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Derivatives are financial products or assets whose structure and value is derived from another asset.

The base asset is called the underlying asset but usually it is simply referred to as the underlying. The linkage of the derivative to the underlying is usually through the payoffs of the derivative.

The payoffs are the revenues paid to the holders of the derivative product.

The payoffs of a derivative are usually determined by the price of the underlying asset, at some point in the derivative contract’s life, often on its expiration date.

The main tool for linking the derivative value to the underlying price is arbitrage.

Terminology

The price of the underlying asset is referred to as the cash price or the spot price to distinguish it from the price of the derivative.

The underlying assets are said to be traded on the cash market, when the underlying is a cash product as is usually (but not always) the case.

Profit and loss may arise from the position of underlying assets. The position may be a single asset or a portfolio of assets.

Assumptions

In teaching the treatment of derivatives, certain simplifying assumptions are often used or placed into effect, unless otherwise stated.

For example:

  1. Transaction costs are usually set to zero.
  2. Unlimited investing or borrowing at the risk free rate is implied.
  3. There are no restrictions on short selling any asset

None of the above assumptions hold in reality, but are assumed in derivative theory. Experiences show they are pretty good assumptions and that reality does not deviate too far from them. Derivative theory built out on these assumptions turns out to be very robust.

Examples of Derivatives

  1. Forwards and futures are contracts that lock in the price two parties will buy and sell an asset for at a some future date.
  2. Options are similar to forwards, but one party as the right not to participate at the time the contract expires.
  3. Swaps are linked to interest rates, allowing a floating interest rate to be switched to a fixed rate.
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