Collateralization and Funding Valuation Adjustments (FVA) for Total Return Swaps and Forward Contracts

34 Pages Posted: 2 Jun 2014 Last revised: 8 Aug 2016

See all articles by Christian P. Fries

Christian P. Fries

Ludwig Maximilian University of Munich - Faculty of Mathematics; DZ Bank AG

Mark Lichtner

Independent

Date Written: May 7, 2016

Abstract

In this paper we consider the valuation of total return swaps (TRS). Since a total return swap is a collateralized derivative referencing the value process of an uncollateralized asset it is in general not possible that both counter parties agree on a unique value. Consequently it is not possible to have cash collateralization of the total return swap matching each counterparts valuation. The total return swap is a collateralized derivative with a natural funding valuation adjustment.

We develop a model for valuation and risk management of TRS where we assume that collateral is posted according to the mid average (or convex combination) of the valuations performed by both counterparts. This results in a coupled and recursive system of equations for the valuation of the TRS.

The main result of the paper is that we can provide explicit formulas for the collateral and the FVA, eliminating the recursiveness which is naturally encountered in such formulas, by assuming a natural collateralization scheme.

Although the paper focuses on total return swaps, the principles developed here are generally applicable in situations where collateralized assets reference uncollaterlized or partially collateralized underlings.

Keywords: Funding Valuation Adjustments, FVA, Collateralization, Repo

JEL Classification: G13, G12

Suggested Citation

Fries, Christian P. and Lichtner, Mark, Collateralization and Funding Valuation Adjustments (FVA) for Total Return Swaps and Forward Contracts (May 7, 2016). Available at SSRN: https://ssrn.com/abstract=2444452 or http://dx.doi.org/10.2139/ssrn.2444452

Christian P. Fries (Contact Author)

Ludwig Maximilian University of Munich - Faculty of Mathematics ( email )

Theresienstrasse 39
Munich
Germany

DZ Bank AG ( email )

60265 Frankfurt am Main
Germany

Mark Lichtner

Independent ( email )

No Address Available

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