Arbitrage‐Free Bilateral Counterparty Risk Valuation Under Collateralization and Application to Credit Default Swaps

22 Pages Posted: 13 Dec 2013

See all articles by Damiano Brigo

Damiano Brigo

Imperial College London - Department of Mathematics

Agostino Capponi

Columbia University

Andrea Pallavicini

Banca IMI; Imperial College London - Department of Mathematics

Date Written: January 2014

Abstract

We develop an arbitrage‐free valuation framework for bilateral counterparty risk, where collateral is included with possible rehypothecation. We show that the adjustment is given by the sum of two option payoff terms, where each term depends on the netted exposure, i.e., the difference between the on‐default exposure and the predefault collateral account. We then specialize our analysis to credit default swaps (CDS) as underlying portfolios, and construct a numerical scheme to evaluate the adjustment under a doubly stochastic default framework. In particular, we show that for CDS contracts a perfect collateralization cannot be achieved, even under continuous collateralization, if the reference entity’s and counterparty’s default times are dependent. The impact of rehypothecation, collateral margining frequency, and default correlation‐induced contagion is illustrated with numerical examples.

Keywords: counterparty risk, CVA, bilateral CVA, arbitrage‐free credit valuation adjustment, credit default swaps, credit spread volatility, default correlation, contagion, stochastic intensity, collateral margining, netting, rehypotecation, wrong way risk

Suggested Citation

Brigo, Damiano and Capponi, Agostino and Pallavicini, Andrea, Arbitrage‐Free Bilateral Counterparty Risk Valuation Under Collateralization and Application to Credit Default Swaps (January 2014). Mathematical Finance, Vol. 24, Issue 1, pp. 125-146, 2014. Available at SSRN: https://ssrn.com/abstract=2367078 or http://dx.doi.org/10.1111/j.1467-9965.2012.00520.x

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

Agostino Capponi

Columbia University ( email )

S. W. Mudd Building
New York, NY 10027
United States

Andrea Pallavicini

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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