Principles of smooth and continuous fit in the determination of endogenous bankruptcy levels
- 165 Downloads
We revisit the previous work of Leland [J Finance 49:1213–1252, 1994], Leland and Toft [J Finance 51:987–1019, 1996] and Hilberink and Rogers [Finance Stoch 6:237–263, 2002] on optimal capital structure and show that the issue of determining an optimal endogenous bankruptcy level can be dealt with analytically and numerically when the underlying source of randomness is replaced by that of a general spectrally negative Lévy process. By working with the latter class of processes we bring to light a new phenomenon, namely that, depending on the nature of the small jumps, the optimal bankruptcy level may be determined by a principle of continuous fit as opposed to the usual smooth fit. Moreover, we are able to prove the optimality of the bankruptcy level according to the appropriate choice of fit.
KeywordsCredit risk Endogenous bankruptcy Scale functions Fluctuation identity Continuous and smooth pasting principles Wiener–Hopf factorization
Mathematics Subject Classification (2000)91B28 91B99 91B72
Unable to display preview. Download preview PDF.
- 3.Chan, T., Kyprianou, A.E.: Smoothness of scale functions for spectrally negative Lévy processes. (preprint, 2005). http://www.maths.bath.ac.uk/~ak257/levyc2version11.pdfGoogle Scholar
- 4.Chen, N. Kou, S.: Credit spreads, optimal capital structure, and implied volatility with endogenous default and jump risk (preprint, 2005). http://www.newton.cam.ac.uk/preprints/NI05031.pdfGoogle Scholar
- 13.Pistorius, M.R.: An excursion theoretical approach to some boundary crossing problems and the Skorokhod embedding for reflected Lévy processes. In: Séminaire de Probabilités. Springer, Berlin Heidelberg New York (to appear, 2006)Google Scholar
- 14.Surya, B.A.: Evaluating scale functions of spectrally negative Lévy processes (preprint, 2006)Google Scholar