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Time-Changed Birth Processes and Multiname Credit Derivatives

Author

Listed:
  • Xiaowei Ding

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

  • Kay Giesecke

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

  • Pascal I. Tomecek

    (J.P. Morgan Securities Inc., Quantitative Research, New York, New York 10017)

Abstract

A credit investor such as a bank granting loans to firms or an asset manager buying corporate bonds is exposed to correlated corporate default risk. A multiname credit derivative is a financial security that allows the investor to transfer this risk to the credit market. In this paper, we study the valuation and risk analysis of multiname derivatives. To capture the complex economic phenomena that drive the pricing of these securities, we introduce a time-changed birth process as a probabilistic model of correlated event timing. The self-exciting property of a time-changed birth process captures the feedback from events that is often observed in credit markets. The stochastic variation of arrival rates between events captures the exposure of firms to common economic risk factors. We derive a closed-form expression for the distribution of a time-changed birth process, and develop analytically tractable pricing relations for a range of multiname derivatives valuation problems. We illustrate our results by calibrating a tranche forward and option pricer to market rates of index and tranche swaps.

Suggested Citation

  • Xiaowei Ding & Kay Giesecke & Pascal I. Tomecek, 2009. "Time-Changed Birth Processes and Multiname Credit Derivatives," Operations Research, INFORMS, vol. 57(4), pages 990-1005, August.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:4:p:990-1005
    DOI: 10.1287/opre.1080.0652
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    References listed on IDEAS

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    Cited by:

    1. Ovidiu Costin & Michael B. Gordy & Min Huang & Pawel J. Szerszen, 2016. "Expectations Of Functions Of Stochastic Time With Application To Credit Risk Modeling," Mathematical Finance, Wiley Blackwell, vol. 26(4), pages 748-784, October.
    2. Justin Sirignano & Kay Giesecke, 2019. "Risk Analysis for Large Pools of Loans," Management Science, INFORMS, vol. 65(1), pages 107-121, January.
    3. Christian Koziol & Philipp Koziol & Thomas Schön, 2015. "Do correlated defaults matter for CDS premia? An empirical analysis," Review of Derivatives Research, Springer, vol. 18(3), pages 191-224, October.
    4. Yinghui Dong & Kam C. Yuen & Guojing Wang & Chongfeng Wu, 2016. "A Reduced-Form Model for Correlated Defaults with Regime-Switching Shot Noise Intensities," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 459-486, June.
    5. Branger, Nicole & Kraft, Holger & Meinerding, Christoph, 2014. "Partial information about contagion risk, self-exciting processes and portfolio optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 18-36.
    6. Lian Tang & Bin Wang & Kai-Nan Xiang, 2016. "Portfolio credit risk with predetermined default orders," Quantitative Finance, Taylor & Francis Journals, vol. 16(1), pages 131-149, January.
    7. Kay Giesecke & Lisa R. Goldberg & Xiaowei Ding, 2011. "A Top-Down Approach to Multiname Credit," Operations Research, INFORMS, vol. 59(2), pages 283-300, April.
    8. K. Giesecke & H. Kakavand & M. Mousavi, 2011. "Exact Simulation of Point Processes with Stochastic Intensities," Operations Research, INFORMS, vol. 59(5), pages 1233-1245, October.
    9. Chang, Charles & Fuh, Cheng-Der & Lin, Shih-Kuei, 2013. "A tale of two regimes: Theory and empirical evidence for a Markov-modulated jump diffusion model of equity returns and derivative pricing implications," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3204-3217.
    10. Kay Giesecke & Dmitry Smelov, 2013. "Exact Sampling of Jump Diffusions," Operations Research, INFORMS, vol. 61(4), pages 894-907, August.
    11. Kay Giesecke & Baeho Kim, 2011. "Risk Analysis of Collateralized Debt Obligations," Operations Research, INFORMS, vol. 59(1), pages 32-49, February.

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