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

Abstract

The objective of this paper is to emphasize the di¤erences between a call and a warrant as well as the di¤erent valuation methods of warrants which have been introduced in the nancial literature. For the sake of simplicity and applicability, we only consider a debt-free equitynanced rm. More recently a formal distinction between structural and reduced form pricing models has been introduced. This distinction is important whether one wishes to price a new warrant issue or outstanding warrants. If we are interested in pricing a new issue of warrants, e.g. in the context of a management incentive package, one has to rely on a structural model. However most of practitioners use the simple Black-Scholes formula. In this context, we analyze the accuracy of the approximation of the "true" price of a warrant by the Black-Scholes formula. We show that in the current low interest rate environment, the quality of the approximation deteriorates and the sensitivity of this approximation to the volatility estimate increases.