Fear tends to manifest itself much more quickly than greed, so volatile markets tend to be on the downside. In up markets, volatility tends to gradually decline. Philip Roth
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. John Hull
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. John Hull
