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Optimal Capital Structure with Endogenous Default and Volatility Risk

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  • Flavia Barsotti

    ()
    (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze)

Abstract

This paper analyzes the capital structure of a firm in an infinite time horizon following Leland (1994) under the more general hypothesis that the firm’s assets value process belongs to a fairly large class of stochastic volatility models. By applying singular perturbation theory, we fully describe the (approximate) capital structure of the firm in closed form as a corrected version of Leland (1994) and analyze the stochastic volatility effect on all financial variables. We propose a corrected version of the smooth-fit principle under volatility risk useful to determine the optimal stopping problem solution (i.e. endogenous failure level) and a corrected version for the Laplace transform of the stopping failure time. The numerical analysis obtained from exploiting optimal capital structure shows enhanced spreads and lower leverage ratios w.r.t. Leland (1994), improving results in a robust model-independent way.

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Bibliographic Info

Paper provided by Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa in its series Working Papers - Mathematical Economics with number 2012-02.

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Length: 37 pages
Date of creation: Jan 2012
Date of revision:
Handle: RePEc:flo:wpaper:2012-02

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Keywords: structural model; stochastic volatility; volatility time scales; endogenous default; optimal stopping;

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  16. Nan Chen & S. G. Kou, 2009. "Credit Spreads, Optimal Capital Structure, And Implied Volatility With Endogenous Default And Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 343-378.
  17. Kyo Yamamoto & Akihiko Takahashi, 2009. "A Remark on a Singular Perturbation Method for Option Pricing Under a Stochastic Volatility Model," Asia-Pacific Financial Markets, Springer, vol. 16(4), pages 333-345, December.
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  19. Bianca Hilberink & L.C.G. Rogers, 2002. "Optimal capital structure and endogenous default," Finance and Stochastics, Springer, vol. 6(2), pages 237-263.
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