Bilateral Counterparty Risk Valuation with Stochastic Dynamical Models and Application to Credit Default Swaps

32 Pages Posted: 19 Dec 2008 Last revised: 19 Nov 2009

Damiano Brigo

Imperial College London - Department of Mathematics

Agostino Capponi

Columbia University

Date Written: November 17, 2009

Abstract

We introduce the general arbitrage-free valuation framework for counterparty risk adjustments in presence of bilateral default risk, including default of the investor. We illustrate the symmetry in the valuation and show that the adjustment involves a long position in a put option plus a short position in a call option, both with zero strike and written on the residual net value of the contract at the relevant default times. We allow for correlation between the default times of the investor, counterparty and underlying portfolio risk factors. We use arbitrage-free stochastic dynamical models. We then specialize our analysis to Credit Default Swaps (CDS) as underlying portfolio, generalizing the work of Brigo and Chourdakis (2008) [5] who deal with unilateral and asymmetric counterparty risk. We introduce stochastic intensity models and a trivariate copula function on the default times exponential variables to model default dependence. Similarly to [5], we find that both default correlation and credit spread volatilities have a relevant and structured impact on the adjustment. Differently from [5], the two parties will now agree on the credit valuation adjustment. We study a case involving British Airways, Lehman Brothers and Royal Dutch Shell, illustrating the bilateral adjustments in concrete crisis situations.

Keywords: Counterparty Risk, Arbitrage-Free Credit Valuation Adjustment, Credit Default Swaps, Contingent Credit Default Swaps, Credit Spread Volatility, Default Correlation, Stochastic Intensity, Copula Functions, Wrong Way Risk

JEL Classification: C15, C63, C65, G12, G13

Suggested Citation

Brigo, Damiano and Capponi, Agostino, Bilateral Counterparty Risk Valuation with Stochastic Dynamical Models and Application to Credit Default Swaps (November 17, 2009). Available at SSRN: https://ssrn.com/abstract=1318024 or http://dx.doi.org/10.2139/ssrn.1318024

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 (Contact Author)

Columbia University ( email )

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

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