Valuation of Callable Warrants

A simple valuation model for callable warrants is derived and tested. The model is expressed in closed form except for one term which can be evaluated numerically. Predictions of 78 warrant prices are compared to market prices and the average error is -.224 percent. By contrast, the Black-Scholes model applied to the same warrants produces an average error of 31.44 percent. Thus the callability feature cannot safely be ignored in determining warrant values.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

• Get 10 units per month
• Download Article/Chapter or eBook
• 1 Unit = 1 Article or 1 Chapter
• Cancel anytime

Buy Now

Price includes VAT (France)

Instant access to the full article PDF.

Rent this article via DeepDyve

Similar content being viewed by others

Rational Theory of Warrant Pricing

Black-scholes approximation of warrant prices: slight return in a low interest rate environment

Developing and Measuring the Concept of Warranty Premium

References

• Black, F., “Fact and Fantasy in the Use of Options.” Financial Analysts Journal 31, 36–41, 61–72, (1975). Google Scholar
• Black, F., and M. Scholes, “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy 81, 399–418, (1973). Google Scholar
• Brennan, M., and E. Schwartz, “Convertible Bonds: Valuation and Optimal Strategies for Call and Conversion.” Journal of Finance 32, 1699–1715, (1977). Google Scholar
• Chen, A., “A Model of Warrant Pricing in a Dynamic Market, #x201D; Journal of Finance 25, 1041–1060, (1975). Google Scholar
• Constantinides, G., “Warrant Exercise and Bond Conversion in Competitive Markets.” Journal of Financial Economics 13, 371–397, (1984). Google Scholar
• Cox, D., and H. Miller, The Theory of Stochastic Processes. New York, NY: John Wiley and Sons, Inc., 1965. Google Scholar
• Cox, J., and S. Ross, “The Valuation of Options for Alternative Stochastic Processes.” Journal of Financial Economics 3, 145–166, (1976). Google Scholar
• Efron, B., “Bootstrap Methods: Another Look at the Jackknife.” Annals of Statistics 7, 1–26, (1979). Google Scholar
• Emanuel, D., “Warrant Valuation and Exercise Strategy.” Journal of Financial Economics 12, 211–235, (1983). Google Scholar
• Ferri, M., S. Moore, and D. Schirm, “Investor Expectations About Callable Warrants.” Journal of Portfolio Management 14, 84–87, (1988). Google Scholar
• Galai, D., “A Note on Equilibrium Warrant Pricing Models and Accounting for Executive Stock Options.” Journal of Accounting Research 27, 313–315, (1989). Google Scholar
• Galai, D., and M. Schneller, “Pricing Warrants and the Value of the Firm.” Journal of Finance 33, 1339–1342, (1978). Google Scholar
• Ingersoll, J., “A Contingent Claims Valuation of Convertible Securities.” Journal of Financial Economics 4, 289–322, (1977). Google Scholar
• Ingersoll, J., Theory of Financial Decision Making. Totowa, NJ: Rowman and Littlefield, 1987. Google Scholar
• Kremer, J., and R. Roenfeldt, “Warrant Pricing: Jump-Diffusion vs. Black-Scholes.” Journal of Financial and Quantitative Analysis 28, 255–272, (1993). Google Scholar
• Lauterbach, B., and P. Schultz, “Pricing Warrants: An Empirical Study of the Black-Scholes Model and Its Alternatives.” Journal of Finance 45, 1181–1209, (1990). Google Scholar
• Leonard, D., and M. Solt, “On Using the Black-Scholes Model to Value Warrants.” Journal of Financial Research 13, 81–92, (1990). Google Scholar
• Merton, R., “The Theory of Rational Option Pricing.” Bell Journal of Economics and Management Science 4, 141–183, (1973). Google Scholar
• Merton, R., “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates.” Journal of Finance 29, 449–470, (1974). Moody's Industrial Manual. New York, NY: Moody's Investor Service, (Various years). Google Scholar
• Noreen, E., and M. Wolfson, “Equilibrium Warrant Pricing Models and Accounting for Executive Stock Options.” Journal of Accounting Research 19, 384–398, (1981). Google Scholar
• Schultz, P., “Calls of Warrants: Timing and Market Reaction.” Journal of Finance 48, 681–696, (1993). Google Scholar
• Schwartz, E., “The Valuation of Warrants: Implementing a New Approach.” Journal of Financial Economics 4, 79–93, (1977). Google Scholar
• Sinkey, J., and J. Miles, “The Use of Warrants in the Bail out of First Pennsylvania Bank: An Application of Option Pricing.” Financial Management 11, 27–32, (1982). Google Scholar

Author information

Authors and Affiliations

1. Wall School of Business Administration and Computer Science, Coastal Carolina University, Conway, SC, 29526 ROBERT B. Burney
2. College of Business Administration, University of South Carolina, Columbia, SC, 29208 WILLIAM T. Moore

1. ROBERT B. Burney