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Valuation of Put Options on Leveraged Equity

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  • Marco Realdon

Abstract

This paper presents new closed form solutions for the valuation of European put options and of "down-an-in" barrier options written on leveraged equity. Unlike in past literature (Toft and Prucyk, 1997) and in keeping with empirical evidence, the model allows equity to retain value even after the firm's default and reorganisation. This stylised fact can significantly alter the valuation of equity put and "down-and-in" options as bankruptcy costs, bargaining power of equity holders, debt maturity and other firm parameters change. The value of "in-the-money" puts often decreases in the firm's assets volatility. The model can produce a variety of realistic implied equity volatility "skews".

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Paper provided by Department of Economics, University of York in its series Discussion Papers with number 03/19.

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Handle: RePEc:yor:yorken:03/19

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Postal: Department of Economics and Related Studies, University of York, York, YO10 5DD, United Kingdom
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Keywords: Equity put options; Leveraged equity; Default and reorganisation; Barrier options; "down-and-in" options;

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  1. Franks, Julian R & Torous, Walter N, 1989. " An Empirical Investigation of U.S. Firms in Reorganization," Journal of Finance, American Finance Association, vol. 44(3), pages 747-69, July.
  2. Fan, Hua & Sundaresan, Suresh M, 2000. "Debt Valuation, Renegotiation, and Optimal Dividend Policy," Review of Financial Studies, Society for Financial Studies, vol. 13(4), pages 1057-99.
  3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  4. Leland, Hayne E, 1994. " Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Journal of Finance, American Finance Association, vol. 49(4), pages 1213-52, September.
  5. Ericsson, Jan & Reneby, Joel, 1996. "Stock Options as Barrier Contingent Claims," Working Paper Series in Economics and Finance 137, Stockholm School of Economics, revised 01 Feb 2002.
  6. Weiss, Lawrence A., 1990. "Bankruptcy resolution: Direct costs and violation of priority of claims," Journal of Financial Economics, Elsevier, vol. 27(2), pages 285-314, October.
  7. Goldstein, Robert & Ju, Nengjiu & Leland, Hayne, 2001. "An EBIT-Based Model of Dynamic Capital Structure," The Journal of Business, University of Chicago Press, vol. 74(4), pages 483-512, October.
  8. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
  9. Pierre Mella-Barral & William R M Perraudin, 1993. "Strategic Debt Service," CEPR Financial Markets Paper 0039, European Science Foundation Network in Financial Markets, c/o C.E.P.R, 77 Bastwick Street, London EC1V 3PZ.
  10. Hayne E. Leland., 1998. "Agency Costs, Risk Management, and Capital Structure," Research Program in Finance Working Papers RPF-278, University of California at Berkeley.
  11. Reneby, Joel & Ericsson, Jan, 2001. "The Valuation of Corporate Liabilities: Theory and Tests," Working Paper Series in Economics and Finance 445, Stockholm School of Economics, revised 19 Dec 2002.
  12. Toft, Klaus Bjerre & Prucyk, Brian, 1997. " Options on Leveraged Equity: Theory and Empirical Tests," Journal of Finance, American Finance Association, vol. 52(3), pages 1151-80, July.
  13. Anderson, Ronald W. & Sundaresan, Suresh & Tychon, Pierre, 1996. "Strategic analysis of contingent claims," European Economic Review, Elsevier, vol. 40(3-5), pages 871-881, April.
  14. Hayne Leland., 1994. "Bond Prices, Yield Spreads, and Optimal Capital Structure with Default Risk," Research Program in Finance Working Papers RPF-240, University of California at Berkeley.
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