The Gibbs phenomenon in option pricing methods

Filtering and other techniques applied to the COS method

Master thesis (2012)

Authors

Contributors

C.W. Oosterlee (mentor)
M.J. Ruijter (mentor)
Programme
Numerical analysis (EEMCS) (TU Delft)
Copyright: © 2012 Versteegh, M.
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Published Date

10-10-2012

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Programme

Numerical analysis

Abstract

There are situations in which the COS method for option pricing has relatively slow convergence as a consequence of the Gibbs phenomenon. This thesis focusses on various methods to improve the convergence rate of the so called spectral methods. Note that we are not just interested in an accurate recovery, but that we also want to be able to perform fast option pricing, so the computational costs should remain relatively low. After a brief description of a wide range of possibilities some of the more promising methods for our subject are analyzed. After discussing the possible improvement methods, we test them in practical situations such as density recovery and option pricing for some popular financial models.