Stochastic Volatility

Abstract

Another possible reason for the implied volatility smile is that instantaneous volatility is itself stochastic. As a model of the real world, this idea is attractive. We could measure the volatility of a stock or index like the FTSE over, say, a one month window and plot it over recent years. Alternatively, we could look at the one month volatility implied from at-the-money options over the last year. We would see that in both cases the volatility increases in times of political turmoil or uncertainty. As we cannot predict such events, it seems reasonable to model volatility itself as a stochastic process.