S&P500 volatility analysis using high-frequency multipower variation volatility proxies

The availability of ultra-high-frequency data has sparked enormous parametric and nonparametric volatility estimators in financial time series analysis. However, some high-frequency volatility estimators are suffering from biasness issues due to the abrupt jumps and microstructure effect that often observed in nowadays global financial markets. Hence, we motivate our studies with two long-memory time series models using various high-frequency multipower variation volatility proxies. The forecast evaluations are illustrated using the S&P500 data over the period from year 2008 to 2013. Our empirical studies found that higher-power variation volatility proxies provide better in-sample and out-of-sample performances as compared to the widely used realized volatility and fractionally integrated ARCH models. Finally, these empirical findings are used to estimate the one-day-ahead value-at-risk of S&P500.     

Risk aversion,fanning preference and volatility smirk on S&P 500 index options

This article proposes a novel way of pricing S&P 500 index options in the presence of jump risk. Our analysis is built upon an equilibrium option pricing rule for a representative agent economy. In particular, we use the weighted utility’s certainty equivalent to specify agent’s risk preference, which displays a fanning-out characteristic. We find that the fanning effect captures a remarkably large portion of the total market risk premium implicit in options. As a result, the model with fanning effect generates pronounced volatility smirks.     

Forecasting volatility of futures market: the S&P 500 and FTSE 100 futures using high frequency returns and implied volatility

We show that historical volatility from high frequency returns outperforms implied volatility when standardized returns by historical volatility tends to be normally distributed. For the FTSE 100 futures, we find that historical volatility using high frequency returns outperforms implied volatility in forecasting future volatility. However, we find that implied volatility outperforms historical volatility in forecasting future volatility for the S&P 500 futures. The results also indicate that historical volatility using high frequency returns could be an unbiased forecast for the FTSE 100 futures.     

S&P 500 Affiliation and Stock Price Informativeness

Abstract

When firms are added to a stock index, more information should be discovered, traded on, and incorporated into their stock prices, making them more informative. We test this hypothesis using a large sample of additions to the S&P 500 index. Using two alternative statistical tests, we find that the stocks added experience more random, less predictable return and, thus, appear to be priced more efficiently information-wise. We further find concurrent increases in institutional ownership and investor awareness, which tend to contribute to the higher pricing efficiency, adding to the literature. These findings should be of interest to academics and practitioners.     

Forecasting the volatility of S&P depositary receipts using GARCH-type models under intraday range-based and return-based proxy measures

We employ four various GARCH-type models, incorporating the skewed generalized t (SGT) errors into those returns innovations exhibiting fat-tails, leptokurtosis and skewness to forecast both volatility and value-at-risk (VaR) for Standard & Poor's Depositary Receipts (SPDRs) from 2002 to 2008. Empirical results indicate that the asymmetric EGARCH model is the most preferable according to purely statistical loss functions. However, the mean mixed error criterion suggests that the EGARCH model facilitates option buyers for improving their trading position performance, while option sellers tend to favor the IGARCH/EGARCH model at shorter/longer trading horizon. For VaR calculations, although these GARCH-type models are likely to over-predict SPDRs' volatility, they are, nevertheless, capable of providing adequate VaR forecasts. Thus, a GARCH genre of model with SGT errors remains a useful technique for measuring and managing potential losses on SPDRs under a turbulent market scenario.     

Forecasting the volatility of S&P depositary receipts using GARCH-type models under intraday range-based and return-based proxy measures

We employ four various GARCH-type models, incorporating the skewed generalized t (SGT) errors into those returns innovations exhibiting fat-tails, leptokurtosis and skewness to forecast both volatility and value-at-risk (VaR) for Standard & Poor's Depositary Receipts (SPDRs) from 2002 to 2008. Empirical results indicate that the asymmetric EGARCH model is the most preferable according to purely statistical loss functions. However, the mean mixed error criterion suggests that the EGARCH model facilitates option buyers for improving their trading position performance, while option sellers tend to favor the IGARCH/EGARCH model at shorter/longer trading horizon. For VaR calculations, although these GARCH-type models are likely to over-predict SPDRs' volatility, they are, nevertheless, capable of providing adequate VaR forecasts. Thus, a GARCH genre of model with SGT errors remains a useful technique for measuring and managing potential losses on SPDRs under a turbulent market scenario.     

Nonlinear dynamics in arbitrage of the S&P 500 index and futures: A threshold error-correction model

Using a three-regime threshold error-correction model, we investigate the nonlinear dynamics of the S&P 500 index and futures. First, using the SupLM statistic, we report estimates of two thresholds for the three-regime model to explain the nonlinear dynamics in arbitrage of the S&P 500 index and futures. This provides empirical evidence of the no-arbitrage band predicted by the cost-of-carry model. Second, using quasi-maximum likelihood estimation, we demonstrate that those indexes that are located outside the no-arbitrage band are a nonlinear stationary process of mean-reversion to the no-arbitrage band. However, index and futures that are located within the no-arbitrage band are non-stationary. Third, we confirm an earlier finding that futures price leads the nonlinear mean-reverting behavior of the index but not vice versa. Impulse response function analysis and forecasting performance of three-regime error-correction model reinforce our findings and our estimation results are robust with different specifications of pricing error terms and endogenous variables.     

