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

Fries, Christian P. and Lichtner, Mark (2014): Collateralization and Funding Valuation Adjustments (FVA) for Total Return Swaps. SSRN

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.

• Item Type: Paper
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Workgroup Financial Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1556-5068
• Language: English