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The optimal capital structure of the firm with stable Lévy assets returns

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.

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References

  • Abate J. and Whitt W. (1995). Numerical Inversion of Laplace Tranforms of probability distributions. ORSA J. Comput. 7: 36–43

    Google Scholar 

  • Bernard C., Le Courtois O. and Quittard-Pinon F. (2005). A new procedure for pricing parisian options. J. Deriv. 12(4): 45–53

    Article  Google Scholar 

  • Bertoin J. (1998). Lévy Processes. Cambridge University Press, Cambridge

    Google Scholar 

  • Bingham N.H. (1975). Fluctuation theory in continuous time. Adv. Appl. Prob. 7: 705–766

    Article  Google Scholar 

  • Black F. and Cox J.C. (1976). Valuing corporate securities: some effects of bond indenture provisions. J. Financ. 31(2): 351–367

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Geman H. and Yor M. (1993). Bessel processes, asian options and perpetuities. Math. Financ. 3: 349–375

    Article  Google Scholar 

  • Hilberink B. and Rogers L.C.G. (2002). Optimal capital structure and endogenous default. Financ. Stoch. 6: 237–263

    Article  Google Scholar 

  • Hull J.C., Predescu M. and White A. (2005). Bond prices, default probabilities, and risk premiums. J. Credit Risk 1(2): 53–60

    Google Scholar 

  • Jarrow R.A. and Turnbull S.M. (1995). Pricing derivatives on financial securities subject to credit risk. J. Financ. 50: 53–85

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Leland H.E. (1994a). Corporate debt value, bond covenants and optimal capital structure. J. Financ. 49(4): 1213–1252

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Madan D. and Unal H. (1998). Pricing the risks of default. Rev. Deriv. Res. 2: 121–160

    Google Scholar 

  • McGill P. (1989). Computing the overshoot of a Lévy process. Stoch. Anal. Path Integ. Dyn. 200: 165–196

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Modigliani F. and Miller M. (1958). The cost of capital, corporation finance and the theory of investment. Am. Econ. Rev. 48(3): 261–297

    Google Scholar 

  • Rogers L.C.G. (2000). Evaluating first-passage probabilities for spectrally one-sided Lévy processes. J. Appl. Prob. 37: 1173–1180

    Article  Google Scholar 

  • Samorodnisky G. and Taqqu M.S. (1994). Stable non-Gaussian Random Processes. Chapman-Hall, London

    Google Scholar 

  • Sarig O. and Warga A. (1989). Some empirical estimates of the risk structure of interest rates. J. Finan. 44(5): 1351–1360

    Article  Google Scholar 

  • Satō K. (1987). Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge

    Google Scholar 

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Correspondence to Olivier Le Courtois.

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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

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  • DOI: https://doi.org/10.1007/s10203-007-0079-3

Keywords

  • Optimal capital structure
  • Default risk
  • Stable processes
  • Credit spreads

JEL Classification

  • C60
  • G32

Mathematics Subject Classification (2000)

  • 60G52
  • 91B28