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Home > Resources > WIKI

Warrants

Warrants are options issued by a company on its own stock. The fundamental difference between a standard option and a warrant is what happens at exercise. In the case of a standard call option, upon exercise, existing stock is delivered to the option holder. In the case of a warrant, upon exercise, the company issues new stock that is then delivered to the warrant holder. The issuance of new stock increases the number of shares outstanding which, in turn, decreases the value of each share. Were it not for this dilution effect, the valuation of options and warrants would be identical.

Technical Details

Consider the case where the price-process for the stock is lognormal. In more detail, the underlying assumptions are that:

• the price volatility of the underlying process is constant;
• the price movements of the underlying process follow a log-normal distribution;
• shares can be bought in continuously and in arbitrary amounts; and
• there are no taxes, margins or transaction costs.

These assumptions are standard assumptions in the Black-Scholes world. Hence, the pricing of warrants under these assumptions is essentially the same as the pricing of standard options with a small change to account for the dilution effect. European style options are priced using a version of the Black-Scholes model, while American style options (which may have time varying strikes etc.) are priced using a binomial tree. Note that it is fairly straightforward to extend the standard binomial tree to account for the varying strikes, discrete dividends and time varying rates.

Analysis Supported

FINCAD warrant functions can be used for the following analysis:

• calculate fair value and risk statistics for a European style warrant. Two models are supported. One assumes the underlying equity follows a log-normal process (the standard Black-Scholes assumption) while the other assumes the total firm value is a log-normal process. The total firm value is the sum of the outstanding equity and the warrants.

• calculate the fair value and risk statistics for a wide range of warrants. The warrants may be American style or Bermudan style and may have any combination of time varying strike prices and time varying lockout periods.

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