The information content of implied volatility indexes for forecasting volatility and market risk

In this paper, we assess the efficiency, information content and unbiasedness of volatility forecasts based on the VIX/VXN implied volatility indexes, RiskMetrics and GARCHtype models at the 5-, 10and 22-day time horizon. Our empirical application focuses on the S&P100 and NASDAQ100 indexes. We also deal with the information content of the competing volatility forecasts in a market risk (VaR type) evaluation framework. The performance of the models is evaluated using LR, independence, conditional coverage and density forecast tests. Our results show that volatility forecasts based on the VIX/VXN indexes have the highest information content, both in the volatility forecasting and market risk assessment frameworks. Because they are easy-to-use and compare very favorably with much more complex econometric models that use historical returns, we argue that options and futures exchanges should compute implied volatility indexes and make these available to investors. ∗The author is from Department of Business Administration & CEREFIM at University of Namur, Rempart de la Vierge, 8, 5000 Namur, Belgium, Phone: +32 (0) 81 724887, Email: [email protected], and Center for Operations Research and Econometrics (CORE) at Université catholique de Louvain, Belgium. We are grateful to Luc Bauwens, Peter Christoffersen, Sébastien Laurent and seminar participants at CORE who offered helpful comments. Forecasting volatility has been and still is one of the major success story in the quantitative finance and financial econometrics literature. Indeed, volatility forecasting models have enjoyed a tremendous success since the early 1980’s.1 In financial econometrics, the seminal paper by Engle (1982) has spurred considerable research into ARCH-type models, i.e. the attempt to forecast volatility based on the information given by (past) squared returns. More simple techniques rely on the use of ‘rolling window estimation’ for the variance of the asset returns.2 On the other hand, there is a growing trend in the applied finance literature to advocate the use of implied volatility as the best estimate of future volatility. In the framework of an option pricing model such as the Black and Scholes (1973) model, the expected volatility of the asset over the life of the option is the volatility embedded in the price of the option. If call or put option prices are available, then the Black and Scholes (1973) pricing formula can be ‘inverted’ such that the expected volatility over the life of the option is computed from the observed market prices of the call or put options. Indeed, when all the other option parameters are known, there is a one-to-one relationship between the option prices and underlying (expected) asset volatility. This yields the so-called implied volatility. Details are provided in Hull (2000). Because of the growing importance of modelling and predicting asset volatility, the relevance of implied volatility vs volatility forecasts based on historical returns in order to deliver unbiased and efficient forecasts of future realized volatility is an important topic in modern finance. While early papers (see a review in Figlewski, 1997) had to rely on somewhat crude datasets, more recent studies use improved databases of actively traded options to evaluate the information content of implied volatility vs volatility computed from historical returns. However, the empirical evidence is rather mixed as to which volatility forecast performs best, although a broad survey of recent papers by Poon and Granger (2003) indicates that, broadly speaking, forecasts based on implied volatility beat forecasts based on historical returns. For example, Day and Lewis (1992) compare the information content of implied volatility of call options on the S&P100 index to GARCH type conditional volatility. Their evidence is rather mixed. Xu and Taylor (1995) focus on the informational efficiency of the PHLX currency