Forecasting daily variability of the S&P 100 stock index using historical,realised and implied volatility measurements

The increasing availability of financial market data at intraday frequencies has not only led to the development of improved volatility measurements but has also inspired research into their potential value as an information source for volatility forecasting. In this paper, we explore the forecasting value of historical volatility (extracted from daily return series), of implied volatility (extracted from option pricing data) and of realised volatility (computed as the sum of squared high frequency returns within a day). First, we consider unobserved components (UC-RV) and long memory models for realised volatility which is regarded as an accurate estimator of volatility. The predictive abilities of realised volatility models are compared with those of stochastic volatility (SV) models and generalised autoregressive conditional heteroskedasticity (GARCH) models for daily return series. These historical volatility models are extended to include realised and implied volatility measures as explanatory variables for volatility. The main focus is on forecasting the daily variability of the Standard & Poor's 100 (S&P 100) stock index series for which trading data (tick by tick) of almost 7 years is analysed. The forecast assessment is based on the hypothesis of whether a forecast model is outperformed by alternative models. In particular, we will use superior predictive ability tests to investigate the relative forecast performances of some models. Since volatilities are not observed, realised volatility is taken as a proxy for actual volatility and is used for computing the forecast error. A stationary bootstrap procedure is required for computing the test statistic and its p-value. The empirical results show convincingly that realised volatility models produce far more accurate volatility forecasts compared to models based on daily returns. Long memory models seem to provide the most accurate forecasts.     

Volatility dependences of stock markets with structural breaks

We develop a Vector Heterogeneous Autoregression model with Continuous Volatility and Jumps (VHARCJ) where residuals follow a flexible dynamic heterogeneous covariance structure. We employ the Bayesian data augmentation approach to match the realised volatility series based on high-frequency data from six stock markets. The structural breaks in the covariance are captured by an exogenous stochastic component that follows a three-state Markov regime-switching process. We find that the stock markets have higher volatility dependence during turmoil periods and that breakdowns in volatility dependence can be attributed to the increase in market volatilities. We also find positive correlations between the Asian stock markets, the European stock market, and the UK stock market. The US stock market has positive correlations with all other markets for most of the sample periods, indicating the leading position of US stock market in the global stock markets. In addition, the proposed three-state VHARCJ model with Dynamic Conditional Correlation (DCC) and break structure under student-t distribution has a superior density forecast performance as compared to the competing models. The forecast models with structural breaks outperform those without structural breaks based on the log predicted likelihood, the log Bayesian factor, and the root mean square loss function.     

Forecasting global stock market volatilities in an uncertain world

We investigate the predictive relationship between uncertainty and global stock market volatilities from a high-frequency perspective. We show that uncertainty contains information beyond fundamentals (volatility) and strongly affects stock market volatility. Using several crucial uncertainty measures (i.e., uncertainty and implied volatility indices), we prove that the CBOE volatility index (VIX) performs best in point (density) forecasting; the financial stress index (FSI) in directional forecasting. Furthermore, VIX's predictive power improved dramatically after the COVID-19 outbreak, and the VIX-based portfolio strategy enables mean-variance investors to achieve higher returns. There are two empirical properties of VIX: (i) it helps reduce significantly forecast variance rather than bias; and (ii) its forecasts encompass other uncertainty forecasts well. Overall, we highlight the importance of considering uncertainty when exploring the expected stock market volatility.     

Fund Volatility Index using equity market state prices

The Fund Volatility Index (FVX) is proposed as a forward measure of volatility with applications in fund hedging and risk management. The method applies equity market state prices to individual fund pay‐offs. FVX is validated as a predictor of short‐term realised volatility for 30 exchange traded funds. Performance of the method is compared with existing methods using a data set of 14 925 non‐traded funds. FVX has lower bias and higher forecast accuracy than existing methods. As a more general measure, it allows for incorporation of terms to capture individual fund skewness and projection of higher moments of returns.     

