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Level-Dependent Annuities: Defaults of Multiple Degrees

Published online by Cambridge University Press:  12 August 2010

Aksel Mjøs  and
Svein-Arne Persson
Aksel Mjøs
Affiliation:
Norwegian School of Economics and Business Administration, Helleveien 30, NO-5045 Bergen, Norway. aksel.mjos@nhh.no.
Svein-Arne Persson
Affiliation:
Norwegian School of Economics and Business Administration, Helleveien 30, NO-5045 Bergen, Norway. svein-arne.persson@nhh.no.
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Abstract

Motivated by the effect on valuation of stopped or reduced debt coupon payments from a company in financial distress, we value a level-dependent annuity contract where the annuity rate depends on the value of an underlying asset process. The range of possible values of this asset is divided into a finite number of regions, with constant annuity rates within each region. We present closed-form formulas for the market value of level-dependent annuities contracts when the market value of the underlying asset is assumed to follow a geometric Brownian motion. Such annuities occur naturally in models of debt with credit risk in financial economics. Our results are applied for valuing both corporate debt with suspended interest payments under the U.S. Chapter 11 provisions and loans with contractual level-dependent interest rates.

Type
Research Articles
Information
Journal of Financial and Quantitative Analysis , Volume 45 , Issue 5 , October 2010 , pp. 1311 - 1339
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2010

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References

Anderson, R. W., and Sundaresan, S.. “The Design and Valuation of Debt Contracts.” Review of Financial Studies, 9 (1996), 37–68.CrossRefGoogle Scholar
Asquith, P.; Beatty, A.; and Weber, J.. “Performance Pricing in Bank Debt Contracts.” Journal of Accounting and Economics, 40 (2005), 101–128.CrossRefGoogle Scholar
Black, F., and Cox, J. C.. “Valuing Corporate Securities: Some Effects of Bond Indenture Provisions.” Journal of Finance, 31 (1976), 351–367.CrossRefGoogle 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), 1341–1377.CrossRefGoogle Scholar
Broadie, M., and Kaya, Ö.. “A Binomial Lattice Method for Pricing Corporate Debt and Modeling Chapter 11 Proceedings.” Journal of Financial and Quantitative Analysis, 42 (2007), 279–312.CrossRefGoogle Scholar
Dixit, A. K., and Pindyck, R. S.. Investment under Uncertainty. Princeton, NJ: Princeton University Press (1994).CrossRefGoogle Scholar
Duffie, D. Dynamic Asset Pricing Theory, 3rd ed.Princeton, NJ: Princeton University Press (2001).Google Scholar
Emanuel, D. “A Theoretical Model for Valuing Preferred Stock.” Journal of Finance, 38 (1983), 1133–1155.CrossRefGoogle Scholar
Geman, H.; El Karoui, N.; and Rochet, J.-C.. “Changes of Numeraire, Changes of Probability Measure and Option Pricing.” Journal of Applied Probability, 32 (1995), 443–458.CrossRefGoogle Scholar
Jamshidian, F. “An Exact Bond Option Formula.” Journal of Finance, 44 (1989), 205–209.CrossRefGoogle Scholar
Lando, D. Credit Risk Modeling: Theory and Applications. Princeton, NJ: Princeton University Press (2004).CrossRefGoogle Scholar
Leland, H. E. “Corporate Debt Value, Bond Covenants, and Optimal Capital Structure.” Journal of Finance, 49 (1994), 1213–1252.CrossRefGoogle Scholar
Mella-Barral, P., and Perraudin, W.. “Strategic Debt Service.” Journal of Finance, 52 (1997), 531–556.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
Mjøs, A., and Persson, S.-A.. “Callable Risky Perpetual Debt with Protection Period.” European Journal of Operational Research, 207 (2010), 391–400.CrossRefGoogle Scholar
Øksendal, B. Stochastic Differential Equations: An Introduction with Applications, 6th ed.Berlin, Germany: Springer-Verlag (2005).Google Scholar