The article begins:
"Paul Wilmott is a 49-year-old Oxford-trained mathematician and arguably the most influential quant today, the brightest star in their insular, nerdy universe. The Financial Times calls him a "cult derivatives lecturer." Nassim Taleb, the mathematician and author of the bestseller The Black Swan, calls him the smartest quant in the world. "He's the only one who truly understands what's going on ... the only quant who uses his own head and has any sense of ethics," says Taleb. Wilmott stands atop a veritable quant empire. His wonk-made-simple textbooks sell for hundreds of dollars. A subscription to his bimonthly magazine, Wilmott, costs $695 a year. His Web site, Wilmott.com, is the nerve center of the quant community, with 65,000 registered users and a chat forum that buzzes over such topics as geodesic stochastic manifolds and swaption vol arbitrage."
It appears as if Wilmott has reassembled a collection of followers whose intent is to rejuvenate the quant world. This world has been around for a while and as I have written, I have been on its periphery as an observer and some time participant. However as one who has implemented many analyses using similar techniques but from an engineering or medical perspective I have always been aware of the hidden flaws which result from the fact that we never really know everything. In addition systems have the perverse characteristic of creating for want of a better term antibodies or new rejection of reaction mechanisms which we did not model or even understand from the outset. It is often these characters who in the end dominate the analysis and the results.
The article continues with an interesting review of the history:
"The watershed came in the mid-1970s when MIT-trained economist Robert Merton along with Myron Scholes, a University of Chicago economist, and Fischer Black of Harvard developed the Black-Scholes equation for pricing options, which eventually garnered a Nobel Prize. Over the past 20 years, quantitative methods gradually spread into commercial and investment banks, fueling a huge demand for math savants. Since the mid-1990s, dozens of master's-degree programs in financial engineering have sprouted up at top universities. (The highest-rated ones are at Carnegie Mellon, Columbia, Stanford and Princeton.) Along with physics Ph.D. programs, these are the primary breeding grounds for the many thousands of quants who have found their way to Wall Street. It's these programs that Wilmott has taken direct aim at with his CQF. "I'm building a new army of quants," he says. His ranks currently stand at 1,273…"
The interesting fact in the above is that these are mathematicians and physicists and for the most part no truly seasoned engineers. My first book, Stochastic Systems and State Estimation (Wiley, 1973) was the first book to address many of these issues. However I started the Preface by saying "The world is filled with uncertainty…" and by that I meant that even modeling uncertainty as I had done now almost 40 years ago, namely establishing all the models the quants now use, I already by that time was a seasoned engineer, having seen the limitations of the models. Outliers were all too common and in true science and engineering we all too often gain insight from the outliers, they teach us about what is wrong with our models and in turn we design for outliers. The quants having for the most part no real world experience both ignored the possibility of outliers as well as designed around them, a deadly approach.
Let me continue with the article and deal with one of those model problems:
"He's just scribbled a handful of equations on a whiteboard, including one called the Heath-Jarrow-Morton model. Developed in the late 1980s, the formula looks horrifically complicated to the layman. But to a mathematician it's elegant, simple—and dangerous. Behind its simplicity lie hidden mistakes, unobservable variables like volatility and correlation that can provide a false sense of security. "With models, you want to see where things go wrong," says Wilmott. "You want to see the dirt. But HJM is actually just a big rug for [mistakes] to be swept under." For the next half hour, Wilmott deconstructs the thing, cautioning students on over reliance. "In the end, we should all like models that wear their faults on their sleeves," he tells the class…"
Let me show simply why the HJM model is clearly an exercise in futility. Simply stated the HJM model says:
The negative in the above results from the bond being determined backwards not forwards. But they then model the rate as a Gaussian process with some mean growth and driven by a Wiener process. Namely:
However this model of interest rate changes is the equivalent of the phrase "if elephants had wings they could fly….but they don't…" It neglects many gross and dominant effects such as:
1. Catastrophic changes or collapses. This is the outlier formulation.
2. Collusion and conspiracy. This is the ganging together of players who want to control the market.
3. Nonlinear effects and stability problems. The model is too simple and too stable by itself. In the real world there are nonlinearities and feedback effects which result in oscillations and instabilities. They are lacking from here and frankly not even understood well enough to be modeled.
4. Really Bad Noise. The "noise" process is benign on the one hand and malignant on the other. The Wiener process is an artifact of mathematics. It allowed Wiener to do certain things but it also leads to white noise and unstable noise spectra.
5. Group Think: This is the herd process which we all know and which is rarely if ever modeled. The Wiener process and the resulting martingales are independent increment processes, nice for analysis but not really reflective of reality. The herd problem is one which is either herding by following or herding by intent. The latter is collusion with few overt colluders.
The article states:
"To Wilmott, Gaussian is an example of how dangerously abstract quant finance has become."We need to get back to testing models rather than revering them," he says. "That's hard work, but this idea that there are these great principles governing finance and that correlations can just be plucked out of the air is totally false." Wilmott spends a lot of time with another former student trying to tackle the biggest problem facing quant finance right now: how to price all those CDOs sitting on the balance sheets of banks, the toxic assets we hear so much about. "We don't have the tools yet to truly price them," Wilmott says. "People thought we did, but they were nowhere near robust enough.""
The reality is that it is not the Gaussian alone that drives the problems it is the total disconnects from the real world. These processes work in the small, and they work better as the group which uses them agrees on their usefulness, like Black-Scholes, but there is always the breakout process where some new player comes along with another hot idea which perturbs the stability of the club and the system as a whole collapses. In many ways it is akin to the Arthur Conan Doyle tale of the League of the Red Headed Men, a collaboration of a group for a purpose independent of its stated intent.
Collusion and collaboration can lead to local stability but that very process has its seeds of destruction in its very DNA, the need to get the advantage with a new set of models. It is not just the models it is the very nature of the people playing these games. It is not some dark bird of doom, it is human nature.
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