A discrete-time model for daily S & P500 returns and realized variations: Jumps and leverage effects

We develop an empirically highly accurate discrete-time daily stochastic volatility model that explicitly distinguishes between the jump and continuous-time components of price movements using nonparametric realized variation and Bipower variation measures constructed from high-frequency intraday data. The model setup allows us to directly assess the structural inter-dependencies among the shocks to returns and the two different volatility components. The model estimates suggest that the leverage effect, or asymmetry between returns and volatility, works primarily through the continuous volatility component. The excellent fit of the model makes it an ideal candidate for an easy-to-implement auxiliary model in the context of indirect estimation of empirically more realistic continuous-time jump diffusion and Lévy-driven stochastic volatility models, effectively incorporating the interdaily dependencies inherent in the high-frequency intraday data.     

Forecasting the volatility of asset returns: The informational gains from option prices

A new class of forecasting models is proposed that extends the realized GARCH class of models through the inclusion of option prices to forecast the variance of asset returns. The VIX is used to approximate option prices, resulting in a set of cross-equation restrictions on the model’s parameters. The full model is characterized by a nonlinear system of three equations containing asset returns, the realized variance, and the VIX, with estimation of the parameters based on maximum likelihood methods. The forecasting properties of the new class of forecasting models, as well as a number of special cases, are investigated and applied to forecasting the daily S&P500 index realized variance using intra-day and daily data from September 2001 to November 2017. The forecasting results provide strong support for including the realized variance and the VIX to improve variance forecasts, with linear conditional variance models performing well for short-term one-day-ahead forecasts, whereas log-linear conditional variance models tend to perform better for intermediate five-day-ahead forecasts.     

FORECASTING REALIZED VOLATILITY WITH LINEAR AND NONLINEAR UNIVARIATE MODELS

Abstract In this paper, we consider a nonlinear model based on neural networks as well as linear models to forecast the daily volatility of the S&P 500 and FTSE 100 futures. As a proxy for daily volatility, we consider a consistent and unbiased estimator of the integrated volatility that is computed from high‐frequency intraday returns. We also consider a simple algorithm based on bagging (bootstrap aggregation) in order to specify the models analysed in this paper.     

Are low-frequency data really uninformative? A forecasting combination perspective

In this study, we investigate whether low-frequency data improve volatility forecasting when high-frequency data are available. To answer this question, we utilize four forecast combination strategies that combine low-frequency and high-frequency volatility models and employ a rolling window and a range of loss functions in the framework of the novel Model Confidence Set test. Out-of-sample results show that combination forecasts with GARCH-class models can achieve high forecast accuracy. However, the combination forecast methods appear not to significantly outperform individual high-frequency volatility models. Furthermore, we find that models that combine low-frequency and high-frequency volatility yield significantly better performance than other models and combination forecast strategies in both a statistical and economic sense.     

Forecasting realized variance measures using time-varying coefficient models

This paper considers the problem of forecasting realized variance measures. These measures are highly persistent estimates of the underlying integrated variance, but are also noisy. Bollerslev, Patton and Quaedvlieg (2016), Journal of Econometrics 192(1), 1–18 exploited this so as to extend the commonly used heterogeneous autoregressive (HAR) by letting the model parameters vary over time depending on the estimated measurement error variances. We propose an alternative specification that allows the autoregressive parameters of HAR models to be driven by a latent Gaussian autoregressive process that may also depend on the estimated measurement error variance. The model parameters are estimated by maximum likelihood using the Kalman filter. Our empirical analysis considers the realized variances of 40 stocks from the S&P 500. Our model based on log variances shows the best overall performance and generates superior forecasts both in terms of a range of different loss functions and for various subsamples of the forecasting period.     

Realized volatility forecasting: Robustness to measurement errors

In this paper, we suggest how to handle the issue of the heteroskedasticity of measurement errors when specifying dynamic models for the conditional expectation of realized variance. We show that either adding a GARCH correction within an asymmetric extension of the $\mathsf{HAR}$  class ($\mathsf{AHAR}$-$\mathsf{GARCH}$), or working within the class of asymmetric multiplicative error models ($\mathsf{AMEM}$) greatly reduces the need for quarticity/quadratic terms to capture attenuation bias. This feature in $\mathsf{AMEM}$ can be strengthened by considering regime specific dynamics. Model Confidence Sets confirm this robustness both in- and out-of-sample for a panel of 28 big caps and the S&P500 index.     

Do high-frequency measures of volatility improve forecasts of return distributions?

Many finance questions require the predictive distribution of returns. We propose a bivariate model of returns and realized volatility (RV), and explore which features of that time-series model contribute to superior density forecasts over horizons of 1 to 60 days out of sample. This term structure of density forecasts is used to investigate the importance of: the intraday information embodied in the daily RV estimates; the functional form for log(RV)$log\left(RV\right)$ dynamics; the timing of information availability; and the assumed distributions of both return and log(RV)$log\left(RV\right)$ innovations. We find that a joint model of returns and volatility that features two components for log(RV)$log\left(RV\right)$ provides a good fit to S&P 500 and IBM data, and is a significant improvement over an EGARCH model estimated from daily returns.     

Stock market volatility forecasting: Do we need high-frequency data?

The general consensus in the volatility forecasting literature is that high-frequency volatility models outperform low-frequency volatility models. However, such a conclusion is reached when low-frequency volatility models are estimated from daily returns. Instead, we study this question considering daily, low-frequency volatility estimators based on open, high, low, and close daily prices. Our data sample consists of 18 stock market indices. We find that high-frequency volatility models tend to outperform low-frequency volatility models only for short-term forecasts. As the forecast horizon increases (up to one month), the difference in forecast accuracy becomes statistically indistinguishable for most market indices. To evaluate the practical implications of our results, we study a simple asset allocation problem. The results reveal that asset allocation based on high-frequency volatility model forecasts does not outperform asset allocation based on low-frequency volatility model forecasts.     

Time-varying asymmetric volatility spillover between global markets and China’s A,B and H-shares using EGARCH and DCC-EGARCH models

This paper investigates the volatility spillover and dynamic conditional correlation between three types of China’s shares including A, B and H-shares with 12 major emerging and developed markets from 2002 to 2017 using EGARCH and multivariate DCC-EGARCH models. Both models found that Chinese equities are more related with their neighbouring countries such as Singapore, Japan, Australia and ASEAN-5 than with US, Germany and UK. The EGARCH model, with an auxiliary term added to capture the volatility spillover, found no volatility spillover between A-share markets and other advanced and emerging markets during the GFC and extended-crisis periods while this behaviour is not observed for B-share and H-share markets. However, the multivariate DCC model found strong evidence of contagion effect in both return correlations and volatility spillover for all China’s markets. In addition, both models found increased regional and global integration in A-share and B-share markets but not the H-share market. Finally, the results from both models provide clear evidence of distinct behaviours associated with return and volatility spillover in these three share types, suggesting foreign investors should consider the heterogeneity in volatility spillover and return correlations of these Chinese share types when forming investment strategies.