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

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Author Info

  • 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.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 12 (2009)
Issue (Month): 01 ()
Pages: 45-62

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Handle: RePEc:wsi:ijtafx:v:12:y:2009:i:01:p:45-62

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Related research

Keywords: CDO; credit derivatives; Markov chain; correlation; Laplace transform; copula; default risk;

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Citations

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Cited by:
  1. Balakrishna, B S, 2010. "Levy Subordinator Model: A Two Parameter Model of Default Dependency," MPRA Paper 26274, University Library of Munich, Germany.
  2. Balakrishna, B S, 2010. "Levy Subordinator Model of Default Dependency," MPRA Paper 21386, University Library of Munich, Germany.
  3. Tino Kluge & L. C. G. Rogers, 2012. "The potential approach in practice," Science & Finance (CFM) working paper archive 1204.5718, Science & Finance, Capital Fund Management.

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