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Credit Default Swap Calibration and Equity Swap Valuation under Counterparty Risk with a Tractable Structural Model

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  • Damiano Brigo
  • Marco Tarenghi

Abstract

In this paper we develop a tractable structural model with analytical default probabilities depending on some dynamics parameters, and we show how to calibrate the model using a chosen number of Credit Default Swap (CDS) market quotes. We essentially show how to use structural models with a calibration capability that is typical of the much more tractable credit-spread based intensity models. We apply the structural model to a concrete calibration case and observe what happens to the calibrated dynamics when the CDS-implied credit quality deteriorates as the firm approaches default. Finally we provide a typical example of a case where the calibrated structural model can be used for credit pricing in a much more convenient way than a calibrated reduced form model: The pricing of counterparty risk in an equity swap.

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File URL: http://arxiv.org/pdf/0912.3028
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 0912.3028.

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Date of creation: Dec 2009
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Handle: RePEc:arx:papers:0912.3028

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Web page: http://arxiv.org/

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References

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  1. Merton, Robert C., 1973. "On the pricing of corporate debt: the risk structure of interest rates," Working papers 684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  2. Damiano Brigo & Aurélien Alfonsi, 2005. "Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model," Finance and Stochastics, Springer, vol. 9(1), pages 29-42, January.
  3. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
  4. Damiano Brigo, 2008. "Constant Maturity Credit Default Swap Pricing with Market Models," Papers 0812.4159, arXiv.org.
  5. Crouhy, Michel & Galai, Dan & Mark, Robert, 2000. "A comparative analysis of current credit risk models," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 59-117, January.
  6. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-67, May.
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Cited by:
  1. Damiano Brigo & Marco Tarenghi, 2009. "Credit Default Swap Calibration and Counterparty Risk Valuation with a Scenario based First Passage Model," Papers 0912.3031, arXiv.org.
  2. Campi, L. & Polbennikov, S.Y. & Sbuelz, A., 2005. "Assessing Credit with Equity: A CEV Model with Jump to Default," Discussion Paper 2005-27, Tilburg University, Center for Economic Research.
  3. Damiano Brigo & Jo\~ao Garcia & Nicola Pede, 2013. "CoCo Bonds Valuation with Equity- and Credit-Calibrated First Passage Structural Models," Papers 1302.6629, arXiv.org.
  4. Luciano Campi & Simon Polbennikov & Sbuelz, 2005. "Assessing Credit with Equity: A CEV Model with Jump to Default," Working Papers 24, University of Verona, Department of Economics.
  5. Sukhomlin, Nikolay & Santana Jiménez, Lisette Josefina, 2010. "Problema de calibración de mercado y estructura implícita del modelo de bonos de Black-Cox = Market Calibration Problem and the Implied Structure of the Black-Cox Bond Model," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 10(1), pages 73-98, December.
  6. 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.
  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. 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.
  9. Campi, L. & Sbuelz, A., 2005. "Close-Form Pricing of Benchmark Equity Default Swaps Under the CEV Assumption," Discussion Paper 2005-28, Tilburg University, Center for Economic Research.

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