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Bilateral counterparty risk valuation with stochastic dynamical models and application to Credit Default Swaps

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  • Damiano Brigo
  • Agostino Capponi

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.

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File URL: http://arxiv.org/pdf/0812.3705
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 0812.3705.

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Date of creation: Dec 2008
Date of revision: Nov 2009
Handle: RePEc:arx:papers:0812.3705

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Web page: http://arxiv.org/

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Cited by:
  1. Damiano Brigo & Mirela Predescu & Agostino Capponi, 2010. "Credit Default Swaps Liquidity modeling: A survey," Papers 1003.0889, arXiv.org, revised Mar 2010.
  2. Damiano Brigo & Massimo Morini & Marco Tarenghi, 2009. "Credit Calibration with Structural Models: The Lehman case and Equity Swaps under Counterparty Risk," Papers 0912.4404, arXiv.org.
  3. Guglielmo D'Amico & Raimondo Manca & Giovanni Salvi, 2011. "Bivariate Semi-Markov Process for Counterparty Credit Risk," Papers 1112.0226, arXiv.org, revised Oct 2012.
  4. Li, Hui, 2009. "Double Impact on CVA for CDS: Wrong-Way Risk with Stochastic Recovery," MPRA Paper 19684, University Library of Munich, Germany.
  5. Damiano Brigo & Cristin Buescu & Massimo Morini, 2011. "Impact of the first to default time on Bilateral CVA," Papers 1106.3496, arXiv.org.
  6. Biffis, Enrico & Blake, David & Pitotti, Lorenzo & Sun, Ariel, 2011. "The cost of counterparty risk and collateralization in longevity swaps," MPRA Paper 35740, University Library of Munich, Germany.
  7. Damiano Brigo, 2011. "Counterparty Risk FAQ: Credit VaR, PFE, CVA, DVA, Closeout, Netting, Collateral, Re-hypothecation, WWR, Basel, Funding, CCDS and Margin Lending," Papers 1111.1331, arXiv.org, revised Jun 2012.
  8. Ying Jiao & Huyên Pham, 2011. "Optimal investment with counterparty risk: a default-density model approach," Finance and Stochastics, Springer, vol. 15(4), pages 725-753, December.
  9. Damiano Brigo & Andrea Pallavicini & Vasileios Papatheodorou, 2009. "Bilateral counterparty risk valuation for interest-rate products: impact of volatilities and correlations," Papers 0911.3331, arXiv.org, revised Feb 2010.

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