QARMA-Beta-t-EGARCH versus ARMA-GARCH: an application to S&P 500

Statistical performance and out-of-sample forecast precision of ARMA-GARCH and QARMA-Beta-t-EGARCH are compared. We study daily returns on the Standard and Poor’s 500 (S&P 500) index and a random sample of 50 stocks from the S&P 500 for period May 2006 to July 2010. Competing models are estimated for periods before and during the US financial crisis of 2008. Out-of-sample point and density forecasts are performed for periods during and after the US financial crisis. The results provide evidence of the superior in-sample statistical and out-of-sample predictive performance of QARMA-Beta-t-EGARCH.     

The impact of large-scale asset purchases on the S&P 500 index,long-term interest rates and unemployment

After the bankruptcy of Lehman Brothers in September 2008 and the financial panic that ensued, the Federal Reserve moved rapidly to reduce the federal funds rate to .25%. It was quickly judged that additional measures were needed to stabilize the US economy. Beginning in December 2008, the Federal Reserve Bank initiated three rounds of unconventional monetary policies known as quantitative easing (QE). These policies were intended to reduce long-term interest rates when the short-term federal funds rates had reached the zero lower bound and could not become negative. It was argued that the lowering of longer-term interest rates would help the stock market and thus the wealth of consumers. This article carefully investigates three hypotheses: QE impacting long-term interest rates, QE impacting the stock market and QE impacting unemployment using a Markov regime switching methodology. We conclude that QE has contributed significantly to increases in the stock market but less significantly to long-term interest rate and unemployment.     

The risk-return relation and VIX: evidence from the S&P 500

A significantly positive risk-return relation for the S&P 500 market index is detected if the squared implied volatility index (VIX) is allowed for as an exogenous variable in the conditional variance equation of the parsimonious GARCH(1,1) model. This result holds for both daily and weekly observations, for extended conditional mean and variance specifications, and is robust to sub-samples. We show that the conditional variance obtained from the GARCH model with VIX has better predictive ability for realized volatility than the conditional variance from GARCH without VIX and VIX itself, thereby documenting an important information content of VIX for conditional variance. The results are interpreted as evidence that adding VIX squared in the conditional variance equation yields a better measure of conditional variance which, subsequently, uncovers a strong risk-return relation.     

Asset pricing with time-varying betas for stocks traded on S&P 500

This study uses a novel approach for capturing time variation in betas whose pattern is treated as a function of market returns. A two-factor model (TFM) is constructed using estimated coefficients of a nonlinear regression. The model is tested against the CAPM and the Fama and French three-factor model in the context of time series regressions. The used stocks are traded on S&P 500. The period spans from 1993 to 2011. The time series regression results depict the superiority of the TFM in explaining portfolio returns including momentum ones. We also provide evidence that the particular portfolios employed at the construction of the new model accommodate different fundamental characteristics and different risk levels.     

Forecasting stock market volatility and information content of implied volatility index

This study investigates the incremental information content of implied volatility index relative to the GARCH family models in forecasting volatility of the three Asia-Pacific stock markets, namely India, Australia and Hong Kong. To examine the in-sample information content, the conditional variance equations of GARCH family models are augmented by incorporating implied volatility index as an explanatory variable. The return-based realized variance and the range-based realized variance constructed from 5-min data are used as proxy for latent volatility. To assess the out-of-sample forecast performance, we generate one-day-ahead rolling forecasts and employ the Mincer–Zarnowitz regression and encompassing regression. We find that the inclusion of implied volatility index in the conditional variance equation of GARCH family model reduces volatility persistence and improves model fitness. The significant and positive coefficient of implied volatility index in the augmented GARCH family models suggests that it contains relevant information in describing the volatility process. The study finds that volatility index is a biased forecast but possesses relevant information in explaining future realized volatility. The results of encompassing regression suggest that implied volatility index contains additional information relevant for forecasting stock market volatility beyond the information contained in the GARCH family model forecasts.     

Crossing of Psychological Price Levels: The Price Dynamics and Interaction between S&P500 Index and Index Futures

The authors provide fresh evidence on the nonfundamental-driven price dynamics and interaction between index and index futures by examining the price movements of the S&P500 index and index futures surrounding the crossing of the 00 psychological barriers and 52-week highs and lows. In contrast to the extant evidence that futures leads in fundamental-driven price movements, the authors show the dominance of the crossing in the index in continuing the price trend after the crossing. Even when synchronized crossings occur, the index rises more than the index futures during upward crossings, whereas the index futures falls more than the index during downward crossings. While volatility is significantly reduced before upward crossings, but not for downward crossings, it is significantly higher during the crossing, and significantly lower after the crossings in both markets. These findings have clear practical implications for index arbitrageurs, investors, and regulators.     