Partial moment volatility indices

Forward‐looking partial moment volatility indices are developed using state‐pricing, called the bear index (BEX) and bull index (BUX). Using S&P 500 index (SPX) option prices, we find that BEX and BUX provide superior forecasts for the lower and upper partial moments of future market realised volatility, respectively. We examine the relation between SPX returns and changes in BEX and BUX at the daily level. Results are consistent with the volatility feedback hypothesis. Further, we show that BEX may be more suitable as the ‘investor fear gauge’ than VIX.     

Earnings guidance and market uncertainty

We study the effect of disclosure on uncertainty by examining how management earnings forecasts affect stock market volatility. Using implied volatilities from exchange-traded options prices, we find that management earnings forecasts increase short-term volatility. This effect is attributable to forecasts that convey bad news, especially when firms release forecasts sporadically rather than on a routine basis. In the longer run, market uncertainty declines after earnings are announced, regardless of whether there is a preceding earnings forecast. This decline is mitigated when the firm issues a forecast that conveys negative news, implying that these forecasts are associated with increased uncertainty.     

Investor Attention and Time‐varying Comovements

This paper analyses the effect of an increase in market‐wide uncertainty on information flow and asset price comovements. We use the daily realised volatility of the 30‐year treasury bond futures to assess macroeconomic shocks that affect market‐wide uncertainty. We use the ratio of a stock's idiosyncratic realised volatility with respect to the S&P500 futures relative to its total realised volatility to capture the asset price comovement with the market. We find that market volatility and the comovement of individual stocks with the market increase contemporaneously with the arrival of market‐wide macroeconomic shocks, but decrease significantly in the following five trading days. This pattern supports the hypothesis that investors shift their (limited) attention to processing market‐level information following an increase in market‐wide uncertainty and then subsequently divert their attention back to asset‐specific information.     

Neural network volatility forecasts

We analyse whether the use of neural networks can improve ‘traditional’ volatility forecasts from time-series models, as well as implied volatilities obtained from options on futures on the Spanish stock market index, the IBEX-35. One of our main contributions is to explore the predictive ability of neural networks that incorporate both implied volatility information and historical time-series information. Our results show that the general regression neural network forecasts improve the information content of implied volatilities and enhance the predictive ability of the models. Our analysis is also consistent with the results from prior research studies showing that implied volatility is an unbiased forecast of future volatility and that time-series models have lower explanatory power than implied volatility. Copyright © 2008 John Wiley & Sons, Ltd.     

Intra–day Behavior of Treasury Sector Index Option Implied Volatilities around Macroeconomic Announcements

If option implied volatility is an unbiased, efficient forecast of future return volatility in the underlying asset, then we should be able to predict its path around macroeconomic announcements from responses in cash markets. Regressions show that volatilities rise the afternoon before announcements that move cash markets, and that post–announcement volatilities return to normal as rapidly as cash prices do. Although implied volatilities are predictable, the Treasury options market is efficient since informed traders do not earn arbitrage profits once we account for trading costs.     

A Likelihood Ratio Test of Price Volatilities: Comparing Stock Index Spot and Futures

This paper uses three methods to estimate the price volatility of two stock market indexes and their corresponding futures contracts. The classic variance measure of volatility is supplemented with two newer measures, derived from the Garman-Klass and Ball-Torous estimators. A likelihood ratio test is used to compare the classic variance measure of price volatilities of two stock market indexes and their corresponding futures contracts during the bull market of the 1980s. The stock market volatilities of the Standard & Poor's 500 (S&P 500) and New York Stock Exchange (NYSE) indexes were found to be significantly lower than their respective futures price volatilities. Since information may flow faster in the futures markets than in the corresponding stock market, our results support Ross's information-volatility hypothesis. It was also noted that the NYSE spot volatility was lower than the S&P 500 spot volatility. If the rate of information flow and firm size are positively related, then the lower NYSE spot volatility is explained by the size effect. The futures price volatilities for the two indexes were insignificantly different from each other. With stock index spot-futures price correlations approaching unity, one implication of our results for index futures activity is that smaller positions in futures contracts may suffice to achieve hedging or arbitrage goals.     

