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On the Valuation of Warrants and Executive Stock Options: Pricing Formulae for Firms with Multiple Warrants/Executive Options

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Author Info
Darsinos, T.
Satchell, S.E.

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Abstract

Textbook treatment the valuation of warrants takes as a state variable the value of the firm and shows that the value of a warrant is equal to that of a call option on the equity of the firm multiplied by a dilution factor. This approach applies only to the case where the firm issues a single warrant, i. e. n warrants with a single exercise price and time to maturity. In this paper we derive distribution-free (and distribution-specific) formulae for the more realist case where firms issue warrants with different maturities, different strike prices and different dilution factors, and for firms that issue warrants of the same maturity but different strike prices (and different dilution factors). The distinction we make between warrants and executive stock options is simply a matter of whether the contract is traded or not. We use the term warrant to cover both cases.

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Publisher Info
Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 0218.

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Length: 29
Date of creation: Jul 2002
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Handle: RePEc:cam:camdae:0218

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Related research
Keywords: valuation; warrants; executive stock options; capital structure; dilution.;

Other versions of this item:

Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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  1. Lauterbach, Beni & Schultz, Paul, 1990. " Pricing Warrants: An Empirical Study of the Black-Scholes Model and Its Alternatives," Journal of Finance, American Finance Association, vol. 45(4), pages 1181-209, September. [Downloadable!] (restricted)
  2. Darsinos, T. & Satchell, S.E., 2002. "The Implied Distribution for Stocks of Companies with Warrants and/or Executive Stock Options," Cambridge Working Papers in Economics 0217, Faculty of Economics, University of Cambridge. [Downloadable!]
  3. Brian J. Hall & Kevin J. Murphy, 2000. "Optimal Exercise Prices for Executive Stock Options," American Economic Review, American Economic Association, vol. 90(2), pages 209-214, May. [Downloadable!] (restricted)
    Other versions:
  4. Constantinides, George M., 1984. "Warrant exercise and bond conversion in competitive markets," Journal of Financial Economics, Elsevier, vol. 13(3), pages 371-397, September. [Downloadable!] (restricted)
  5. Viral Acharya & Kose John & Rangarajan K. Sundaram, 1999. "On the Optimality of Resetting Executive Stock Options," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-087, New York University, Leonard N. Stern School of Business-.
    Other versions:
  6. Carpenter, Jennifer N & Remmers, Barbara, 2001. "Executive Stock Option Exercises and Inside Information," Journal of Business, University of Chicago Press, vol. 74(4), pages 513-34, October. [Downloadable!] (restricted)
  7. Emanuel, David C., 1983. "Warrant valuation and exercise strategy," Journal of Financial Economics, Elsevier, vol. 12(2), pages 211-235, August. [Downloadable!] (restricted)
  8. Chance, Don M. & Kumar, Raman & Todd, Rebecca B., 2000. "The 'repricing' of executive stock options," Journal of Financial Economics, Elsevier, vol. 57(1), pages 129-154, July. [Downloadable!] (restricted)
  9. Howe, John S & Wei, Peihwang, 1993. " The Valuation Effects of Warrant Extensions," Journal of Finance, American Finance Association, vol. 48(1), pages 305-14, March. [Downloadable!] (restricted)
  10. Carter, Mary Ellen & Lynch, Luann J., 2001. "An examination of executive stock option repricing," Journal of Financial Economics, Elsevier, vol. 61(2), pages 207-225, August. [Downloadable!] (restricted)
  11. Jennifer N. Carpenter, 2000. "Does Option Compensation Increase Managerial Risk Appetite?," Journal of Finance, American Finance Association, vol. 55(5), pages 2311-2331, October. [Downloadable!] (restricted)
  12. Jérôme B. Detemple & Suresh Sundaresan, 1999. "Non-Traded Asset Valuation with Portfolio Constraints: A Binomial Approach," CIRANO Working Papers 99s-08, CIRANO. [Downloadable!]
  13. Schultz, Paul, 1993. " Calls of Warrants: Timing and Market Reaction," Journal of Finance, American Finance Association, vol. 48(2), pages 681-96, June. [Downloadable!] (restricted)
  14. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166. [Downloadable!] (restricted)
  15. Johnson, Shane A. & Tian, Yisong S., 2000. "Indexed executive stock options," Journal of Financial Economics, Elsevier, vol. 57(1), pages 35-64, July. [Downloadable!] (restricted)
  16. Detemple, Jerome & Sundaresan, Suresh, 1999. "Nontraded Asset Valuation with Portfolio Constraints: A Binomial Approach," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 12(4), pages 835-72.
  17. Galai, Dan & Schneller, Meir I, 1978. "Pricing of Warrants and the Value of the Firm," Journal of Finance, American Finance Association, vol. 33(5), pages 1333-42, December. [Downloadable!] (restricted)
  18. Brenner, Menachem & Sundaram, Rangarajan K. & Yermack, David, 2000. "Altering the terms of executive stock options," Journal of Financial Economics, Elsevier, vol. 57(1), pages 103-128, July. [Downloadable!] (restricted)
    Other versions:
  19. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144. [Downloadable!] (restricted)
    Other versions:
  20. 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. [Downloadable!] (restricted)
  21. Longstaff, Francis A, 1990. " Pricing Options with Extendible Maturities: Analysis and Applications," Journal of Finance, American Finance Association, vol. 45(3), pages 935-57, July. [Downloadable!] (restricted)
  22. Spatt, Chester S & Sterbenz, Frederic P, 1988. " Warrant Exercise, Dividends, and Reinvestment Policy," Journal of Finance, American Finance Association, vol. 43(2), pages 493-506, June. [Downloadable!] (restricted)
  23. Schulz, G. Uwe & Trautmann, Siegfried, 1994. "Robustness of option-like warrant valuation," Journal of Banking & Finance, Elsevier, vol. 18(5), pages 841-859, October. [Downloadable!] (restricted)
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