AN INTRODUCTION.
Warrants and convertible securities are among the earliest corporate financial innovations. Warrants are typically of a shorter duration, are detachable from the securities from which they are issued, and carry an exercise price, which requires a cash payment when used. They are frequently issued with private placement bonds and occasionally with public bond issues. They are also occasionally used as compensation for investment bankers and as part of restructuring packages for firms reorganising after bankruptcy. The most common warrant is a long-term call option that is attached to a bond or a stock issue.

Valuation of Warrants: Warrants are American call options and can be valued using the Black-Scholes model. Like any other American option, the value depends on the share price, exercise price, the volatility, the interest rate, and the time required for it to mature. Warrant valuation is done keeping in view the fact that the exercise of the warrant results in an increase in the number of shares outstanding. This causes dilution and needs to be adjusted.
The value of a warrant at maturity can be written as:
Value at maturity

Where

q = number of warrants issued per share outstanding
N = number of shares outstanding
EX = exercise price of the warrant
V = value of the equity of the firm after the issue of the warrant

In effect, the warrant is worth 1/(1+q) times the value of a call option written on the stock of an alternate firm with the same equity V and outstanding shares N, but with no warrants. This would require calculating the value of the share price of the notional firm and also adjusting the volatility (standard deviation) of its equity to reflect the balance sheet of the notional firm. The above example shows the calculations involved.

CONVERTIBLE SECURITIES.
The typical convertible security is a long-term option that is attached to a bond or a preferred stock and gives its holder the option to exchange the bond or preferred stock for another security of the company, usually the common stock.

The value of a convertible bond is equal to the value of the bond component plus the value of the option component. Convertible bonds and warrant holders are not entitled to receive any cash dividends till they exercise these bonds and warrants. Their exercise prices are automatically adjusted for any stock split or stock dividends. Corporates usually have call options on the convertible bonds they issue. This allows them to call the bonds to force conversion of the same. The optimal rule for calling convertible securities is to call them when the value of the convertible security reaches the call price.

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