Valuation of Callable Warrants
Theory and Evidence
ROBERT B. BURNEY
Wall School of Business Administration and Computer Science, Coastal Carolina University,
Conway, SC 29526
WILLIAM T. MOORE
College of Business Administration, University of South Carolina, Columbia, SC 29208
Abstract. 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.
Key words: Callable warrants, option pricing, asset valuation
In the early 1980s firms began issuing warrants that were callable due to explicit contrac-
tual redemption rights or due to provisions whereby expiration dates could be accelerated.
By the mid-1980s, call provisions had become common features. For example, analysis of
contracts of 167 of the warrant issues registered with the Securities and Exchange
Commission (SEC) in 1983 revealed that forty-two were explicitly callable and seven had
provisions allowing issuing firms to accelerate expiration.
Merton (1973) was perhaps the first to offer a valuation model for a callable warrant.
He was able to show that a callable perpetual warrant with exercise price E and call price
K was worth (K/(K ϩ E))S, where S ϭ stock price. Galai and Schneller (1978) showed that
a warrant could be valued in terms of a call option on the issuing firm’s stock; hence, the
Black and Scholes (1973) option pricing model or one of its many variants may be used
to value noncallable warrants. Given that many warrants are callable and most are not per-
petual, a pricing method is needed that goes beyond Merton (1973) and Galai and
Schneller (1978). One can always solve the Merton (1974) partial differential equation
describing the value evolution of any contingent claim as Ingersoll (1977) does for many
callable, convertible securities, but as far as we are aware, no simple pricing model for
callable warrants has been set forth and tested. In this study, we describe and test a simple
model, and we find that it appears to describe callable warrant prices more accurately than
the Black and Scholes (1973) model.
Our findings add to the literature of tests of various option pricing models on war-
rants—such as Chen (1975), Schwartz (1977), Noreen and Wolfson (1981), Sinkey and
Review of Quantitative Finance and Accounting, 8 (1997): 5–18
© 1997 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.