According to Wikipedia:

“In finance, a **derivative** is a special type of contract that *derives* its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often called the “underlying”. Derivatives can be used for a number of purposes – including insuring against price movements (hedging), increasing exposure to price movements for speculation or getting access to otherwise hard to trade assets or markets.

Some of the more common derivatives include futures, forwards, swaps, options, and variations of these such as caps, floors, collars, and credit default swaps. Most derivatives are traded over-the-counter (off-exchange) or on an exchange such as the Chicago Mercantile Exchange, while most insurance contracts have developed into a separate industry. Derivatives are one of the three main categories of financial instruments, the other two being equities (i.e. stocks or shares) and debt (i.e. bonds and mortgages).

Derivatives are used for the following:

- Hedge or mitigate risk in the underlying, by entering into a derivative contract whose value moves in the opposite direction to their underlying position and cancels part or all of it out
- Create option ability where the value of the derivative is linked to a specific condition or event (e.g. the underlying reaching a specific price level)
- Obtain exposure to the underlying where it is not possible to trade in the underlying (e.g. weather derivatives)
- Provide leverage (or gearing), such that a small movement in the underlying value can cause a large difference in the value of the derivative
- Speculate and make a profit if the value of the underlying asset moves the way they expect (e.g. moves in a given direction, stays in or out of a specified range, reaches a certain level)
- Switch asset allocations between different asset classes without disturbing the underlying assets, as part of transition management
- Avoid paying taxes. For example, an equity swap allows an investor to receive steady payments, e.g. based on LIBOR rate, while avoiding paying capital gains tax and keeping the stock.”

Given the broad usage of derivatives and the size of the derivatives market, it is interesting to conceive new derivatives. In particular, it is possible to construct derivatives based on the complexity of an underlying as well as on the rate of complexity. Below are a few examples of a trivial **complexity derivative** based on the following stocks: GE, CAT, PFE, BA, DIS, TRV, INTC, MMM, NKE and MRK.

Building derivatives based on complexity is simple and has a tremendous advantage: it produces a direct measure of its own complexity. Derivatives are said to be highly complex hence potentially dangerous. While this may be true, it is unclear how similar statements may be substantiated without actually measuring the complexity of derivatives! There may in fact exist financial products the dynamics of which may be more complex than that of some derivatives.

More elaborate complexity derivatives may be established based on the rate of change of complexity, D = dC(t)/dt, i.e. a derivative of complexity versus time.

Derivatives may also be constructed using as underlying a market index. The example below illustrates the evolution of complexity of the S&P index over a decade. It is interesting to note how complexity is increasing but at a slowing pace. This may point to a ‘saturation’ of the system.

The creation of complexity-based derivatives may also allow regulators to do the following:

1. Classify, rank and rate the complexity and resilience of derivatives. Establish maximum allowable levels of complexity and minimum allowable resilience of financial products. Products with low resilience contribute to making the system (economy) more fragile.

2. Once the most complex (dangerous) derivatives have been identified, they should be withdrawn progressively from circulation in order to reduce the fragility of the global financial system.

The hallmark of modern finance is complexity. Why not trade complexity?

More soon.

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