Treasury Secretary Tim Geithner asked the public for suggestions about valuation of the toxic waste taxpayers are going to be choking on under his plan. This is a complicated problem, but there is a place to start.

A big part of the toxic waste is securitized assets. This is a debt issued by a special purpose vehicle, like a business trust or a limited liability company. The SPV is set up by a commercial bank, or an investment bank, or some other financial institution. The sponsor sells the debt to investors, and the money is used to buy a portfolio of assets. The SPV has no other business, so revenue from the assets is the only source of a return for the investors.

The simplest form is mortgage pass-through bonds. The pool consists of a single class of asset, like home mortgage notes or commercial real estate notes. Each month the cash received is used to pay for administrative expenses, and the balance is used to pay first interest, then principal to the investors. The principal reductions come when people sell or refinance, or lose the home in foreclosure.

Then things get complicated. The special purpose vehicle can issue several classes of securities. Most of the securities are debt instruments, like bonds or debentures. There is also an equity class, like stock, which gets anything left over. The terms of the bonds are set out in long documents, written by highly trained and expensively educated lawyers who ought to have real work instead of this serfdom. I hope most of them are or will soon be looking for jobs at Legal Aid, trying to expiate their guilt or at least pick up a paycheck. But I digress.

The point of the complicated documents is that there are several levels of priority of the debt instruments. When the SPV makes the bond payments, it pays one class in full what ever it is entitled to at that time, then the next class gets paid in full, and the next class. If there is not enough for one class, then too bad, and the lower priority people get nothing. The people in the know call these levels tranches (pronounced “traunsh” because the word is French for slice). The tranches have names like Senior, Senior Subordinated, Mezzanine, and trash equity. The losses fall first on the equity, then on the Mezzanines, and then the next higher tranche.

From here, things get really complicated. CDOs can have all kinds of assets in them: stocks, bonds, other CDO securities, corporate loans, even credit default swaps, and all kinds of combinations.

It isn’t that hard to value the simplest form, the pass-through mortgage backed securities. The pools are large enough that historical statistics are valid for each pool at the outset, and as we get experience with the pool, that is, as we see how the borrowers are doing, we can make pretty close estimates of the value of the bonds. If we really cared, we could sample the borrowers whose mortgages are in the pool about their jobs and savings. The data in these calculations is historical data about the performance of the actual mortgages in the pool, so we can feel pretty good about it and our valuation.

It isn’t so easy when we get into the more complicated asset pools. The current scheme for valuing these is mathematical, at least at the outset when valuing them for initial sale. Here is a popular description. Detailed explanations of models are available on the web. I like the abstract of this one:

Gaussian copula is by far the most popular copula used in the financial industry in default dependency modeling. However, it has a major drawback— it does not exhibit tail dependence, a very important property for copula. The essence of tail dependence is the interdependence when extreme events occur, say, defaults of corporate bonds. In this paper we show that some tail dependence can be restored by introducing stochastic volatility on a Gaussian copula. Using perturbation methods we then derive an approximate copula—called perturbed Gaussian copula in this paper.

The author is saying that when things get to the extremes, like really serious recessions, the most popular model simply doesn’t work. Obviously no one will use that model to value toxic waste.

That suggests that the first step is collection of actual data about each of the assets comprising each and every piece of toxic waste. So, I asked my stockbroker, an old-timer, about this. He says in all the meetings and conference calls he has sat through on this stuff, no one has ever said this kind of data collection was under way.

Maybe they’re trying to introduce stochastic volatility into the Gaussian copula model at the tail by getting taxpayers to bail them out of their stupidity, which would be really perturbing.