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

  • Darsinos, T.
  • Satchell, S.E.

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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File URL: http://www.econ.cam.ac.uk/research/repec/cam/pdf/wp0218.pdf
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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
Date of revision:
Handle: RePEc:cam:camdae:0218
Note: EM
Contact details of provider: Web page: http://www.econ.cam.ac.uk/index.htm

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  1. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
  2. Acharya, Viral V. & John, Kose & Sundaram, Rangarajan K., 2000. "On the optimality of resetting executive stock options," Journal of Financial Economics, Elsevier, vol. 57(1), pages 65-101, July.
  3. 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.
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  7. 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.
  8. Detemple, Jerome & Sundaresan, Suresh, 1999. "Nontraded Asset Valuation with Portfolio Constraints: A Binomial Approach," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 835-72.
  9. 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.
  10. Carpenter, Jennifer N & Remmers, Barbara, 2001. "Executive Stock Option Exercises and Inside Information," The Journal of Business, University of Chicago Press, vol. 74(4), pages 513-34, October.
  11. 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.
  12. Constantinides, George M., 1984. "Warrant exercise and bond conversion in competitive markets," Journal of Financial Economics, Elsevier, vol. 13(3), pages 371-397, September.
  13. 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.
  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.
  15. Menachem Brenner & Rangarajan K. Sundaram & David Yermack, 1998. "Altering the Terms of Executive Stock Options," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-010, New York University, Leonard N. Stern School of Business-.
  16. Emanuel, David C., 1983. "Warrant valuation and exercise strategy," Journal of Financial Economics, Elsevier, vol. 12(2), pages 211-235, August.
  17. Brian J. Hall & Kevin J. Murphy, 2000. "Optimal Exercise Prices for Executive Stock Options," NBER Working Papers 7548, National Bureau of Economic Research, Inc.
  18. 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.
  19. Schulz, G. Uwe & Trautmann, Siegfried, 1994. "Robustness of option-like warrant valuation," Journal of Banking & Finance, Elsevier, vol. 18(5), pages 841-859, October.
  20. Johnson, Shane A. & Tian, Yisong S., 2000. "Indexed executive stock options," Journal of Financial Economics, Elsevier, vol. 57(1), pages 35-64, July.
  21. Jennifer N. Carpenter, 2000. "Does Option Compensation Increase Managerial Risk Appetite?," Journal of Finance, American Finance Association, vol. 55(5), pages 2311-2331, October.
  22. Carpenter, Jennifer N., 1998. "The exercise and valuation of executive stock options," Journal of Financial Economics, Elsevier, vol. 48(2), pages 127-158, May.
  23. 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.
  24. Veld, C.H., 1994. "Warrant pricing : A review of empirical research," Discussion Paper 1994-34, Tilburg University, Center for Economic Research.
  25. 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.
  26. Schultz, Paul, 1993. " Calls of Warrants: Timing and Market Reaction," Journal of Finance, American Finance Association, vol. 48(2), pages 681-96, June.
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