Finding, measuring and using mean reversion in financial data

George Papanicolaou

Abstract: It is common experience that financial markets are more volatile at some times than at others. It is natural to suppose that once volatility has increased, it then reverts towards a mean level. Indeed, mean reversion of volatility for the S&P500, or other equity indices, has been observed for a long time. However, it is difficult to quantify by the usual econometric methods, as are its implications for derivative pricing. I will review the inadequate status of understanding of mean reversion in the literature and show that it is not possible to make a simple 'stylized' assessment of it. In fact there are at least two distinct rates of mean reversion that can be identified in the S&P500 and in the Dow Jones. I will then show how mean reversion can be incorporated in stochastic volatility models for pricing derivatives and the results that come out. I will also comment on mean reversion in interest rates and its implications.

References: Maturity cycles in implied volatility. Jean-Pierre Fouque, George Papanicolaou, K. Ronnie Sircar and K. Solna. To appear in Finance and Stochastics in 2003 (PDF)