As the financial meltdown began with overly aggressive lending and securitization techniques, all on the back of faulty quantitative models, it would be useful to re-examine the foundations of quantitative finance.
Emmanuel Derman, in a paper entitled The Boy's Guide to Pricing & Hedging, wrote that “[o]ver the years I’ve seen a few too many fresh graduates who, on being asked why one believes that one can obtain a credible value for an option, reply that it’s because of Girsanov’s theorem.”
Falling in love with the technology
The above comments from the students reminds me of the process of learning to drive. When I first learned to drive, we began with theory such as the rules of the road, e.g. when to signal, etc. I then proceeded to a simulator and then into a car. In my first hour in the car, all I was expected to do was to drive straight. No one expected me to merge or change three lanes and head for an exit in 60 mph freeway traffic.
To be sure, there were technological aids. As examples, crumple zones and air bags of various designs helped to mitigate the effects of a crash. As well, borrowing from the aircraft cockpits, fancy systems such as cockpit management systems and HUD (heads up displays) helped the driver with his situational awareness.
Somewhere along the way, we fell in love with the technology. Would you put your son or daughter in a school bus driven by a ten-year-old, no matter what kind of cockpit management systems, collision avoidance and mitigation systems and other technology it has?
Imagine the following ad:
BUS DRIVER WANTED: Looking for a recent graduate from a top driving school; must be in the top 20% of class. Familiarity with safety management systems, cockpit management systems…
What is quantitative finance?
Derman wrote that:
To begin with, you must distinguish between price and value. Price is what you pay to acquire a security; value is what it is worth. The price is fair when it is equal to the value.
He summarized quantitative finance as:
If you want to know the value of a security, use the price of another security that’s as similar to it as possible. All the rest is modeling. Go and build.
He then added[emphasis are mine]:
Models are only models, toy-like descriptions of idealized worlds. Simple models envisage a simple future; more sophisticated models incorporate a more complex set of future scenarios that can better approximate actual markets. But no mathematical model will capture the intricacies of human psychology. If you listen to the models’ siren song for too long, you may end up on the rocks or in the whirlpool.
Adult supervision needed
The guild of sorcerer’s apprentices took over Wall Street with the acquiescence of the Powers That Be. Where else could you come out of grad school and work as a derivatives trader [see above ad] for 300K plus a year? The results are now clear.
Quantitative models tend to work well at the micro level, such as trading strategies and some forms of risk analysis. However, they can experience catastrophic failure at the level of capturing system wide risks and dynamics. For that, you need adult supervision.