Forecasting Volatility

This monograph puts together results from several lines of research that I have pursued over a period of years, on the general topic of volatility forecasting for option pricing applications. It is not meant to be a complete survey of the extensive literature on the subject, nor is it a definitive set of prescriptions on how to get the best volatility prediction. While at the outset, I had hoped to find the Best Method to obtain a volatility input for use in pricing options, as the reader will quickly determine, it seems that I have been more successful in uncovering the flaws and difficulties in the methods that are widely used than I have been in determining a single optimal strategy myself. Given that I am not able to reveal the optimal technique for volatility forecasting, the main objective of this work is to share with the reader a variety of observations and thoughts about the general problem of volatility prediction and the ways in which it is customarily approached, that I have arrived at after investigating the issues from a number of different angles. Along with describing the theory and the implementation of the standard techniques, I try to point out several areas in which common procedures and ways of thinking about volatility forecasting turn out to involve assumptions or ideas that do not stand up under close examination. Two major themes emerge, both having to do with the connection, or perhaps more correctly, the possibility of a disconnection between theory and practice in dealing with volatility prediction and its role in option valuation. There are two general classes of theories involved. First, there is the statistical theory used in fitting models of price behavior in financial markets. Section I brings out the distinction between physical processes and economic processes in terms of the stability of their internal structure and the prospects for making accurate predictions about them. We argue that routinely applying the classical estimation methodology appropriate for physical processes to the economic process of price behavior in a financial market can lead one to build models that are too complex and to hold inappropriately high expectations about the potential accuracy of volatility forecasts from those models. The second area of conflict between theory and practice arises in the use of implied volatility from option market prices, because there is a significant disparity between the trading strategies arbitrage–based derivatives valuation models assume investors follow and what options market participants actually do. In theory, the implied volatility is the options market's well–informed prediction of the underlying asset's future volatility. Academic researchers typically treat it as such. In practice, however, the arbitrage trading that is supposed to force option prices into conformance with the market's volatility expectations may not be done very actively at all. In many markets it is very hard to execute, and it also will normally be less profitable and will entail more risk than a simple market making strategy that reacts to the market, maximizes order flow and earns profits from the bid–ask spread. The latter, however, may do little to enforce theoretical pricing against the noisy forces of supply and demand in the market. Thus the implied volatility derived from market option prices need not be a good proxy for the market's best forecast of future volatility of the underlying asset. In both cases, I try to point out important implications for volatility estimation that tend to be overlooked by those following traditional lines of thought. It is my hope that in the end, the reader will acquire a broader perspective to see more clearly what is involved in obtaining the volatility input to a derivatives valuation model, and what questions need to be asked of any proposed technique.