The model raft June 23, 2012 at 12:16 pm
… you cannot tame chance. That is what makes it chance. At base, implicitly attributing the kind of predictability these individuals seemed to ascribe to chance was a fundamental error, a category-mistake.
This is a lovely turn of phrase, but it is false. You can, sometimes, tame chance. Black-Scholes is an important piece of work because it shows some circumstances under which you can. Yes, those circumstances are limited, and sometimes not realized in practice. But a lot of the time Black-Scholes hedging of simple derivatives works really well. If you combine it with prudent vega hedges and risk limits to constrain the consequences of model breakdown, it works even more of the time.
Next, a piece of farrago derived from the MacKensie/Spears paper.
If a quant comes up with a model and says up front, hey this is just a sketch of something, it’s not totally realistic, but it’s better than nothing, and then the investment bank ignored the quant’s misgivings and bets the house on the model, who is responsible for the resulting risk?
The person who put the trade on is responsible, as is the head of risk. The quant certainly isn’t. This is for two reasons.
First, no financial model is totally realistic. They are all sketches. Some are better than others. That’s why we have risk limits, that’s why we look at how well hedges perform, that’s why we diversify. Buying $50B of AAA ABS isn’t within limit, it isn’t hedged, and it isn’t diversified. In short it has nothing to do with a quant trading strategy and everything to do with a positive carry position that dishonest managers could pretend didn’t have much risk.
Second and relatedly, it is really important to understand the fundamental shift that happened in the crisis from models-producing-hedge-ratios to models-predicting-values. Copula models, like most pricing models, were originally designed to predict hedge ratios, specifically hedge ratios of bespoke CBOs in the underlying bonds. They were not built to predict the risk or absolute value of CDO tranches, although they did that too. Like all hedging models, they needed to be calibrated. The problems arose when (1) the models were used for something they were not designed for – predicting absolute risk and value – and (2) they were mis-calibrated using historical data that turned out to reflect future reality rather badly. The category error was not confusing statistical variation with uncertainty; it was using a model designed for one thing for something else entirely. Rafts are fun to play on on a quiet lake close to the shore; but only the foolhardy try to cross the ocean on one.