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Single and joint default in a structural model with purely discontinuous assets

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Author Info

  • Filippo Fiorani
  • Elisa Luciano
  • Patrizia Semeraro

Abstract

Structural models of credit risk are known to present both vanishing spreads at very short maturities and a poor spread fit over longer maturities. The former shortcoming, which is due to the diffusive behavior assumed for asset values, can be circumvented by considering discontinuous assets. In this paper we resort to a pure jump process of the Variance-Gamma type. First we calibrate the corresponding Merton type structural model to single-name data for the DJ CDX NA IG and CDX NA HY components. By so doing, we show that it circumvents also the diffusive structural models difficulties over longer horizons. In particular, it corrects for underprediction of low risk spreads and overprediction of high risk ones. Then we extend the model to joint default, resorting to a recent formulation of the VG multivariate model and without superimposing a copula choice. We fit default correlation for a sample of CDX NA names, using equity correlation. The main advantage of our joint model with respect to the existing non diffusive ones is that it allows calibration without the equicorrelation assumption, but still in a parsimonious way. As an example of the default assessments which the calibrated model can provide, we price a FtD swap.

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Bibliographic Info

Paper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 41.

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Length: 36 pages
Date of creation: 2007
Date of revision:
Handle: RePEc:cca:wpaper:41

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Related research

Keywords: credit risk; structural models; Lévy asset prices; default probability; joint default.;

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References

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  1. Elisa Luciano & Wim Schoutens, 2006. "A Multivariate Jump-Driven Financial Asset Model," Carlo Alberto Notebooks 29, Collegio Carlo Alberto.
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Cited by:
  1. Flavia Barsotti, 2012. "Optimal Capital Structure with Endogenous Default and Volatility Risk," DiMaD Working Papers 2012-02, Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze.
  2. Antonio Romero Medina & Mateo Triossi, 2007. "Games of capacities : a (close) look to Nash Equilibria," Economics Working Papers we075933, Universidad Carlos III, Departamento de Economía.
  3. Elisa Luciano, 2007. "Copula-Based Default Dependence Modelling: Where Do We Stand?," ICER Working Papers - Applied Mathematics Series 21-2007, ICER - International Centre for Economic Research.

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  1. Variance gamma process in Wikipedia (English)

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