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Title: Option valuation under the VG process by a DG method (English)
Author: Hozman, Jiří
Author: Tichý, Tomáš
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 66
Issue: 6
Year: 2021
Pages: 857-886
Summary lang: English
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Category: math
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Summary: The paper presents a discontinuous Galerkin method for solving partial integro-differential equations arising from the European as well as American option pricing when the underlying asset follows an exponential variance gamma process. For practical purposes of numerical solving we introduce the modified option pricing problem resulting from a localization to a bounded domain and an approximation of small jumps, and we discuss the related error estimates. Then we employ a robust numerical procedure based on piecewise polynomial generally discontinuous approximations in the spatial domain. This technique enables a simple treatment of the American early exercise constraint by a direct encompassing it as an additional nonlinear source term to the governing equation. Special attention is paid to the proper discretization of non-local jump integral components, which is based on splitting integrals with respect to the domain according to the size of the jumps. Moreover, to preserve sparsity of resulting linear algebraic systems the pricing equation is integrated in the temporal variable by a semi-implicit Euler scheme. Finally, the numerical results demonstrate the capability of the numerical scheme presented within the reference benchmarks.\looseness -1 (English)
Keyword: option pricing
Keyword: variance gamma process
Keyword: integro-differential equation
Keyword: American style options
Keyword: discontinuous Galerkin method
Keyword: semi-implicit discretization
MSC: 35Q91
MSC: 65M15
MSC: 65M60
MSC: 91G60
MSC: 91G80
idZBL: Zbl 07442410
idMR: MR4342612
DOI: 10.21136/AM.2021.0345-20
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Date available: 2021-11-18T15:27:51Z
Last updated: 2024-01-01
Stable URL: http://hdl.handle.net/10338.dmlcz/149267
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