Cross Currency Valuation and Hedging in the Multiple Curve Framework

42 Pages Posted: 25 Feb 2020 Last revised: 16 Mar 2021

See all articles by Alessandro Gnoatto

Alessandro Gnoatto

University of Verona - Department of Economics

Nicole Seiffert

affiliation not provided to SSRN

Date Written: March 16, 2021

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 Fuji et al (2010).

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.

Keywords: FX, cross-currency basis, multiple curves, FVA, CollVA, Basel III, Collateral

JEL Classification: E43, G12

Suggested Citation

Gnoatto, Alessandro and Seiffert, Nicole, Cross Currency Valuation and Hedging in the Multiple Curve Framework (March 16, 2021). Available at SSRN: https://ssrn.com/abstract=3528307 or http://dx.doi.org/10.2139/ssrn.3528307

Alessandro Gnoatto (Contact Author)

University of Verona - Department of Economics ( email )

Via dell'Artigliere, 8
37129 Verona
Italy

Nicole Seiffert

affiliation not provided to SSRN

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