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Total value adjustment of Bermudan option valuation under pure jump Lévy fluctuations
Yuan, Gangnan1; Ding, Deng1; Duan, Jinqiao2; Lu, Weiguo1; Wu, Fengyan1,3
2022-02-01
Source PublicationChaos
ISSN1054-1500
Volume32Issue:2
Abstract

During the COVID-19 pandemic, many institutions have announced that their counterparties are struggling to fulfill contracts. Therefore, it is necessary to consider the counterparty default risk when pricing options. After the 2008 financial crisis, a variety of value adjustments have been emphasized in the financial industry. The total value adjustment (XVA) is the sum of multiple value adjustments, which is also investigated in many stochastic models, such as the Heston [B. Salvador and C. W. Oosterlee, Appl. Math. Comput. 391, 125489 (2020)] and Bates [L. Goudenège et al., Comput. Manag. Sci. 17, 163-178 (2020)] models. In this work, a widely used pure jump Lévy process, the Carr-Geman-Madan-Yor process has been considered for pricing a Bermudan option with various value adjustments. Under a pure jump Lévy process, the value of derivatives satisfies a fractional partial differential equation (FPDE). Therefore, we construct a method that combines Monte Carlo with a finite difference of FPDE to find the numerical approximation of exposure and compare it with the benchmark Monte Carlo simulation and Fourier-cosine series method. We use the discrete energy estimate method, which is different from the existing works, to derive the convergence of the numerical scheme. Based on the numerical results, the XVA is computed by the financial exposure of the derivative value.

DOI10.1063/5.0072500
URLView the original
Indexed BySCIE ; SSCI
Language英語English
WOS Research AreaMathematics ; Physics
WOS SubjectMathematics, Applied ; Physics, Mathematical
WOS IDWOS:000761046800005
Scopus ID2-s2.0-85125561553
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Department of Mathematics, University of Macau, 999078, Macao
2.Department of Applied Mathematics, Illinois Institute of Technology, Chicago, 60616, United States
3.College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Yuan, Gangnan,Ding, Deng,Duan, Jinqiao,et al. Total value adjustment of Bermudan option valuation under pure jump Lévy fluctuations[J]. Chaos,2022,32(2).
APA Yuan, Gangnan,Ding, Deng,Duan, Jinqiao,Lu, Weiguo,&Wu, Fengyan.(2022).Total value adjustment of Bermudan option valuation under pure jump Lévy fluctuations.Chaos,32(2).
MLA Yuan, Gangnan,et al."Total value adjustment of Bermudan option valuation under pure jump Lévy fluctuations".Chaos 32.2(2022).
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