Wednesday, May 7, 2008

Paul Wilmott on the Black Scholes option pricing model.

Paul Wilmott had an interesting post last week about his tryst with the Black Scholes option pricing model. On how his opinion of the model has changed with time and experience.

I had gone from a naïve belief in Black-Scholes with all its simplifying assumptions at the start of my quant career, via some very sophisticated modelling, full circle back to basic Black-Scholes. But by making that journey I learned a lot about the robustness of Black-Scholes, when it works and when it doesn’t, and have learned to appreciate the model despite its flaws. This is a journey that to me seems, in retrospect, an obvious one to take. However, most people I know working as quants rarely get even half way along. (As discussed elsewhere, I believe this to be because most people rather like being blinded by science.) "

"My research now continues to be aimed at questioning commonly held beliefs, about the nature of ‘value,’ about how to use stochastic calculus to make money rather than in a no-arbitrage world, about the validity of calibration (it’s not valid!), and how people price risk (inconsistently is how!). All the time I strive to keep things understandable and meaningful, in the maths sweet spot that I’ve mentioned before. "

The many improvements on Black-Scholes are rarely improvements, the best that can be said for many of them is that they are just better at hiding their faults. Black Scholes also has its faults, but at least you can see them. It’s simply that more complexity is not the same as better, and the majority of models that people use in preference to Black-Scholes are not the great leaps forward that they claim, more often than not they are giant leaps backward.

Wilmott has posted some good stuff on this topic, and I suggest you check out his blog.