Penalty methods for bilateral XVA pricing in European and American contingent claims by a partial differential equation model

Yuwei Chen and Christina C. Christara

Journal of Computational Finance

Abstract: Accounting for default risk in the valuation of financial derivatives has become increasingly important, especially since the 2007–8 financial crisis. Under some assumptions, the valuation of financial derivatives, including a value adjustment to account for default risk (the so-called XVA), gives rise to a nonlinear partial differential equation (PDE). We propose numerical methods for handling the nonlinearity in this PDE, the most efficient of which are the discrete penalty iteration methods. We first formulate a penalty iteration method for the case of European contingent claims and study its convergence. We then extend the method to the case of American contingent claims, which results in a double-penalty iteration. We also propose boundary conditions and their discretization for the XVA PDE problem in the case of a call option, a put option and a forward contract. Numerical results demonstrate the effectiveness of our methods.

References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.risk.net/journal-of-computational-fina ... ntial-equation-model (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:rsk:journ0:7814116

Access Statistics for this article

More articles in Journal of Computational Finance from Journal of Computational Finance
Bibliographic data for series maintained by Thomas Paine ().