The Risk-Shifting Effect and the Value of a Warrant

Abstract

The exercise of a warrant leads to the well-known dilution phenomenon, whose effects have been extensively studied over the last four decades. In contrast, the existing literature has paid inadequate attention to the volatility spillover between stockholders and warrant holders. This “risk-shifting effect” has significant implications on warrant pricing, since any formula that assumes a constant volatility of stock returns produces a bias. In this paper we show that a CEV process with a specific elasticity parameter properly models the stochastic volatility of stock returns for a firm with warrants outstanding. Besides, we propose an approximate analytical formula, exclusively based on observable market variables, able to absorb the risk-shifting bias.

Keywords: warrant pricing, CEV models, risk shifting

JEL Classification: G10, G13, G14