I wrote a couple of days ago about how quantitative finance keeps working in the same paradigm — pick a process, calibrate it to liquid securities, calculate the value of illiquid ones, and then asked ‘Is that all there is?’
I received several emails in response, some agreeing with me, and one or two chiding me for being pessimistic, so I want to expand a little.
I’m not pessimistic. So many new markets (synthetic CDOs, etc) have exploded in part because of the applicability of some form of derivatives technology to hedging them. What I was saying was that I was a little bored at seeing derivatives technology applied over and over again. I do the same thing myself, because the theory is so clean and so tempting, so people in glass houses … but nevertheless.
But there are interesting things that can be done and are being done in at least two other areas.
One is the behavior of underlyers rather than derivatives — how do stocks, currencies, etc evolve beyond lognormality? Variance gamma, Mandelbrot, Stanley & co, etc? This is long overdue.
The second is valuation in incomplete markets. Since most things trade in incomplete markets, in the sense that you cannot replicate them with something more primitive, this is related to modeling underlyers.