Abstract
This article builds a new structural default model under the assumption that a firm’s assets return follows a dynamics displaying jumps of both signs. In essence, we expand the work of Hilberink and Rogers (itself an extension of the Leland and Toft framework), which deals only with negative jumps. In contrast, we make use of stable Lévy processes, and we compute the values of the firm, debt and equity under this assumption. Theoretical credit spreads can also be obtained in our framework. They prove to be consistent with the empirical credit spreads observed in financial markets.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abate J. and Whitt W. (1995). Numerical Inversion of Laplace Tranforms of probability distributions. ORSA J. Comput. 7: 36–43
Bernard C., Le Courtois O. and Quittard-Pinon F. (2005). A new procedure for pricing parisian options. J. Deriv. 12(4): 45–53
Bertoin J. (1998). Lévy Processes. Cambridge University Press, Cambridge
Bingham N.H. (1975). Fluctuation theory in continuous time. Adv. Appl. Prob. 7: 705–766
Black F. and Cox J.C. (1976). Valuing corporate securities: some effects of bond indenture provisions. J. Financ. 31(2): 351–367
Carr P., Geman H. and MadanD.B. Yor M. (2002). The fine structure of asset returns: an empirical investigation. J. Bus. 75(2): 305–332
Chen, N., Kou, S.G.: Credit spreads, optimal capital structure, and implied volatility with endogenous default and jump risk. Working Paper (2005)
Dao, T.B., Jeanblanc, M.: Double exponential jump-diffusion process: a structural model of endogenous default barrier with roll-over debt structure. Working Paper (2005)
Doney R.A. (1987). On Wiener-Hopf factorisation and the distribution of extrema for certain stable processes. Ann. Prob. 15(4): 1352–1362
Geman H. and Yor M. (1993). Bessel processes, asian options and perpetuities. Math. Financ. 3: 349–375
Hilberink B. and Rogers L.C.G. (2002). Optimal capital structure and endogenous default. Financ. Stoch. 6: 237–263
Hull J.C., Predescu M. and White A. (2005). Bond prices, default probabilities, and risk premiums. J. Credit Risk 1(2): 53–60
Jarrow R.A. and Turnbull S.M. (1995). Pricing derivatives on financial securities subject to credit risk. J. Financ. 50: 53–85
Jensen M.C. and Meckling W.H. (1976). Theory of the firm: managerial behavior, agency costs and ownership structure. J. Financ. Econ. 3: 305–360
Le Courtois O. and Quittard-Pinon F. (2006). Risk-neutral and actual default probabilities with an endogenous bankruptcy jump-diffusion model. Asia-Pacific Financ. Markets 13: 11–39
Leland H.E. (1994a). Corporate debt value, bond covenants and optimal capital structure. J. Financ. 49(4): 1213–1252
Leland, H.E.: Bond prices, yield spreads, and optimal capital structure with default risk. Working Paper No. 240, IBER, University of California, Berkeley (1994b)
Leland H.E. (2004). Predictions of default probabilities in structural models of debt. J. Invest. Manage. 2(2): 5–20
Leland H.E. and Toft K. (1996). Optimal capital structure, endogenous bankruptcy and the term structure of credit spreads. J. Finance 51(3): 987–1019
Longstaff F.A. and Schwartz E.S. (1995). A simple approach to valuing risky fixed and floating rate debt. J. Financ. 50(3): 789–819
Madan D. and Unal H. (1998). Pricing the risks of default. Rev. Deriv. Res. 2: 121–160
McGill P. (1989). Computing the overshoot of a Lévy process. Stoch. Anal. Path Integ. Dyn. 200: 165–196
McGill, P.: A Plug for Wiener-Hopf methods. Preprint (2003)
Merton R.C. (1974). On the pricing of corporate debt: the risk structure of interest rates. J. Financ 29(2): 449–470
Modigliani F. and Miller M. (1958). The cost of capital, corporation finance and the theory of investment. Am. Econ. Rev. 48(3): 261–297
Rogers L.C.G. (2000). Evaluating first-passage probabilities for spectrally one-sided Lévy processes. J. Appl. Prob. 37: 1173–1180
Samorodnisky G. and Taqqu M.S. (1994). Stable non-Gaussian Random Processes. Chapman-Hall, London
Sarig O. and Warga A. (1989). Some empirical estimates of the risk structure of interest rates. J. Finan. 44(5): 1351–1360
Satō K. (1987). Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Le Courtois, O., Quittard-Pinon, F. The optimal capital structure of the firm with stable Lévy assets returns. Decisions Econ Finan 31, 51–72 (2008). https://doi.org/10.1007/s10203-007-0079-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10203-007-0079-3