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Endogenizing exogenous default barrier models: The MM algorithm

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  • Forte, Santiago
  • Lovreta, Lidija

Abstract

In this paper, we propose a Maximization–Maximization (MM) algorithm for the assessment of hidden parameters in structural credit risk models. Step M1 updates the value, volatility, and expected return on the firm’s assets by maximizing the log-likelihood function for the time series of equity prices; Step M2 updates the default barrier by maximizing the equity holders’ participation in the firm’s asset value. The main contribution of the method lies in the M2 step, which allows for ‘endogenizing’ the default barrier in light of actual data on equity prices. Using a large international sample of companies, we demonstrate that theoretical credit spreads based on the MM algorithm offer the lowest CDS pricing errors when compared to other, traditional default barrier specifications: smooth-pasting condition value, maximum likelihood estimate, KMV’s default point, and nominal debt.

Suggested Citation

  • Forte, Santiago & Lovreta, Lidija, 2012. "Endogenizing exogenous default barrier models: The MM algorithm," Journal of Banking & Finance, Elsevier, vol. 36(6), pages 1639-1652.
    • Handle: RePEc:eee:jbfina:v:36:y:2012:i:6:p:1639-1652
    DOI: 10.1016/j.jbankfin.2012.01.010
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    References listed on IDEAS

    as
    1. Li, Ka Leung & Wong, Hoi Ying, 2008. "Structural models of corporate bond pricing with maximum likelihood estimation," Journal of Empirical Finance, Elsevier, vol. 15(4), pages 751-777, September.
    2. Bruche, Max, 2005. "Estimating structural bond pricing models via simulated maximum likelihood," LSE Research Online Documents on Economics 24647, London School of Economics and Political Science, LSE Library.
    3. Leland, Hayne E & Toft, Klaus Bjerre, 1996. "Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads," Journal of Finance, American Finance Association, vol. 51(3), pages 987-1019, July.
    4. Delianedis, Gordon & Geske, Robert, 2001. "The Components of Corporate Credit Spreads: Default, Recovery, Tax, Jumps, Liquidity, and Market Factors," University of California at Los Angeles, Anderson Graduate School of Management qt32x284q3, Anderson Graduate School of Management, UCLA.
    5. Leland, Hayne E, 1994. "Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Journal of Finance, American Finance Association, vol. 49(4), pages 1213-1252, September.
    6. 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.
    7. 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.
    8. 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.
    9. Hoi Ying Wong & Tsz Wang Choi, 2009. "Estimating default barriers from market information," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 187-196.
    10. Pierre Collin‐Dufresne & Robert S. Goldstein, 2001. "Do Credit Spreads Reflect Stationary Leverage Ratios?," Journal of Finance, American Finance Association, vol. 56(5), pages 1929-1957, October.
    11. Joseph P. Ogden, 1987. "Determinants Of The Ratings And Yields On Corporate Bonds: Tests Of The Contingent Claims Model," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 10(4), pages 329-340, December.
    12. Ericsson, Jan & Jacobs, Kris & Oviedo, Rodolfo, 2009. "The Determinants of Credit Default Swap Premia," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 44(1), pages 109-132, February.
    13. Jean-Paul Décamps & Stéphane Villeneuve, 2014. "Rethinking Dynamic Capital Structure Models With Roll-Over Debt," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 66-96, January.
    14. repec:bla:jfinan:v:59:y:2004:i:2:p:831-868 is not listed on IDEAS
    15. Max Bruche, 2006. "Estimating Structural Models of Corporate Bond Prices," Working Papers wp2006_0610, CEMFI.
    16. 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.
    17. Anderson, Ronald & Sundaresan, Suresh, 2000. "A comparative study of structural models of corporate bond yields: An exploratory investigation," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 255-269, January.
    18. Young Ho Eom, 2004. "Structural Models of Corporate Bond Pricing: An Empirical Analysis," The Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 499-544.
    19. 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.
    20. Longstaff, Francis A & Schwartz, Eduardo S, 1995. "A Simple Approach to Valuing Risky Fixed and Floating Rate Debt," Journal of Finance, American Finance Association, vol. 50(3), pages 789-819, July.
    21. Santiago Forte, 2011. "Calibrating structural models: a new methodology based on stock and credit default swap data," Quantitative Finance, Taylor & Francis Journals, vol. 11(12), pages 1745-1759.
    22. Jan Ericsson & Joel Reneby, 2005. "Estimating Structural Bond Pricing Models," The Journal of Business, University of Chicago Press, vol. 78(2), pages 707-735, March.
    23. Ronn, Ehud I & Verma, Avinash K, 1986. "Pricing Risk-Adjusted Deposit Insurance: An Option-Based Model," Journal of Finance, American Finance Association, vol. 41(4), pages 871-895, September.
    24. 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.
    25. Zhou, Chunsheng, 2001. "The term structure of credit spreads with jump risk," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 2015-2040, November.
    26. Geske, Robert, 1977. "The Valuation of Corporate Liabilities as Compound Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 541-552, November.
    27. Pierre Collin-Dufresn & Robert S. Goldstein & J. Spencer Martin, 2001. "The Determinants of Credit Spread Changes," Journal of Finance, American Finance Association, vol. 56(6), pages 2177-2207, December.
    28. Jarrow, Robert A., 2011. "Credit market equilibrium theory and evidence: Revisiting the structural versus reduced form credit risk model debate," Finance Research Letters, Elsevier, vol. 8(1), pages 2-7, March.
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    Citations

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    Cited by:

    1. Bougias, Alexandros & Episcopos, Athanasios & Leledakis, George N., 2022. "The role of asset payouts in the estimation of default barriers," International Review of Financial Analysis, Elsevier, vol. 81(C).
    2. 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.
    3. 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.
    4. Corvino, Raffaele & Fusai, Gianluca, 2022. "Default risk premium and asset prices," Journal of Financial Stability, Elsevier, vol. 60(C).
    5. Forte, Santiago & Lovreta, Lidija, 2023. "Credit default swaps, the leverage effect, and cross-sectional predictability of equity and firm asset volatility," Journal of Corporate Finance, Elsevier, vol. 79(C).
    6. Lovreta, Lidija & Silaghi, Florina, 2020. "The surface of implied firm’s asset volatility," Journal of Banking & Finance, Elsevier, vol. 112(C).

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    More about this item

    Keywords

    Structural credit risk models; Hidden parameters; Iterative algorithm;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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