In this paper, we assess the information content of volatility forecasts based on the VIX and VXN implied volatility indexes in a daily market risk evaluation framework. Our empirical application focuses on the S&P100 and NASDAQ100 indexes and we high-light the models’ performances in distinct historical time periods which include bull/bear markets and high/low volatility markets. The performance of the VaR models is evaluated using a wide range of tests which span LR, independence, conditional coverage and density forecast tests. Our results show that straightforward volatility forecasts based on the implied volatility indexes provide meaningful results when market risk must be quantified. Furthermore, the models’ performances do not deteriorate in challenging trading environments.
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. Moreover volatility forecasting has found numerous applications in quantitative finance, such as portfolio management, option pricing or risk management. In these three fields, volatility forecasts are one of the main inputs to the relevant models and are thus of paramount importance in the empirical application.
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 options market. According to Jorion (1995) who deals with FOREX data, implied volatility is an efficient but biased forecast of future volatility. Canina and Figlewski (1993) (see also Figlewski, 1997) show that there is almost no correlation between implied volatility and future realized volatility. Christensen and Prabhala (1998) argue that the use of overlapping data and the inclusion of the October 1987 market crash in the Canina and Figlewski (1993) paper is one of the main explanation as to why implied volatility was found inefficient and biased and compared so poorly with volatility forecasts based on historical returns. They show that implied volatility indeed outperforms past volatility in forecasting future volatility and features a high information content. For the S&P100 index and VIX implied volatility index, Blair, Poon, and Taylor (2001) show that historical returns do not provide much incre- mental information compared to the information given by the VIX index of implied volatility. For three class of assets (stock index, exchange rate and oil), Martens and Zein (2002) show that implied volatility measures do provide superior volatility forecasts compared to daily GARCH-type models. However the switch to high-frequency intraday returns and realized volatility modelled using long memory models alters the outcome of the tests as “long memory volatility forecasts can compete with implied volatility”. For foreign exchange volatility and using intraday returns, Neely (2002) argues that implied volatility is a biased estimator of future realized volatility and that volatility forecasts from econometric models should be taken into account. Ederington and Guan (2002) examine the relevance of implied volatility forecasts using S&P500 futures options data and conclude that “implied volatility has strong predictive power and generally subsumes the information in historical volatility”. Giot (2003) compares the incremental information content of lagged implied volatility to GARCH models of conditional volatility for a collection of agricultural commodities traded on the New York Board of Trade and shows that past squared returns only marginally improve the information content provided by the lagged implied volatility.
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Implied volatility indexes and daily Value-at-Risk models
