Balakrishna, B. S. (2010): Levy subordinator model: A two parameter model of default dependency.
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Abstract
The May 2005 crisis and the recent credit crisis have indicated to us that any realistic model of default dependency needs to account for at least two risk factors, firmspecific and catastrophic. Unfortunately, the popular Gaussian copula model has no identifiable support to either of these. In this article, a two parameter model of default dependency based on the Levy subordinator is presented accounting for these two risk factors. Subordinators are Levy processes with nondecreasing sample paths. They help ensure that the loss process is nondecreasing 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. 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 onefactor Gaussian copula model and can easily be implemented within the framework of the existing 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. It admits a tractable framework of random recovery. It 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.
Item Type:  MPRA Paper 

Original Title:  Levy subordinator model: A two parameter model of default dependency 
Language:  English 
Keywords:  default risk; correlation smile; CDO; Levy process; subordinator; semianalytical; FFT; copula; catastrophe 
Subjects:  G  Financial Economics > G1  General Financial Markets > G13  Contingent Pricing ; Futures Pricing 
Item ID:  32882 
Depositing User:  S Balakrishna 
Date Deposited:  19. Aug 2011 11:16 
Last Modified:  02. Jan 2016 10:35 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/32882 
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Levy Subordinator Model: A Two Parameter Model of Default Dependency. (deposited 31. Oct 2010 17:09)

Levy Subordinator Model: A Two Parameter Model of Default Dependency. (deposited 23. Mar 2011 20:10)

Levy Subordinator Model: A Two Parameter Model of Default Dependency. (deposited 28. Jun 2011 20:25)
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Levy Subordinator Model: A Two Parameter Model of Default Dependency. (deposited 28. Jun 2011 20:25)

Levy Subordinator Model: A Two Parameter Model of Default Dependency. (deposited 23. Mar 2011 20:10)