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Single and joint default in a structural model with purely discontinuous asset prices

Author

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  • 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 behaviour assumed for asset values, can be circumvented by considering discontinuous asset prices. In this paper the authors resort to a pure jump process of the Variance-Gamma type. First the authors 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, they show that it also circumvents the diffusive structural models difficulties over longer horizons. Particularly, it corrects for the underprediction of low-risk spreads and the overprediction of high-risk ones. Then the authors extend the model to joint default, resorting to a recent formulation of the VG multivariate model and without superimposing a copula choice. They 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 full calibration without the equicorrelation assumption, but still in a parsimonious way. As an example of the default assessments which the calibrated model can provide, the authors price an FtD swap.

Suggested Citation

  • Filippo Fiorani & Elisa Luciano & Patrizia Semeraro, 2010. "Single and joint default in a structural model with purely discontinuous asset prices," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 249-263.
    • Handle: RePEc:taf:quantf:v:10:y:2010:i:3:p:249-263
    DOI: 10.1080/14697680902991965
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    Citations

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    Cited by:

    1. Laura Ballotta & Ioannis Kyriakou, 2015. "Convertible bond valuation in a jump diffusion setting with stochastic interest rates," Quantitative Finance, Taylor & Francis Journals, vol. 15(1), pages 115-129, January.
    2. Farouk Mselmi, 2022. "Generalized linear model for subordinated Lévy processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 772-801, June.
    3. Hatem Ben‐Ameur & Rim Chérif & Bruno Rémillard, 2020. "Dynamic programming for valuing American options under a variance‐gamma process," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(10), pages 1548-1561, October.
    4. Erdinc Akyildirim & Alper A. Hekimoglu & Ahmet Sensoy & Frank J. Fabozzi, 2023. "Extending the Merton model with applications to credit value adjustment," Annals of Operations Research, Springer, vol. 326(1), pages 27-65, July.
    5. Flavia Barsotti, 2012. "Optimal Capital Structure with Endogenous Default and Volatility Risk," Working Papers - Mathematical Economics 2012-02, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    6. Fang Liu & Jing-Sheng Song, 2012. "Good and Bad News About the ( S , T ) Policy," Manufacturing & Service Operations Management, INFORMS, vol. 14(1), pages 42-49, January.
    7. Winston Buckley & Sandun Perera, 2019. "Optimal demand in a mispriced asymmetric Carr–Geman–Madan–Yor (CGMY) economy," Annals of Finance, Springer, vol. 15(3), pages 337-368, September.

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