On the theoretical side, I was concerned with stochastic resonance.
Alan White and I spent the next two or three years working together on this.
We developed what is known a stochastic volatility model. This is a model where the volatility as well as the underlying asset price moves around in an unpredictable way.
Briefly speaking, our conclusion is that stochastic volatility does not make a huge difference as far as the pricing is concerned if you get the average volatility right. It makes a big difference as far as hedging is concerned.
Last Update: May, 2020