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Credit Default Swap Calibration and Counterparty Risk Valuation with a Scenario based First Passage Model

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  • Damiano Brigo
  • Marco Tarenghi

Abstract

In this work we develop a tractable structural model with analytical default probabilities depending on a random default barrier and possibly random volatility ideally associated with a scenario based underlying firm debt. We show how to calibrate this model using a chosen number of reference Credit Default Swap (CDS) market quotes. In general this model can be seen as a possible extension of the time-varying AT1P model in Brigo and Tarenghi (2004). The calibration capability of the Scenario Volatility/Barrier model (SVBAT1P), when keeping time-constant volatility, appears inferior to the one of AT1P with time-varying deterministic volatility. The SVBAT1P model, however, maintains the benefits of time-homogeneity and can lead to satisfactory calibration results, as we show in a case study where we compare different choices on scenarios and parameters. Similarly to AT1P, SVBAT1P is suited to pricing hybrid equity/credit derivatives and to evaluate counterparty risk in equity payoffs, and more generally to evaluate hybrid credit/equity payoffs. We consider the equity return swap in Brigo and Tarenghi (2004) and show its valuation under SVBAT1P with the same CDS and equity calibration input used earlier for AT1P, and further we hint at equity default swap valuation in the conclusions.

Suggested Citation

  • 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.
  • Handle: RePEc:arx:papers:0912.3031
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    File URL: http://arxiv.org/pdf/0912.3031
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    References listed on IDEAS

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    1. C. F. Lo & H. C. Lee & C. H. Hui, 2003. "A simple approach for pricing barrier options with time-dependent parameters," Quantitative Finance, Taylor & Francis Journals, vol. 3(2), pages 98-107.
    2. Fisher, Lawrence, 1984. " Contingent Claims Analysis of Corporate Capital Structures: An Empirical Investigation," Journal of Finance, American Finance Association, vol. 39(3), pages 625-627, July.
    3. Damiano Brigo & Marco Tarenghi, 2009. "Credit Default Swap Calibration and Equity Swap Valuation under Counterparty Risk with a Tractable Structural Model," Papers 0912.3028, arXiv.org.
    4. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    5. Jones, E Philip & Mason, Scott P & Rosenfeld, Eric, 1984. " Contingent Claims Analysis of Corporate Capital Structures: An Empirical Investigation," Journal of Finance, American Finance Association, vol. 39(3), pages 611-625, July.
    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 351-367, May.
    7. 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.
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    Cited by:

    1. Chen, Chang-Chih & Shyu, So-De & Yang, Chih-Yuan, 2011. "Counterparty effects on capital structure decision in incomplete market," Economic Modelling, Elsevier, vol. 28(5), pages 2181-2189, September.
    2. 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.
    3. Campi, Luciano & Polbennikov, Simon & Sbuelz, Alessandro, 2009. "Systematic equity-based credit risk: A CEV model with jump to default," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 93-108, January.
    4. 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.

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