in this thesis we will present alternative approaches without
using a FFT.
Keywords
Option Pricing, Stochastic Volatility, Lévy Processes, Bates Model,
operator splitting technique, Jump-diffusion process,
finite elements,
nonlinear partial integro differential equation (PIDE)
References:
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