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Structural Credit Risk Model with Stochastic Volatility: A Particle-filter Approach

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  • Di Bu
  • Yin Liao

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Abstract

This paper extends Merton's structural credit risk model to account for the fact that the firm's asset volatility follows a stochastic process. With the presence of stochastic volatility, the transformed-data maximum likelihood estimation (MLE) method of Duan (1994, 2000) can no longer be applied to estimate the model. We devise a particle filtering algorithm to solve this problem. This algorithm is based on the general non-linear and non-Gaussian filtering with sequential parameter learning, and a simulation study is conducted to ascertain its finite sample performance. Meanwhile, we implement this model on the real data of companies in Dow Jones industrial average and find that incorporating stochastic volatility into the structural model can largely improve the model performance.

Suggested Citation

  • Di Bu & Yin Liao, 2013. "Structural Credit Risk Model with Stochastic Volatility: A Particle-filter Approach," NCER Working Paper Series 98, National Centre for Econometric Research.
  • Handle: RePEc:qut:auncer:2013_91
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    File URL: http://www.ncer.edu.au/papers/documents/WP98.pdf
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    References listed on IDEAS

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    1. Jones, E Philip & Mason, Scott P & Rosenfeld, Eric, 1984. "Contingent Claims Analysis of Corporate Capital Structures: An Empirical Investigation," Journal of Finance, American Finance Association, vol. 39(3), pages 611-625, July.
    2. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000. "Do Call Prices and the Underlying Stock Always Move in the Same Direction?," Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 549-584.
    3. Jin‐Chuan Duan, 2000. "Correction: Maximum Likelihood Estimation Using Price Data of the Derivative Contract (Mathematical Finance 1994, 4/2, 155–167)," Mathematical Finance, Wiley Blackwell, vol. 10(4), pages 461-462, October.
    4. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    5. Huang, Shirley J. & Yu, Jun, 2010. "Bayesian analysis of structural credit risk models with microstructure noises," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2259-2272, November.
    6. Stein, Jeremy, 1989. " Overreactions in the Options Market," Journal of Finance, American Finance Association, vol. 44(4), pages 1011-1023, September.
    7. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    8. Duan, Jin-Chuan & Fulop, Andras, 2009. "Estimating the structural credit risk model when equity prices are contaminated by trading noises," Journal of Econometrics, Elsevier, vol. 150(2), pages 288-296, June.
    9. Jin‐Chuan Duan, 1994. "Maximum Likelihood Estimation Using Price Data Of The Derivative Contract," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 155-167, April.
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    Cited by:

    1. Jessen, Cathrine & Lando, David, 2015. "Robustness of distance-to-default," Journal of Banking & Finance, Elsevier, vol. 50(C), pages 493-505.

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    More about this item

    Keywords

    Credit risk; Merton model; Stochastic volatility; Particle Filtter; Default probability; CDS;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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