S&P 500 volatility,volatility regimes,and economic uncertainty

We assess the relationship between regime-dependent volatility in S&P 500, economic policy uncertainty, the S&P 500 bull and bear sentiment spread (bb_sp), as well as the Chicago Board Options Exchange's VIX over the period 2000–2018. Our findings from two-covariate GARCH–MIDAS (GM) methodology, regime switching Markov Chain, and quantile regressions suggest that the association of realized volatility and sentiment varies across high- and low-volatility regimes and depends on investors’ sensitivity toward incidents of market uncertainties under these regimes. The findings suggest that these indicators may not be useful in volatility forecasting, especially under high-volatility regimes.     

THE LEAD–LAG RELATION BETWEEN THE S&P500 SPOT AND FUTURES MARKETS: AN INTRADAY-DATA ANALYSIS USING A THRESHOLD REGRESSION MODEL

In this paper we examine the lead–lag interaction between the futures and spot markets of the S&P500 using the threshold regression model on intraday data. The use of threshold variables to model the changes in the regression structure with respect to different market conditions enables us to investigate the lead–lag interaction in a data-based approach and avoid stratifying the data arbitrarily. Using the basis as the threshold variable, we find that the short-selling restrictions in the spot market reduce the effect of the spot index as the leading variable. To study the effect of market-wide information on the interaction between the spot and futures markets, we use the coefficient of determination in the regression of the S&P500 on the Morgan–Stanley Composite Index-US and the Major Market Index as the threshold variable. We find that the lead effect of the futures market over the spot market is stronger when there is more market-wide information. On the other hand, the lead effect of the cash market over the futures market is weaker when there is more market-wide information. In addition, we also use the lagged 45-min return of the spot market as the threshold variable. We find that the lead effect of the spot market is stronger in periods of directionless trading than in periods of good or bad markets.     

A note on the estimated GARCH coefficients from the S&P1500 universe

ABSTRACT

We employ 1440 stocks listed in the S&P Composite 1500 Index of the NYSE. Three benchmark GARCH models are estimated for the returns of each individual stock under three alternative distributions (Normal, t and GED). We provide summary statistics for all the GARCH coefficients derived from 11,520 regressions. The EGARCH model with GED errors emerges as the preferred choice for the individual stocks in the S&P 1500 universe when non-negativity and stationarity constraints in the conditional variance are imposed. 57% of the constraint’s violations are taking place in the S&P small cap stocks.     

Forecasting the realized volatility: the role of jumps

This article investigates the role of jump components dependent on the ABD-LM jump test in forecasting volatility. Our out-of-sample forecasting results show that compared with the ABD-LM jump component, its decomposition forms based on signed returns can significantly improve the models’ forecasting performance and our findings have important implications for investors and policymakers.     

Forecasting the oil futures price volatility: A new approach

This study provides a new perspective of modelling and forecasting realized range-based volatility (RRV) for crude oil futures. We are the first to improve the Heterogeneous Autoregressive model of Realized Range-based Volatility (HAR-RRV) model by considering the significant jump components, signed returns and volatility of realized range-based volatility. The empirical results show that the volatility of volatility significantly exists in the oil futures market. Moreover, our new proposed models with significant jump components, signed returns and volatility of volatility can gain higher forecast accuracy than HAR-RRV-type models. The results are robust to different forecasting windows and forecasting horizons. Our new findings are strategically important for investors making better decisions.     

Forecasting the aggregate stock market volatility in a data-rich world

ABSTRACT

In this article, we utilize the basic lasso and elastic net models to revisit the predictive performance of aggregate stock market volatility in a data-rich world. Motivated by the existing literature, we determine several candidate predictors that have 22 technical indicators and 14 macroeconomic and financial variables. Our out-of-sample results reveal several noteworthy findings. First, few macroeconomic and financial variables and most of technical indicators have superior performance relative to the benchmark model. Second, combination forecasts are able to significantly beat the benchmark and some signal predictors Third, the lasso and elastic models with all predictors can generate more accurate forecasts than the benchmark and some other predictors in both the statistical and economic sense. Fourth, the lasso and elastic models exhibit higher forecast accuracy during periods of expansions and recessions. Finally, our findings are robust to several tests, such as different forecasting windows, forecasting models, and forecasting evaluations.     

Forecasting volatility in the Chinese stock market under model uncertainty

Volatility forecasting is an important issue in empirical finance. In this paper, the main purpose is to apply the model averaging techniques to reduce volatility model uncertainty and improve volatility forecasting. Six GARCH-type models are considered as candidate models for model averaging. As to the Chinese stock market, the largest emerging market in the world, the empirical study shows that forecast combination using model averaging can be a better approach than the individual forecasts.