Warrant


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Equity Warrant Definition and Valuation


FinPricing provides valuation models for the following warrants and rights:


1. Equity Warrant Introduction

An equity warrant gives the holder the right to purchase shares at a fixed price from the firm. It is an option on the common stock of a firm issued by the same firm. Warrants are in many ways similar to equity options, but a few key differences distinguish them.

Warrants tend to have longer durations than do exchange-traded equity options. They are traded over the counter more often than on an exchange. Investors cannot write warrants like they can options. Warrants do not pay dividends or come with voting rights. When warrants are exercised, the company typically issues new shares at the exercise price to fill the order. The resulting increase in shares outstanding dilutes the share value.

Investors are attracted to warrants as a means of leveraging their positions in a security. Warrants provide investors a way to hedge risk or speculate. They can be used to exploiting arbitrage opportunities.

Warrants frequently attached to fixed rate bonds or preferred stock as a sweetener can be used to enhance the yield of the fixed rate bond and make them more attractive to potential buyers. Most commonly issued warrants are often detachable, meaning that they can be separated from the fixed rate bond and sold on the secondary market before expiration. Wedded or wedding warrants are not detachable. The investor must surrender the fixed rate bond or preferred stock the warrant is “wedded” to in order to exercise it. Naked warrants are issued on their own, without accompanying fixed rate bonds or preferred stock.


2. Equity Warrant Payoffs

If there were m outstanding shares and n outstanding warrants exercised, the dilution factor corresponding to the percentage of the firm value that is represented by the warrants is given by 
  α = m / (m + n)

The payoff of the warrant at maturity T is given by

Equity warrant payoff in FinPricing

3. Equity Warrant Valuation

Warrants can be categored into three categories: European, American, and Callable/Call:

European warrants can only be exercised on the expiration date. An European warrants can be valued by the diluted Black-Scholes model and some modifications must be made to the parameters.

The price of the warrant under the diluted Black-Scholes model is given by

Equity Warrant valuation in FinPricing

Strictly speaking, A is the asset price of the firm and s is the volatility of the firm (not stock). Both of them are not observable.

An American warrant allows the warrant holder to exercise their right to buy or sell the underlying on any date until expiry, The valuation of an American warrant is more complex. There is no closed form solution. One needs to use numeric approach to price it.

A Callable warrant or call warrant gives the writer the right to recall/terminate the warrant on pre-determined dates for a pre-determined price. This callable (call) feature allows the writer to limit the warrant buyer's profit by activating an embedded call feature so as the position is closed out before the maturity.

Callable warrants or call warrants typically have contractual restaints that limit issuing firms' options. For instance, an issuer can force the warrant to exercise on or after a future date, in event that stock price has been in excess of a threhold (usually 150% of exercise price) on any 20 trading days within a period of 30 consecutive trading days.

There is no closed form solution for callable warrants or call warrants, one has to reach for numerical approaches, such as PDE or Monte-Carlo.


4. Related Topics