Forecasting aggregate stock market volatility with industry volatilities: The role of spillover index

In this paper, we aim to improve the predictability of aggregate stock market volatility with industry volatilities. The empirical results show that individual industry volatilities can provide useful predictive information, while the predictive contribution is limited. We further consider the spillover index between industry volatilities and find it displays strong predictive power for stock market volatility. Based on the portfolio exercise, we find that a mean-variance investor can achieve sizeable economic gains by using volatility forecasts of the spillover index. In addition, we conduct three extended analyses and further demonstrate the superior performance of the spillover index. Also, our results show robustness to a series of alternative settings. Finally, we investigate why the spillover index performs better and answer what information it contains. The results show that the spillover index can reflect and explain investor sentiments that are related to stock market volatility.     

Persistence of announcement effects on the intraday volatility of stock returns: Evidence from individual data

We analyze the persistence effects in the empirical relationship between announcement releases and return volatilities of four major companies of the French stock market using high frequency data over the period 1995–1999. Besides its institutional stability, this sample period avoids the econometric difficulties inherent to simultaneous news arrivals. Our approach contributes to the relevant literature in that we focus on individual stock volatilities rather than indices, we distinguish firm‐specific and macroeconomic announcements, and we endogenize both the durations of announcement effects and the response patterns of equity prices. We find that our individual volatilities are affected by a systematic market effect, calendar effects, announcements related to the firms’ macroeconomic environment and announcements related to the firms’ and their competitors’ strategic dealings and commercial outcomes. We find evidence that all volatility responses are gradual with persistence horizons ranging from one to three hours, revealing a significant degree of inefficiency of the French stock market over the period. This inefficiency can be viewed as a breeding ground for the implementation of more performant informational and trading systems that allowed markets to move towards more efficiency.     

Analysis of efficiency for Shenzhen stock market based on multifractal detrended fluctuation analysis

We divided the whole series of Shenzhen stock market into two sub-series at the criterion of the date of a reform and their scale behaviors are investigated using multifractal detrended fluctuation analysis (MF-DFA). Employing the method of rolling window, we find that Shenzhen stock market was becoming more and more efficient by analyzing the change of Hurst exponent and a new efficient measure, which is equal to multifractality degree sometimes. We also study the change of Hurst exponent and multifractality degree of volatility series. The results show that the volatility series still have significantly long-range dependence and multifractality indicating that some conventional models such as GARCH and EGARCH cannot be used to forecast the volatilities of Shenzhen stock market. At last, the abnormal phenomenon of multifractality degrees for return series is discussed. The results have very important implications for analyzing the influence of policies, especially under the environment of financial crisis.     

Timing the volatility risk of beta anomaly: Evidence from hedge fund strategies

Hedge funds are known to engage in the betting-against-beta (BAB) strategy arising from beta-anomaly-related market mispricing. This paper examines if equity-oriented hedge funds time the volatility risk when executing the BAB strategy. We apply realised and downside volatility risk measures to assess the BAB strategy. We show that for top volatility risk timers, older funds tend to be better risk timers, while among the bottom volatility risk timers, younger and larger-sized funds stand out as stronger timers of BAB volatility. We observe that the Long/Short Equity funds show evidence as the strongest volatility risk timers of BAB strategy when the market condition turned bad. This is supported by their other effective timing strategies at the same time, including timing the market sentiment. Our findings provide important references for private investors when selecting hedge funds as risk management is crucial to the success/failure of any investments.     

