Abstract

http://ssrn.com/abstract=1318024
 
 

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


Damiano Brigo


Imperial College London - Department of Mathematics; Capco

Agostino Capponi


Columbia University

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.

Number of Pages in PDF File: 32

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

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Date posted: December 19, 2008 ; Last revised: November 19, 2009

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: http://ssrn.com/abstract=1318024 or http://dx.doi.org/10.2139/ssrn.1318024

Contact Information

Damiano Brigo
Imperial College London - Department of Mathematics ( email )
South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom
HOME PAGE: http://www.damianobrigo.it
Capco ( email )
120 Broadway, 15th Floor
New York, NY 10271
United States
HOME PAGE: http://www.capco.com/capco-insights
Agostino Capponi (Contact Author)
Columbia University ( email )
S. W. Mudd Building
New York, NY 10027
United States
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