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Estimating the structural credit risk model when equity prices are contaminated by trading noises

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  • Duan, Jin-Chuan
  • Fulop, Andras

Abstract

The transformed-data maximum likelihood estimation (MLE) method for structural credit risk models developed by Duan [Duan, J.-C., 1994. Maximum likelihood estimation using price data of the derivative contract. Mathematical Finance 4, 155-167] 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 [Merton, R.C., 1974. On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance 29, 449-470]. 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.

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  • 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.
    • Handle: RePEc:eee:econom:v:150:y:2009:i:2:p:288-296
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    4. Michele Leonardo Bianchi, 2012. "An empirical comparison of alternative credit default swap pricing models," Temi di discussione (Economic working papers) 882, Bank of Italy, Economic Research and International Relations Area.
    5. Han-Hsing Lee & Kuanyu Shih & Kehluh Wang, 2016. "Measuring sovereign credit risk using a structural model approach," Review of Quantitative Finance and Accounting, Springer, vol. 47(4), pages 1097-1128, November.
    6. 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.
    7. Forte, Santiago & Lovreta, Lidija, 2012. "Endogenizing exogenous default barrier models: The MM algorithm," Journal of Banking & Finance, Elsevier, vol. 36(6), pages 1639-1652.
    8. Xiao, Weilin & Zhang, Xili, 2016. "Pricing equity warrants with a promised lowest price in Merton’s jump–diffusion model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 219-238.
    9. Chung, Tsz-Kin & Hui, Cho-Hoi & Li, Ka-Fai, 2013. "Explaining share price disparity with parameter uncertainty: Evidence from Chinese A- and H-shares," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 1073-1083.
    10. Amaya, Diego & Boudreault, Mathieu & McLeish, Don L., 2019. "Maximum likelihood estimation of first-passage structural credit risk models correcting for the survivorship bias," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 297-313.
    11. Michael Pitt & Sheheryar Malik & Arnaud Doucet, 2014. "Simulated likelihood inference for stochastic volatility models using continuous particle filtering," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 527-552, June.
    12. Benedikt Rotermann & Bernd Wilfling, 2015. "Estimating rational stock-market bubbles with sequential Monte Carlo methods," CQE Working Papers 4015, Center for Quantitative Economics (CQE), University of Muenster.
    13. Kleppe, Tore Selland & Yu, Jun & Skaug, Hans J., 2014. "Maximum likelihood estimation of partially observed diffusion models," Journal of Econometrics, Elsevier, vol. 180(1), pages 73-80.
    14. Duan, Jin-Chuan, 2016. "Local-momentum autoregression and the modeling of interest rate term structure," Journal of Econometrics, Elsevier, vol. 194(2), pages 349-359.
    15. Fulop, Andras & Li, Junye, 2013. "Efficient learning via simulation: A marginalized resample-move approach," Journal of Econometrics, Elsevier, vol. 176(2), pages 146-161.
    16. Flavia Barsotti & Simona Sanfelici, 2012. "Microstructure effect on firm’s volatility risk," Working Papers - Mathematical Economics 2012-05, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    17. Flavia Barsotti & Simona Sanfelici, 2016. "Market Microstructure Effects on Firm Default Risk Evaluation," Econometrics, MDPI, vol. 4(3), pages 1-31, July.
    18. Kensuke Kato & Nobuhiro Nakamura, 2024. "PDE-Based Bayesian Inference of CEV Dynamics for Credit Risk in Stock Prices," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 31(2), pages 389-421, June.
    19. Guarin, Alexander & Liu, Xiaoquan & Ng, Wing Lon, 2014. "Recovering default risk from CDS spreads with a nonlinear filter," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 87-104.
    20. Bu, Di & Liao, Yin, 2014. "Corporate credit risk prediction under stochastic volatility and jumps," Journal of Economic Dynamics and Control, Elsevier, vol. 47(C), pages 263-281.
    21. Boudreault, Mathieu & Gauthier, Geneviève & Thomassin, Tommy, 2015. "Estimation of correlations in portfolio credit risk models based on noisy security prices," Journal of Economic Dynamics and Control, Elsevier, vol. 61(C), pages 334-349.
    22. 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.

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