Impact of Multiple Curve Dynamics in Credit Valuation Adjustments under Collateralization

28 Pages Posted: 31 Jul 2015 Last revised: 14 Sep 2015

See all articles by Giacomo Bormetti

Giacomo Bormetti

University of Bologna - Department of Mathematics

Damiano Brigo

Imperial College London - Department of Mathematics

Marco Francischello

Imperial College London - Department of Mathematics

Andrea Pallavicini

Banca IMI; Imperial College London - Department of Mathematics

Date Written: September 13, 2015

Abstract

We present a detailed analysis of interest rate derivatives valuation under credit risk and collateral modeling. We show how the credit and collateral extended valuation framework in Pallavicini et al (2011), and the related collateralized valuation measure, can be helpful in defining the key market rates underlying the multiple interest rate curves that characterize current interest rate markets. A key point is that spot Libor rates are to be treated as market primitives rather than being defined by no-arbitrage relationships. We formulate a consistent realistic dynamics for the different rates emerging from our analysis and compare the resulting model performances to simpler models used in the industry. We include the often neglected margin period of risk, showing how this feature may increase the impact of different rates dynamics on valuation. We point out limitations of multiple curve models with deterministic basis considering valuation of particularly sensitive products such as basis swaps. We stress that a proper wrong way risk analysis for such products requires a model with a stochastic basis and we show numerical results confirming this fact.

Keywords: Yield Curve Dynamics, Multiple Curve Framework, HJM Framework, Interest Rate Derivatives, Basis Swaps, Counterparty Credit Risk, Liquidity Risk, Funding Costs, Collateral Modeling, Overnight Rates

JEL Classification: G13

Suggested Citation

Bormetti, Giacomo and Brigo, Damiano and Francischello, Marco and Pallavicini, Andrea, Impact of Multiple Curve Dynamics in Credit Valuation Adjustments under Collateralization (September 13, 2015). Available at SSRN: https://ssrn.com/abstract=2638229 or http://dx.doi.org/10.2139/ssrn.2638229

Giacomo Bormetti

University of Bologna - Department of Mathematics ( email )

Piazza di Porta S. Donato , 5
Bologna, Bologna 40126
Italy

Damiano Brigo

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www.imperial.ac.uk/people/damiano.brigo

Marco Francischello

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

Andrea Pallavicini (Contact Author)

Banca IMI ( email )

Largo Mattioli 3
Milan, MI 20121
Italy
+39 02 7261 (Phone)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

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