Horribly complex derivatives do exist: a "snowball", for example, "is a structured swap with a funding leg and a coupon stream whereby the coupon paid on a given date is given by the sum of a fraction of the coupon paid in the previous period plus an amount determined by the realization of the rate process in the coupon period itself"

However, while estimating the value of a snowball requires so much computer power that researchers are designing custom hardware and offloading computation onto graphics chips, the difficulty of valuing a derivative does not depend on the derivative itself being complex. The mortgage backed securities which are the most obvious cause of the current problem are actually quite straightforward. That doesn't make them easy to value.

The point of the complexity is in fact to make them easier to value. After all, no amount of differential calculus will tell you whether Mr Bloggs at number 11 will default on his mortgage, if you don't know whether he has a job, and what his credit card balance is, and whether house prices on his street are going up or down. If you have good statistics, however, you might have a decent stab at how much a thousand mortgages are worth, or how much the best 400 out of a thousand are worth.

That was the theory. It failed, not because of the complexity of the derivatives, or because of errors in the mathematics, but because the statistics were crap. Statistics collected over ten years during which house prices only ever went up were not of much use when prices started to fall. Statistics collected on mortgages originated by lenders with their own money cannot be used to accurately model mortgages originated by lenders working only for commission. Et cetera.

The other bugbear instruments in some commentary are the "weapons of financial mass destruction", credit default swaps. These are simpler still; just a guarantee by one party of a debt owed by another. The main problem with them is their very simplicity - rather than selling them on like securities, someone holding one would just create a new one to cancel it out. That's what makes it so difficult to sort things out when a participant like Lehman defaults - its net position is manageable, but that net consists of astronomical credits and debits that almost, but not quite, cancel each other out. If the CDSs were more sophisticated (with central clearing), the problems would be smaller.

I think that this New York Times piece is very good, except for the one point, that the difficulty of valuing a mortgage derivative is not due to its inherent complexity, but mostly just because it's made out of mortgages.

Labels: finance