While this isn't directly related to the mortgage/real estate/liquidity melt-down, it is highly instructive to see how derivatives blow up. One of the reasons why these mortgage CDO's are being valued at pennies to dimes on the dollar is due to the way the derivatives bundled inside the CDO's have blown up.

http://bloomberg.com/apps/news?pid=20601208&sid=ay5LDbjbjy6c&refer=finance

In addition to the loss of tax revenues from declining real estate values, now localities have to deal with being hoodwinked by the finance sector.

I'd like to explain one of my personal pet peeves with derivatives, finance types and their products: the abuse of mathematics to dissuade people from their own common sense.

One of the components buried within many derivatives is the use of a probability function that is supposed to be part of the computation that prices the derivative. The probability function is used to compute the 'envelope' of possible prices and their historic or possible price outcomes given either past history (ie, past history of price movement) or probability of underlying price or value movement of what the derivative is derived from. In the case of this article, the value of the derivative is computed off interest rates at specific maturities.

Clear as mud so far?

OK, there are dozens upon dozens of what are called "probability distribution functions" (PDFs) in probability and statistics. One example would be the "uniform distribution" where the probability of any outcome has an identical, non-zero probability. Another example is the "normal" or "Gaussian" distribution, aka "the bell curve" -- one of the most commonly used PDF's in mathematics.

There's a theory in statistics called "the law of large numbers" which, informally stated, says "any random event, when sampled in large enough numbers, can have its probability distribution approximated by the Gaussian distribution."

This "law of large numbers" is one of the reasons why the Gaussian/normal distribution is so frequently used in applied statistics. Another is that formal proofs of theories in applied statistics with distributions other than the Gaussian distribution can often become mind-bendingly difficult. As it turns out, the Gaussian distribution's use in formal mathematics of stats works out rather nicely for proving theories and applications.

So in things like options pricing, we see a "Nobel-prize-winning!" theory of option price discovery is the Black-Scholes formula. I'll let folks Google it to see where it comes from and the details. Suffice to say, the B-S formula has taken the options world by storm and many programs and options traders now simply assume the B-S pricing when trading options.

Where's my beef in all of this?

Remember back up there when I informally stated the "law of large numbers?" What did I say? "any random event..."

OK, so how do markets actually set prices? Is it random? Do traders just whip numbers out from twixt their buttocks and put in a bid?

Heck no.

Furthermore, do prices take random excursions from their historical means?

Absolutely not.

Anyone who has been a trader for a little while knows that once prices fall (or rise, but let's assume the fear side) below a certain point, the selling pressure will shoot through the roof as there is a huge jump in the number of traders who want out. There's a clear and obvious correlation going on here (duh!) - when enough selling has occurred to push the price down to a point when a lot of people are seeing a loss quickly enough, more selling pressure comes into the market. This is the very definition of not just a correlation, ie, two random events occurring at the same time - it is also clearly causation. - ie, after the price has dropped to a certain point, suddenly the price movement of future trades is caused by the trades just before it. These are clearly NOT a random event unless you're a pie-in-the-sky finance PhD or mathematics PhD spouting theory. The traders on the floor, most all of whom don't know (or care) about the mathematics behind "random-walk" hypothesis nonsense look at the price action and make their next buy or sell based on what they see on the tape. The traders will tell you this. They'll advise you to do the same thing. Yet the finance/math rocket scientists will try to tell you that the price action follows a random movement.

To this, any rational person says "Bullcrap."

This is true for stocks, bonds (and by reflex, interest rates) and commodities. So it is with derivatives. Some derivatives have the additional problem of being illiquid, but let's put that aside for right now.

This theory:reality disconnect is why derivatives "blow up" in the real world and bite the inexperienced in the butt. The people peddling these things talk in all sorts of mathematical models, and show how they've "tested" their model(s), usually with Monte Carlo analysis, which is also utter nonsense in the markets. Markets can be approximated by Monte Carlo analysis only when everyone is calm and rational. Once prices fall below a certain point, calm and rational thought is exhibited by only a vanishingly small sub-population of those in a market. The reality of derivatives is that they can (and do) blow up under exogenous event and market panic price movements - and blow up BIG - and the reason why is that the price excursions are not going to be nice, random events that can be modeled by a Gaussian distribution when the crap hits the fan.

This is also why people should simply not believe the claims of any financial product any PhD tries to sell you with a fancy model and back-testing, showing you that "you can't lose." The financial equivalent to the second law of thermodynamics is "TANSTAAFL" -- There Ain't No Such Thing As A Free Lunch (coined by Robert Heinlein in The Moon Is A Harsh Mistress). There's always a possibility of losing. With derivatives, the loss and probability of loss are skewed; the chance of a loss might become more infrequent, but when it happens, the loss is vastly amplified.

That some bank or adviser told school districts and school boards that these swaps were a good thing to get into should be made a criminal act. It is literally like a three-card monty huckster (and his shill) taking money from children.

One of the things quickly being noticed in this mortgage melt-down is the part that derivatives are playing. There are a ton of derivatives that have been created, packaged and sold with securitized mortgage debt, and it is one of the things least understood by the regulators, ratings agencies and indeed, the people buying the debt.