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A Dynamic Approach To The Modeling Of Correlation Credit Derivatives Using Markov Chains

Author

Listed:
  • GIUSEPPE DI GRAZIANO

    (Deutsche Bank AG, Great Winchester Street, London EC2N 2DB, UK)

  • L. C. G. ROGERS

    (Statistical Laboratory, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK)

Abstract

The modeling of credit events is in effect the modeling of the times to default of various names. The distribution of individual times to default can be calibrated from CDS quotes, but for more complicated instruments, such as CDOs, the joint law is needed. Industry practice is to model this correlation using a copula/base correlation approach, which suffers significant deficiencies. We present a new approach to default correlation modeling, where defaults of different names are driven by a common continuous-time Markov process. Individual default probabilities and default correlations can be calculated in closed form. We provide semi-analytic formulas for the pricing of CDO tranches via Laplace-transform techniques which are both fast and easy to implement. The model calibrates to quoted tranche prices with a high degree of precision and allows one to price non-standard tranches in a consistent and arbitrage-free manner. The number of parameters of the model is flexible and can be adjusted to adapt to the set of market data one is calibrating to. More importantly, the model is dynamically consistent and can be used to price options on tranches and other exotic path-dependent products.

Suggested Citation

  • Giuseppe Di Graziano & L. C. G. Rogers, 2009. "A Dynamic Approach To The Modeling Of Correlation Credit Derivatives Using Markov Chains," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(01), pages 45-62.
    • Handle: RePEc:wsi:ijtafx:v:12:y:2009:i:01:n:s0219024909005142
    DOI: 10.1142/S0219024909005142
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    Citations

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    Cited by:

    1. Balakrishna, B S, 2010. "Levy Subordinator Model of Default Dependency," MPRA Paper 21386, University Library of Munich, Germany.
    2. Shaojie Deng & Kay Giesecke & Tze Leung Lai, 2012. "Sequential Importance Sampling and Resampling for Dynamic Portfolio Credit Risk," Operations Research, INFORMS, vol. 60(1), pages 78-91, February.
    3. 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.
    4. Herbertsson, Alexander & Frey, Rüdiger, 2016. "Cds Index Options Under Incomplete Information," Working Papers in Economics 685, University of Gothenburg, Department of Economics.
    5. Chao Xu & Yinghui Dong & Guojing Wang, 2019. "The pricing of defaultable bonds under a regime-switching jump-diffusion model with stochastic default barrier," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(9), pages 2185-2205, May.
    6. Balakrishna, B S, 2010. "Levy Subordinator Model: A Two Parameter Model of Default Dependency," MPRA Paper 26274, University Library of Munich, Germany.
    7. Damien Ackerer & Damir Filipović, 2020. "Linear credit risk models," Finance and Stochastics, Springer, vol. 24(1), pages 169-214, January.

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