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Estimating the Structural Credit Risk Model When Equity Prices Are Contaminated by Trading Noises




The transformed-data maximum likelihood estimation (MLE) method for structural credit risk models developed by Duan (1994) is extended to account for the fact that observed equity prices may have been contaminated by trading noises. With the presence of trading noises, the likelihood function based on the observed equity prices can only be evaluated via some nonlinear filtering scheme. We devise a particle filtering algorithm that is practical for conducting the MLE estimation of the structural credit risk model of Merton (1974). We implement the method on the Dow Jones 30 firms and on 100 randomly selected firms, and find that ignoring trading noises can lead to significantly over-estimating the firm’s asset volatility. The estimated magnitude of trading noise is in line with the direction that a firm’s liquidity will predict based on three common liquidity proxies. A simulation study is then conducted to ascertain the performance of the estimation method.

Suggested Citation

  • Duan, Jin-Chuan & Fulop, Andras, 2006. "Estimating the Structural Credit Risk Model When Equity Prices Are Contaminated by Trading Noises," ESSEC Working Papers DR 06015, ESSEC Research Center, ESSEC Business School.
  • Handle: RePEc:ebg:essewp:dr-06015

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    References listed on IDEAS

    1. Jarrow, Robert A. & Turnbull, Stuart M., 2000. "The intersection of market and credit risk," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 271-299, January.
    2. Luc Laeven, 2002. "Bank Risk and Deposit Insurance," World Bank Economic Review, World Bank Group, vol. 16(1), pages 109-137, June.
    3. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521471626, March.
    4. Madhavan, Ananth & Richardson, Matthew & Roomans, Mark, 1997. "Why Do Security Prices Change? A Transaction-Level Analysis of NYSE Stocks," Review of Financial Studies, Society for Financial Studies, vol. 10(4), pages 1035-1064.
    5. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    6. 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.
    7. Yacine Aït-Sahalia, 2005. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 351-416.
    8. Duan, Jin-Chuan & Simonato, Jean-Guy, 2002. "Maximum likelihood estimation of deposit insurance value with interest rate risk," Journal of Empirical Finance, Elsevier, vol. 9(1), pages 109-132, January.
    9. Lehar, Alfred, 2005. "Measuring systemic risk: A risk management approach," Journal of Banking & Finance, Elsevier, vol. 29(10), pages 2577-2603, October.
    10. Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, vol. 79(3), pages 655-692, March.
    11. Duan, Jin-Chuan & Yu, Min-Teh, 1995. "Assessing the cost of Taiwan's deposit insurance," Pacific-Basin Finance Journal, Elsevier, vol. 3(1), pages 139-139, May.
    12. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    13. Ericsson, Jan & Reneby, Joel, 2003. "Valuing Corporate Liabilities," SIFR Research Report Series 15, Institute for Financial Research.
    14. Hasbrouck, Joel, 1993. "Assessing the Quality of a Security Market: A New Approach to Transaction-Cost Measurement," Review of Financial Studies, Society for Financial Studies, vol. 6(1), pages 191-212.
    15. Harris, Lawrence, 1990. "Estimation of Stock Price Variances and Serial Covariances from Discrete Observations," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(03), pages 291-306, September.
    16. Jan Ericsson, 2005. "Estimating Structural Bond Pricing Models," The Journal of Business, University of Chicago Press, vol. 78(2), pages 707-735, March.
    17. Jin-Chuan Duan, 1994. "Maximum Likelihood Estimation Using Price Data Of The Derivative Contract," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 155-167.
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    More about this item


    Credit Risk; Maximum Likelihood; Microstructure; Option Pricing; Particle Filtering;

    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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