Derivatives are financial tools to manage risk in which the value of the derivative is derived from the value of an underlying asset.

There are several types of derivatives.

With a forward derivative, the parties enter in an advance agreement in which both agree to settlement and delivery at a later date. The party obligated to buy takes a long position and the party obligated to sell takes a short position.

A futures derivative is similar to a forward derivative except that a future derivative is more standardized and traded on an organized market. Additionally, margin requirements and periodic marking to the market are characteristic of a future derivative. With daily marking to the market, when the market value increases, the party holding the long position receives that value which is paid by the short party.

Swaps, such as a currency swap or interest rate swap, are agreements between two parties to exchange the cash flows of one security for the cash flows of another security from time to time. The currency swap, which originated from the concept of house swapping, provides for the use of another currency without actually exchanging the currency across national borders. Interest rate swaps are more prevalent than currency swaps.

Options provide for the right to buy or sell at a specified future date. Call options are options to buy a security at a later date at the presently agreed upon price. Similarly, a put option is an option to sell a security at a later date at the presently agreed upon price. That agreed upon price is known as the exercise price or striking price for the contract. An option that can be immediately exercised profitably is called "in-the-money." Conversely options that cannot be exercised profitably are out-of-the-money. The rare instance when the market price of an asset exactly equals the exercise price is said to be at-the-money.
Put options can be combined with long positions in the underlying asset to synthesize calls and calls can be combined with short positions in the underlying asset to synthesize puts. The popular practice of buying cheap puts, combining them with long positions in the stock and selling calls profitably is known as conversion.
Warrants, which provide for earning additional revenue from shares and provide protection for the value of the asset, are oftentimes given to company executives in the form of compensation or employee stock options.

When pricing derivatives, we assume that it is always possible to develop perfect tracking portfolios and there are no opportunities for arbitrage.

Dilution resulting from warrent exercise
The warrant dilution effect deals with what happens to the underlying company when a warrant is exercised. Warrants are issued by the company. Call options are issued by people who already own (usually) previousl issued shares in the company. So when warrants are exercised more shares are issued. When calls are exercised existing shares simply transfer from one stockholder to another. Both warrants and calls are exercised when the exercise price is below the stock's market price. Otherwise it is pointless to exercise them. When a call is exercised there is no effect on the number of shares outstanding. Al that changes is who owns them. When a warrant is exercised new shares are purchased from the company at a price that is below the market price. The dilution effect is that these new lower price shares have all the same rights as pre-existing shares. So on average the shares are reduced in average cost. The people who are negatively affected by dilution are pre-existing shareholders. The difference is often modest and can then be ignored.

Sample derivative problems