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

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.