Assessing the compensation for volatility risk implicit in interest rate derivatives

We use the risk neutral volatilities which market participants use to price dollar, euro and pound swaptions to the aim of assessing the size and the sign of the daily compensation for interest rate volatility risk between October 1998 and August 2006. The measurement of the unobservable volatility risk premium rests on a simple garch model, which generates the parameters of the volatility process under the physical measure and produces paths of future volatilities, whose averages represent the realized volatility forecasts. Results show that interest rate volatility has embodied a large — negative — compensation for volatility risk, in line with other studies focusing on different asset classes. We also document that the volatility risk premium has exhibited a term structure across the analyzed maturity spectrum and that it has changed through time, but much less than risk neutral volatilities. Compensation for volatility risk is positively related to risk neutral volatility, although the relation is not completely linear, and it is influenced, as expected, by the level of the short term rate and its realized volatility. Also a small but robust number of macroeconomic surprises affect compensation for volatility risk, with macroeconomic uncertainty in one country spilling over to other currencies. Estimates of the risk aversion coefficient computed over the same sample as the volatility risk premium suggest that (minus) the volatility risk premium can be almost directly read as risk aversion.     

Stock volatility predictability in bull and bear markets

The recent literature on stock return predictability suggests that it varies substantially across economic states, being strongest during bad economic times. In line with this evidence, we document that stock volatility predictability is also state dependent. In particular, in this paper, we use a large data set of high-frequency data on individual stocks and a few popular time-series volatility models to comprehensively examine how volatility forecastability varies across bull and bear states of the stock market. We find that the volatility forecast horizon is substantially longer when the market is in a bear state than when it is in a bull state. In addition, over all but the shortest horizons, the volatility forecast accuracy is higher when the market is in a bear state. This difference increases as the forecast horizon lengthens. Our study concludes that stock volatility predictability is strongest during bad economic times, proxied by bear market states.     

Asymmetric volatility spillover among Chinese sectors during COVID-19

Inter-sectoral volatility linkages in the Chinese stock market are understudied, especially asymmetries in realized volatility connectedness, accounting for the catastrophic event associated with the COVID-19 outbreak. In this paper, we examine the asymmetric volatility spillover among Chinese stock market sectors during the COVID-19 pandemic using 1-min data from January 2, 2019 to September 30, 2020. In doing so, we build networks of generalized forecast error variances by decomposition of a vector autoregressive model, controlling for overall market movements. Our results show evidence of the asymmetric impact of good and bad volatilities, which are found to be time-varying and substantially intense during the COVID-19 period. Notably, bad volatility spillover shocks dominate good volatility spillover shocks. The findings are useful for Chinese investors and portfolio managers constructing risk hedging portfolios across sectors and for Chinese policymakers monitoring and crafting stimulating policies for the stock market at the sectoral level.     

Credit Derivatives and the Default Risk of Large Complex Financial Institutions

This paper proposes and implements a multivariate model of the coevolution of the first and second moments of two broad credit default swap indices and the equity prices of sixteen large complex financial institutions. We use this empirical model to build a bank default risk model, in the vein of the classic Merton-type, which utilises a multi-equation framework to model forward-looking measures of market and credit risk using the credit default swap (CDS) index market as a measure of the conditions of the global credit environment. In the first step, we estimate the dynamic correlations and volatilities describing the evolution of the CDS indices and the banks’ equity prices and then impute the implied assets and their volatilities conditional on the evolution and volatility of equity. In the second step, we show that there is a substantial ‘asset shortfall’ and that substantial capital injections and/or asset insurance are required to restore the stability of our sample institutions to an acceptable level following large shocks to the aggregate level of credit risk in financial markets.     

Market volatility and momentum

We investigate the predictive power of market volatility for momentum. We find that (1) market volatility has significant power to forecast momentum payoffs, which is robust after controlling for market state and business cycle variables; (2) market volatility absorbs much of the predictive power of market state; (3) after controlling for market volatility and market state, other variables do not have incremental predictive power; (4) the time-series predictive power of market volatility is centered on loser stocks; and (5) default probability helps explain the predictive power of market volatility for momentum. These findings jointly present a significant challenge to existing theories on momentum.     

Combining long memory and level shifts in modelling and forecasting the volatility of asset returns

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in most high-frequency measures of volatility, whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons.