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On the Pricing of Credit Spread Options: A Two Factor HW–BK Algorithm

Author

Listed:
  • Joao B. C. Garcia

    (Senior Quantitative Analyst, Risk Methodology, Dexia Holding, Square de Meeus 1, B-1012 Brussels, Belgium)

  • Helmut van Ginderen

    (Risk Methodology, Dexia Bank, Galileilaan 5, B-1012 Brussels, Belgium)

  • Reinaldo C. Garcia

    (Department Energy, Transportation and Environment, DIW - Deutsches Institut fur Wirtschaftsforschung, Königin Luise-Straβe 5, D 14195 Berlin, Germany)

Abstract

In this article we describe what a credit spread option (CSO) is and show a tree algorithm to price it. The tree algorithm we have opted for is a two factor model composed by a Hull and White (HW) one factor for the interest rate process and a Black-Karazinsky (BK) one factor for the default intensity. As opposed to the tree model of Schonbucher 1999 the intensity process cannot become negative. Having as input the risk free yield curve and market implied default probability curve the model by construction will price correctly the associated defaultable bond. We then use Market data to calibrate the model to price an at the money (ATM) CSO call and then test it to price an out of the money (OTM) Bermudan CSO call on a CDS. Furthermore the discussions in this paper show in practice the difficulties and challenges faced by financial institutions in marking to market those instruments.

Suggested Citation

  • Joao B. C. Garcia & Helmut van Ginderen & Reinaldo C. Garcia, 2003. "On the Pricing of Credit Spread Options: A Two Factor HW–BK Algorithm," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(05), pages 491-505.
    • Handle: RePEc:wsi:ijtafx:v:06:y:2003:i:05:n:s0219024903002031
    DOI: 10.1142/S0219024903002031
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    References listed on IDEAS

    as
    1. Schönbucher, Philipp J., 2000. "A Libor Market Model with Default Risk," Bonn Econ Discussion Papers 15/2001, University of Bonn, Bonn Graduate School of Economics (BGSE).
    2. Schönbucher, Philipp J., 2000. "A Tree Implementation of a Credit Spread Model for Credit Derivatives," Bonn Econ Discussion Papers 17/2001, University of Bonn, Bonn Graduate School of Economics (BGSE).
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