Cross Currency Valuation and Hedging in the Multiple Curve Framework

Alessandro Gnoatto and Nicole Seiffert

Papers from arXiv.org

Abstract: We generalize the results of Bielecki and Rutkowski (2015) on funding and collateralization to a multi-currency framework and link their results with those of Piterbarg (2012), Moreni and Pallavicini (2017), and Fujii et al. (2010b). In doing this, we provide a complete study of absence of arbitrage in a multi-currency market where, in each single monetary area, multiple interest rates coexist. We first characterize absence of arbitrage in the case without collateral. After that we study collateralization schemes in a very general situation: the cash flows of the contingent claim and those associated to the collateral agreement can be specified in any currency. We study both segregation and rehypothecation and allow for cash and risky collateral in arbitrary currency specifications. Absence of arbitrage and pricing in the presence of collateral are discussed under all possible combinations of conventions. Our work provides a reference for the analysis of wealth dynamics, we also provide valuation formulas that are a useful foundation for cross-currency curve construction techniques. Our framework provides also a solid foundation for the construction of multi-currency simulation models for the generation of exposure profiles in the context of xVA calculations.

Date: 2020-01, Revised 2021-03
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Published in SIAM Journal on Financial Mathematics (2021) forthcoming

Downloads: (external link)
http://arxiv.org/pdf/2001.11012 Latest version (application/pdf)

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:arx:papers:2001.11012

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().