UM  > Faculty of Science and Technology  > DEPARTMENT OF MATHEMATICS
Affiliated with RCfalse
Total value adjustment of Bermudan option valuation under pure jump Lévy fluctuations
Yuan, Gangnan1; Ding, Deng1; Duan, Jinqiao2; Lu, Weiguo1; Wu, Fengyan1,3
Source PublicationChaos

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.

URLView the original
Indexed BySCIE ; SSCI
WOS Research AreaMathematics ; Physics
WOS SubjectMathematics, Applied ; Physics, Mathematical
WOS IDWOS:000761046800005
Scopus ID2-s2.0-85125561553
Fulltext Access
Citation statistics
Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
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).
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Yuan, Gangnan]'s Articles
[Ding, Deng]'s Articles
[Duan, Jinqiao]'s Articles
Baidu academic
Similar articles in Baidu academic
[Yuan, Gangnan]'s Articles
[Ding, Deng]'s Articles
[Duan, Jinqiao]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Yuan, Gangnan]'s Articles
[Ding, Deng]'s Articles
[Duan, Jinqiao]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.