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Stochastic Volatility Effects on Defaultable Bonds

Author

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  • Jean-Pierre Fouque
  • Ronnie Sircar
  • Knut Sølna

Abstract

This paper studies the effect of introducing stochastic volatility in the first-passage structural approach to default risk. The impact of volatility time scales on the yield spread curve is analyzed. In particular it is shown that the presence of a short time scale in the volatility raises the yield spreads at short maturities. It is argued that combining first passage default modelling with multiscale stochastic volatility produces more realistic yield spreads. Moreover, this framework enables the use of perturbation techniques to derive explicit approximations which facilitate the complicated issue of calibration of parameters.

Suggested Citation

  • Jean-Pierre Fouque & Ronnie Sircar & Knut Sølna, 2006. "Stochastic Volatility Effects on Defaultable Bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(3), pages 215-244.
    • Handle: RePEc:taf:apmtfi:v:13:y:2006:i:3:p:215-244
    DOI: 10.1080/13504860600563127
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    References listed on IDEAS

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    1. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
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    Citations

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    Cited by:

    1. Michael B. Gordy & SØren Willemann, 2012. "Constant Proportion Debt Obligations: A Postmortem Analysis of Rating Models," Management Science, INFORMS, vol. 58(3), pages 476-492, March.
    2. Thorsten Schmidt & Alexander Novikov, 2008. "A Structural Model with Unobserved Default Boundary," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 183-203.
    3. Masaaki Fukasawa, 2011. "Asymptotic analysis for stochastic volatility: martingale expansion," Finance and Stochastics, Springer, vol. 15(4), pages 635-654, December.
    4. Jeon, Jaegi & Kim, Geonwoo & Huh, Jeonggyu, 2021. "An asymptotic expansion approach to the valuation of vulnerable options under a multiscale stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Lotfaliei, Babak, 2018. "The variance risk premium and capital structure," ESRB Working Paper Series 70, European Systemic Risk Board.
    6. Luca Vincenzo Ballestra & Graziella Pacelli, 2009. "A Numerical Method to Price Defaultable Bonds Based on the Madan and Unal Credit Risk Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 17-36.
    7. Andreou, Elena & Ghysels, Eric, 2008. "Quality control for structural credit risk models," Journal of Econometrics, Elsevier, vol. 146(2), pages 364-375, October.
    8. Rodrigo Alfaro & Natán Golberger, 2013. "The Impact of Persistence in Volatility over the Probability of Default," Working Papers Central Bank of Chile 689, Central Bank of Chile.
    9. Robert F. Engle & Emil N. Siriwardane, 2018. "Structural GARCH: The Volatility-Leverage Connection," Review of Financial Studies, Society for Financial Studies, vol. 31(2), pages 449-492.
    10. Hoi Ying Wong & Chun Man Chan, 2008. "Turbo warrants under stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 8(7), pages 739-751.
    11. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011.
    12. Issouf Soumaré & Ernest Tafolong, 2017. "Risk-based capital for credit insurers with business cycles and dynamic leverage," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 597-612, April.
    13. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5, July-Dece.

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