Sometimes you really need to work with something that, while not perfect, is just good enough and is understandable enough that you don’t do more harm than good. And that’s Black–Scholes. I had gone from a naive 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. They say traders don’t use Black–Scholes because traders use an implied volatility skew and smile that is inconsistent with the model. (Do these same people complain about the illegitimate use of the ‘bastard greek’ vega? This is a far worse sin.) I think this is a red herring.
Yes, sometimes traders use the model in ways not originally intended but they are still using a model that is far simpler than modern-day ‘improvements.’
One of the most fascinating things about the Black–Scholes model is how well it performs compared with many of these improvements. For example, the deterministic volatility model is an attempt by quants to make Black–Scholes consistent with the volatility smile. But the complexity of the calibration of this model, its sensitivity to initial data and ultimately its lack of stability make this far more dangerous in practice than the inconsistent ‘trader approach’ it tries to ‘correct’! The Black–Scholes assumptions are famously poor.
(
Читать дальше )