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Monte Carlo Algorithms for Default Timing Problems

Author

Listed:
  • Kay Giesecke

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

  • Baeho Kim

    (Korea University Business School, Anam-dong, Sungbuk-gu, Seoul 136-701, Korea)

  • Shilin Zhu

    (Department of Statistics, Stanford University, Stanford, California 94305)

Abstract

Dynamic, intensity-based point process models are widely used to measure and price the correlated default risk in portfolios of credit-sensitive assets such as loans and corporate bonds. Monte Carlo simulation is an important tool for performing computations in these models. This paper develops, analyzes, and evaluates two simulation algorithms for intensity-based point process models. The algorithms extend the conventional thinning scheme to the case where the event intensity is unbounded, a feature common to many standard model formulations. Numerical results illustrate the performance of the algorithms for a familiar top-down model and a novel bottom-up model of correlated default risk. This paper was accepted by Assaf Zeevi, stochastic models and simulation.

Suggested Citation

  • Kay Giesecke & Baeho Kim & Shilin Zhu, 2011. "Monte Carlo Algorithms for Default Timing Problems," Management Science, INFORMS, vol. 57(12), pages 2115-2129, December.
    • Handle: RePEc:inm:ormnsc:v:57:y:2011:i:12:p:2115-2129
    DOI: 10.1287/mnsc.1110.1411
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    References listed on IDEAS

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    1. Antje Berndt & Rohan Douglas & Darrell Duffie & Mark Ferguson, "undated". "Measuring Default Risk Premia from Default Swap Rates and EDFs," GSIA Working Papers 2006-E31, Carnegie Mellon University, Tepper School of Business.
    2. Fan Yu, 2007. "Correlated Defaults In Intensity‐Based Models," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 155-173, April.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    4. Robert A. Jarrow & David Lando & Fan Yu, 2008. "Default Risk And Diversification: Theory And Empirical Implications," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 19, pages 455-480, World Scientific Publishing Co. Pte. Ltd..
    5. Mark Broadie & Özgür Kaya, 2006. "Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes," Operations Research, INFORMS, vol. 54(2), pages 217-231, April.
    6. Jun Pan & Kenneth J. Singleton, 2008. "Default and Recovery Implicit in the Term Structure of Sovereign CDS Spreads," Journal of Finance, American Finance Association, vol. 63(5), pages 2345-2384, October.
    7. Louis Paulot, 2009. "A Dynamic Model for Credit Index Derivatives," Papers 0911.1662, arXiv.org.
    8. Francis A. Longstaff & Arvind Rajan, 2008. "An Empirical Analysis of the Pricing of Collateralized Debt Obligations," Journal of Finance, American Finance Association, vol. 63(2), pages 529-563, April.
    9. Peter Carr & Vadim Linetsky, 2006. "A jump to default extended CEV model: an application of Bessel processes," Finance and Stochastics, Springer, vol. 10(3), pages 303-330, September.
    10. Robert A. Jarrow & Fan Yu, 2008. "Counterparty Risk and the Pricing of Defaultable Securities," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 20, pages 481-515, World Scientific Publishing Co. Pte. Ltd..
    11. Edward I. Altman & Brooks Brady & Andrea Resti & Andrea Sironi, 2005. "The Link between Default and Recovery Rates: Theory, Empirical Evidence, and Implications," The Journal of Business, University of Chicago Press, vol. 78(6), pages 2203-2228, November.
    12. Erhan Bayraktar & Bo Yang, 2009. "Multi-Scale Time-Changed Birth Processes for Pricing Multi-Name Credit Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(5), pages 429-449.
    13. Azizpour, Shahriar & Giesecke, Kay & Kim, Baeho, 2011. "Premia for correlated default risk," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1340-1357, August.
    14. Nicolas Merener & Paul Glasserman, 2003. "Numerical solution of jump-diffusion LIBOR market models," Finance and Stochastics, Springer, vol. 7(1), pages 1-27.
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    Cited by:

    1. Dianfa Chen & Jun Deng & Jianfen Feng & Bin Zou, 2017. "An Explicit Default Contagion Model and Its Application to Credit Derivatives Pricing," Papers 1706.06285, arXiv.org, revised Aug 2018.
    2. Dassios, Angelos & Zhao, Hongbiao, 2017. "A generalised contagion process with an application to credit risk," LSE Research Online Documents on Economics 68558, London School of Economics and Political Science, LSE Library.
    3. Xiaowei Zhang & Jose Blanchet & Kay Giesecke & Peter W. Glynn, 2015. "Affine Point Processes: Approximation and Efficient Simulation," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 797-819, October.
    4. Angelos Dassios & Hongbiao Zhao, 2017. "A Generalized Contagion Process With An Application To Credit Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-33, February.
    5. Dassios, Angelos & Zhao, Hongbiao, 2017. "Efficient simulation of clustering jumps with CIR intensity," LSE Research Online Documents on Economics 74205, London School of Economics and Political Science, LSE Library.

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