Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-25T15:11:14.176Z Has data issue: false hasContentIssue false
  • English
  • Français

A Binomial Lattice Method for Pricing Corporate Debt and Modeling Chapter 11 Proceedings

Published online by Cambridge University Press:  06 April 2009

Mark Broadie  and
Özgür Kaya
Mark Broadie
Affiliation:
[email protected], Columbia University, Graduate School of Business, 3022 Broadway, New York, NY 10027
Özgür Kaya
Affiliation:
[email protected], Lehman Brothers, 745 Seventh Avenue, New York, NY 10019.
Get access Rights & Permissions [Opens in a new window]

Abstract

The pricing of corporate debt is still a challenging and active research area in corporate finance. Starting with Merton (1974), many authors proposed a structural approach in which the value of the assets of the firm is modeled by a stochastic process, and all other variables are derived from this basic process. These structural models have become more complex over time in order to capture more realistic aspects of bankruptcy proceedings. The literature in this area emphasizes closed-form solutions that are derived by either partial differential equation methods or analytical pricing techniques. However, it is not always possible to build a comprehensive model with realistic model features and achieve a closed-form solution at the same time. In this paper, we develop a binomial lattice method that can be used to handle complex structural models such as ones that include Chapter 11 proceedings of the U.S. bankruptcy code. Although lattice methods have been widely used in the option pricing literature, they are relatively new in corporate debt pricing. In particular, the limited liability requirement of the equity holders needs to be handled carefully in this context. Our method can be used to solve the Leland (1994) model and its extension to the finite maturity case, the more complex model of Broadie, Chernov, and Sundaresan (2007), and others.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 42 , Issue 2 , June 2007 , pp. 279 - 312
Copyright
Copyright © School of Business Administration, University of Washington 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, R. W., and Sundaresan, S.. “The Design and Valuation of Debt Contracts.” Review of Financial Studies, 9 (1996), 37–68.CrossRefGoogle Scholar
Anderson, R. W.; Sundaresan, S.; and Tychon, P.. “Strategic Analysis of Contingent Claims.” European Economic Review, 40 (1996), 871–881.CrossRefGoogle Scholar
Anderson, R. W., and Tu, C.. “Numerical Analysis of Strategic Contingent Claim Models.” Journal of Computational Economics, 11 (1998), 3–19.CrossRefGoogle Scholar
Black, F., and Cox, J.. “Valuing Corporate Securities: Some Effects of Bond Indenture Provisions.” Journal of Finance, 31 (1976), 351–367.CrossRefGoogle Scholar
Boyle, L. L., and Lau, S. H.. “Bumping Up Against the Barrier with the Binomial Method.” Journal of Derivatives, 1 (1994), 6–14.CrossRefGoogle Scholar
Brennan, M. J., and Schwartz, E. S.. “Corporate Income Taxes, Valuation, and the Problem of Optimal Capital Structure.” Journal of Business, 51 (1978), 103–114.CrossRefGoogle Scholar
Brezinski, C., and Zaglia, M.. Extrapolation Methods: Theory and Practice. New York, NY: North-Holland (1991).Google Scholar
Broadie, M.; Chernov, M.; and Sundaresan, S.. “Optimal Debt and Equity Values in the Presence of Chapter 7 and Chapter 11.” Journal of Finance, 62 (2007), 1339–1375.CrossRefGoogle Scholar
Broadie, M., and Detemple, J. B.. “American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods.” Review of Financial Studies, 9 (1996), 1211–1250.CrossRefGoogle Scholar
Cox, J. C.; Ross, S. A.; and Rubinstein, M.. “Option Pricing: A Simplified Approach.” Journal of Financial Economics, 7 (1979), 229–263.CrossRefGoogle Scholar
Derman, E.; Kani, I.; Ergener, D.; and Bardhan, I.. “Enhanced Numerical Methods for Options with Barriers.” Financial Analysts Journal, 51 (1995), 65–74.CrossRefGoogle Scholar
Dixit, A. K., and Pindyck, R. S.. Investment under Uncertainty. Princeton, NJ: Princeton University Press (1994).CrossRefGoogle Scholar
Fan, H., and Sundaresan, S.. “Debt Valuation, Renegotiation, and Optimal Dividend Policy.” Review of Financial Studies, 13 (2000), 1057–1099.CrossRefGoogle Scholar
François, P., and Morellec, E.. “Capital Structure and Asset Prices: Some Effects of Bankruptcy Procedures.” Journal of Business, 77 (2004), 387–441.CrossRefGoogle Scholar
Galai, D.; Raviv, A.; and Wiener, Z.. “Liquidation Triggers and the Valuation of Equity and Debt.” Working Paper, Hebrew University of Jerusalem (2003).CrossRefGoogle Scholar
Gobet, E. “Analysis of the Zigzag Convergence for Barrier Options with Binomial Trees.” Preprint, Université Paris VI (1999).Google Scholar
Leland, H. “Corporate Debt Value, Bond Covenants, and Optimal Capital Structure.” Journal of Finance, 49 (1994), 1213–1252.CrossRefGoogle Scholar
Leland, H., and Toft, K. B.. “Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads.” Journal of Finance, 51 (1996), 987–1019.CrossRefGoogle Scholar
Merton, R. C. “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates.” Journal of Finance, 29 (1974), 449–470.Google Scholar
Moraux, F. “Valuing Corporate Liabilities When the Default Threshold is not an Absorbing Barrier.” Working Paper, Université de Rennes I (2002).Google Scholar
Paseka, A. “Debt Valuation with Endogenous Default and Chapter 11 Reorganization.” Working Paper, University of Arizona (2003).Google Scholar
Press, W. H.; Teukolsky, S. A; Vetterling, W. T.; and Flannery, B. P.. “Numerical Recipes in C.” Cambridge, MA: Cambridge University Press (1992).Google Scholar
Sarig, O., and Warga, A.. “Some Empirical Estimates of the Risk Structure of Interest Rates.” Journal of Finance, 44 (1989), 1351–1360.CrossRefGoogle Scholar