What's A Derivative?

From NPR's Ask a Banker, here is a great primer on derivatives from Matt Levine.  Excerpt:

I will tell you what a derivative is, but I will take a while to get there, and since I won't use words like "put option" or "synthetic CDO" you may feel cheated. That is okay. If you want to understand derivatives, you must learn to live with uncertainty, and also with feeling cheated.
In your finance textbook, if you have one, which I hope you don't because I'm just making this up, a derivative is defined as a contract whose payoffs are determined by reference to the price of some underlying variable. Derivatives, which include options, futures, forwards and swaps, allow levered and/or nonlinear bets and ...
... and let's start somewhere else.
There is a world. That world will have a future, and that future is uncertain. There are different possible states of the world, and different things will happen to you in those different states. If it's cold this winter, you will be sad, or perhaps happy if that's what you're into. If it rains tomorrow, you will get wet. If you take an economics course, you will start to talk like this.
If you are a company or an investment fund, the outcomes that you care about can pretty much be reduced to money: if it's cold this winter, individual workers and managers might be happy or sad, but the company has no feelings. The company just has money. If it's cold this winter, the company might have more money, if it's an oil company, because people will buy more oil to heat their homes. Or it might have less money, if it's in the agriculture business, because its crops will freeze. Or it might have the same amount of money, if it's, like, Facebook or whatever.
One thing you can do is graph future states of the world versus the amount of money you will have in those states. So for instance here is the money that an oil company will make this year (y-axis), graphed against the temperature this winter (x-axis):

The world is not this simple.
This is a simple chart but you should see immediately that it's wrong, or at least not right.
Of course you can't predict how much money an oil company will make just by knowing the weather: there are many other things going on.

Matt follows this intro with more great charts and graphs to explain hedging, prediction, and risk in the derivatives market, and concludes with "Next time, maybe: What I did in banking, or, derivatives for regulatory arbitrage, or, why everything above was false."  Levine also wrote "What Investment Bankers Do All Day," another snarky and fascinating piece ("The short answer: nothing. The long answer: They're "obsequious and needy" "middlemen" who find people looking to invest money).