Pricing early-exercise and discrete barrier options by Shannon wavelet expansions

S. C. Maree; Luis Ortiz-Gracia; C.W. Oosterlee

doi:10.1007/s00211-016-0858-2

Pricing early-exercise and discrete barrier options by Shannon wavelet expansions

S. C. Maree^*, Luis Ortiz-Gracia, C.W. Oosterlee

^*Corresponding author for this work

Numerical Analysis

Research output: Contribution to journal › Article › Scientific › peer-review

18 Citations (Scopus)

Abstract

We present a pricing method based on Shannon wavelet expansions for early-exercise and discretely-monitored barrier options under exponential Lévy asset dynamics. Shannon wavelets are smooth, and thus approximate the densities that occur in finance well, resulting in exponential convergence. Application of the Fast Fourier Transform yields an efficient implementation and since wavelets give local approximations, the domain boundary errors can be naturally resolved, which is the main improvement over existing methods.

Original language	English
Pages (from-to)	1035-1070
Number of pages	36
Journal	Numerische Mathematik
Volume	136
Issue number	4
DOIs	https://doi.org/10.1007/s00211-016-0858-2
Publication status	Published - 2017

Keywords

65D30
91B24
65T60

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10.1007/s00211-016-0858-2

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abstract = "We present a pricing method based on Shannon wavelet expansions for early-exercise and discretely-monitored barrier options under exponential L{\'e}vy asset dynamics. Shannon wavelets are smooth, and thus approximate the densities that occur in finance well, resulting in exponential convergence. Application of the Fast Fourier Transform yields an efficient implementation and since wavelets give local approximations, the domain boundary errors can be naturally resolved, which is the main improvement over existing methods.",

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AU - Ortiz-Gracia, Luis

AU - Oosterlee, C.W.

PY - 2017

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N2 - We present a pricing method based on Shannon wavelet expansions for early-exercise and discretely-monitored barrier options under exponential Lévy asset dynamics. Shannon wavelets are smooth, and thus approximate the densities that occur in finance well, resulting in exponential convergence. Application of the Fast Fourier Transform yields an efficient implementation and since wavelets give local approximations, the domain boundary errors can be naturally resolved, which is the main improvement over existing methods.

AB - We present a pricing method based on Shannon wavelet expansions for early-exercise and discretely-monitored barrier options under exponential Lévy asset dynamics. Shannon wavelets are smooth, and thus approximate the densities that occur in finance well, resulting in exponential convergence. Application of the Fast Fourier Transform yields an efficient implementation and since wavelets give local approximations, the domain boundary errors can be naturally resolved, which is the main improvement over existing methods.

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Pricing early-exercise and discrete barrier options by Shannon wavelet expansions

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Keywords

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