IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0912.4404.html
   My bibliography  Save this paper

Credit Calibration with Structural Models: The Lehman case and Equity Swaps under Counterparty Risk

Author

Listed:
  • Damiano Brigo
  • Massimo Morini
  • Marco Tarenghi

Abstract

In this paper we develop structural first passage models (AT1P and SBTV) with time-varying volatility and characterized by high tractability, moving from the original work of Brigo and Tarenghi (2004, 2005) [19] [20] and Brigo and Morini (2006)[15]. The models can be calibrated exactly to credit spreads using efficient closed-form formulas for default probabilities. Default events are caused by the value of the firm assets hitting a safety threshold, which depends on the financial situation of the company and on market conditions. In AT1P this default barrier is deterministic. Instead SBTV assumes two possible scenarios for the initial level of the default barrier, for taking into account uncertainty on balance sheet information. While in [19] and [15] the models are analyzed across Parmalat's history, here we apply the models to exact calibration of Lehman Credit Default Swap (CDS) data during the months preceding default, as the crisis unfolds. The results we obtain with AT1P and SBTV have reasonable economic interpretation, and are particularly realistic when SBTV is considered. The pricing of counterparty risk in an Equity Return Swap is a convenient application we consider, also to illustrate the interaction of our credit models with equity models in hybrid products context.

Suggested Citation

  • 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.
  • Handle: RePEc:arx:papers:0912.4404
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0912.4404
    File Function: Latest version
    Download Restriction: no

    References listed on IDEAS

    as
    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. Briys, Eric & de Varenne, François, 1997. "Valuing Risky Fixed Rate Debt: An Extension," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 32(02), pages 239-248, June.
    3. 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.
    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. 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.
    6. 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.
    7. Pierre Collin-Dufresne, 2001. "Do Credit Spreads Reflect Stationary Leverage Ratios?," Journal of Finance, American Finance Association, vol. 56(5), pages 1929-1957, October.
    8. Damiano Brigo, 2008. "Constant Maturity Credit Default Swap Pricing with Market Models," Papers 0812.4159, arXiv.org.
    9. Damiano Brigo & Agostino Capponi, 2008. "Bilateral counterparty risk valuation with stochastic dynamical models and application to Credit Default Swaps," Papers 0812.3705, arXiv.org, revised Nov 2009.
    10. Damiano Brigo & Naoufel El-Bachir, 2007. "An exact formula for default swaptions’ pricing in the SSRJD stochastic intensity model," ICMA Centre Discussion Papers in Finance icma-dp2007-14, Henley Business School, Reading University.
    11. 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.
    12. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:0912.4404. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators). General contact details of provider: http://arxiv.org/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.