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Levy Subordinator Model: A Two Parameter Model of Default Dependency

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  • Balakrishna, B S
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    Abstract

    Subordinators are Levy processes with non-decreasing sample paths. They are natural processes to model default dependency. They help ensure that the loss process is non-decreasing leading to a promising class of dynamic models. The simplest subordinator is the Levy subordinator, a maximally skewed stable process with index of stability 1/2. Interestingly, this simplest subordinator turns out to be the appropriate choice as the basic process in modeling default dependency. It involves just two parameters to assess dependency risk, a measure of correlation and that of the likelihood of a catastrophe. Its attractive feature is that it admits a closed form expression for its distribution function. This helps in automatic calibration to individual hazard rate curves and efficient pricing with Fast Fourier Transform techniques. It is structured similar to the one-factor Gaussian copula model and can easily be implemented within the framework of the existing computational infrastructure. As it turns out, the Gaussian copula model can itself be recast into this framework highlighting its limitations. The model can also be investigated numerically with a Monte Carlo simulation algorithm. As is now well appreciated, random recovery is helpful in better pricing of the senior tranches and the model admits a tractable framework of random recovery. The model is investigated numerically and the implied base correlations are presented over a wide range of its parameters. The investigation also demonstrates its ability to generate reasonable hedge ratios.

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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 26274.

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    Date of creation: 28 Oct 2010
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    Handle: RePEc:pra:mprapa:26274

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    Related research

    Keywords: default risk; correlation smile; CDO; Levy process; subordinator; semi-analytical; FFT; copula; catastrophe;

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    References

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    1. Balakrishna, B S, 2010. "Levy Subordinator Model of Default Dependency," MPRA Paper 21386, University Library of Munich, Germany.
    2. Damiano Brigo & Andrea Pallavicini & Roberto Torresetti, 2008. "Default correlation, cluster dynamics and single names: The GPCL dynamical loss model," Papers 0812.4163, arXiv.org.
    3. Balakrishna, B S, 2007. "Delayed Default Dependency and Default Contagion," MPRA Paper 14921, University Library of Munich, Germany, revised 15 May 2007.
    4. Balakrishna, B S, 2008. "Levy Density Based Intensity Modeling of the Correlation Smile," MPRA Paper 14922, University Library of Munich, Germany, revised 06 Apr 2009.
    5. Damiano Brigo & Andrea Pallavicini & Roberto Torresetti, 2009. "Credit models and the crisis, or: how I learned to stop worrying and love the CDOs," Papers 0912.5427, arXiv.org, revised Feb 2010.
    6. Alexander Chapovsky & Andrew Rennie & Pedro Tavares, 2007. "Stochastic Intensity Modeling For Structured Credit Exotics," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 633-652.
    7. 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.
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