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Bayesian Inference for a Structural Credit Risk Model with Stochastic Volatility and Stochastic Interest Rates

Author

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  • Abel Rodríguez
  • Enrique ter Horst
  • Samuel Malone

Abstract

We develop a novel structural credit risk model that extends the original Merton model by allowing for stochastic interest rates and stochastic volatility. The model is estimated using Bayesian methods implemented via a Markov chain Monte Carlo algorithm, in light of the demonstrable advantages of likelihood approaches and the importance of taking into account parameter uncertainty documented in the literature. We solve the nontrivial computational problem of contingent claim valuation in our set-up by using a Taylor series approximation to the expectation of the claim payoffs under the risk-neutral measure. Finally, we illustrate our model and compare it against the Merton model with real data on a nonfinancial firm (Ford Motor Company) and three financial firms (Citigroup, Goldman Sachs, and Lehman Brothers) during the recent financial crisis.

Suggested Citation

  • Abel Rodríguez & Enrique ter Horst & Samuel Malone, 2015. "Bayesian Inference for a Structural Credit Risk Model with Stochastic Volatility and Stochastic Interest Rates," Journal of Financial Econometrics, Oxford University Press, vol. 13(4), pages 839-867.
    • Handle: RePEc:oup:jfinec:v:13:y:2015:i:4:p:839-867.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbu018
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    References listed on IDEAS

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    1. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    2. Bauwens, L. & Lubrano, M., 1997. "Bayesian Option Pricing Using Asymmetric GARCH," G.R.E.Q.A.M. 97a40, Universite Aix-Marseille III.
    3. Nikola A. Tarashev, 2008. "An Empirical Evaluation of Structural Credit-Risk Models," International Journal of Central Banking, International Journal of Central Banking, vol. 4(1), pages 1-53, March.
    4. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
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    Cited by:

    1. Claußen, Arndt & Rösch, Daniel & Schmelzle, Martin, 2019. "Hedging parameter risk," Journal of Banking & Finance, Elsevier, vol. 100(C), pages 111-121.
    2. Tunaru, Radu & Zheng, Teng, 2017. "Parameter estimation risk in asset pricing and risk management: A Bayesian approach," International Review of Financial Analysis, Elsevier, vol. 53(C), pages 80-93.

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    More about this item

    Keywords

    Bayesian statistics; credit default swaps; structural credit risk models;
    All these keywords.

    JEL classification:

    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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