The role of high-frequency data in volatility forecasting: evidence from the China stock market

This research investigates the role of high-frequency data in volatility forecasting of the China stock market by particularly feeding different frequency return series directly into a large number of GARCH versions. The contributions of this research are as follows. 1) We provide clear evidence to support that the superiority of traditional time series models in volatility forecasting remains by taking advantage of high-frequency data. 2) We incorporate different distribution assumptions in GARCH models to capture the stylized facts of high-frequency data. The result shows that: 1) data frequency in GARCH application substantially influence the accuracy of volatility forecasting, as the higher the frequency is of the return series, the better are the forecasts provided; 2) non-normal distributions such as skewed student-t and generalized error distribution are more capable at reproducing the stylized facts of both intraday and daily return series than normal distribution; and 3) GARCH estimated by 5-min returns not only outperforms other GARCH alternatives, but also considerably beats RV-based models such as HAR and ARFIMA at volatility forecasting

Modeling and Forecasting Realized Volatility

This paper provides a general framework for integration of high-frequency intraday data into the measurement forecasting of daily and lower frequency volatility and return distributions. Most procedures for modeling and forecasting financial asset return volatilities, correlations, and distributions rely on restrictive and complicated parametric multivariate ARCH or stochastic volatility models, which often perform poorly at intraday frequencies. Use of realized volatility constructed from high-frequency intraday returns, in contrast, permits the use of traditional time series procedures for modeling and forecasting. Building on the theory of continuous-time arbitrage-free price processes and the theory of quadratic variation, we formally develop the links between the conditional covariancematrix and the concept of realized volatility. Next, using continuously recorded observations for the Deutschemark Dollar and Yen / Dollar spot exchange rates covering more than a decade, we find that forecasts from a simple long-memory Gaussian vector autoregression for the logarithmic daily realized volatilities perform admirably compared to popular daily ARCH and related models. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal-normal mixture distribution implied by the theoretically and empirically grounded assumption of normally distributed standardized returns, gives rise to well-calibrated density forecasts of future returns, and correspondingly accurate quantile estimates. Our results hold promise for practical modeling and forecasting of the large covariance matrices relevant in asset pricing, asset allocation and financial risk management applications.

The Volatility of Realized Volatility

Using unobservable conditional variance as measure, latent–variable approaches, such as GARCH and stochastic–volatility models, have traditionally been dominating the empirical finance literature. In recent years, with the availability of high–frequency financial market data modeling realized volatility has become a new and innovative research direction. By constructing “observable” or realized volatility series from intraday transaction data, the use of standard time series models, such as ARFIMA models, have become a promising strategy for modeling and predicting (daily) volatility. In this paper, we show that the residuals of the commonly used time–series models for realized volatility exhibit non–Gaussianity and volatility clustering. We propose extensions to explicitly account for these properties and assess their relevance when modeling and forecasting realized volatility. In an empirical application for S&P500 index futures we show that allowing for time–varying volatility of realized volatility leads to a substantial improvement of the model’s fit as well as predictive performance. Furthermore, the distributional assumption for residuals plays a crucial role in density forecasting.Finance, Realized Volatility, Realized Quarticity, GARCH, Normal Inverse Gaussian Distribution, Density Forecasting

Modeling and Forecasting Realized Volatility

This paper provides a general framework for integration of high-frequency intraday data into the measurement, modeling and forecasting of daily and lower frequency volatility and return distributions. Most procedures for modeling and forecasting financial asset return volatilities, correlations, and distributions rely on restrictive and complicated parametric multivariate ARCH or stochastic volatility models, which often perform poorly at intraday frequencies. Use of realized volatility constructed from high-frequency intraday returns, in contrast, permits the use of traditional time series procedures for modeling and forecasting. Building on the theory of continuous-time arbitrage-free price processes and the theory of quadratic variation, we formally develop the links between the conditional covariance matrix and the concept of realized volatility. Next, using continuously recorded observations for the Deutschemark/Dollar and Yen /Dollar spot exchange rates covering more than a decade, we find that forecasts from a simple long-memory Gaussian vector autoregression for the logarithmic daily realized volatitilies perform admirably compared to popular daily ARCH and related models. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal-normal mixture distribution implied by the theoretically and empirically grounded assumption of normally distributed standardized returns, gives rise to well-calibrated density forecasts of future returns, and correspondingly accurate quintile estimates. Our results hold promise for practical modeling and forecasting of the large covariance matrices relevant in asset pricing, asset allocation and financial risk management applications.

Realized Volatility Risk

In this paper we document that realized variation measures constructed from high- frequency returns reveal a large degree of volatility risk in stock and index returns, where we characterize volatility risk by the extent to which forecasting errors in realized volatility are substantive. Even though returns standardized by ex post quadratic variation measures are nearly gaussian, this unpredictability brings considerably more uncertainty to the empirically relevant ex ante distribution of returns. Carefully modeling this volatility risk is fundamental. We propose a dually asymmetric realized volatility (DARV) model, which incorporates the important fact that realized volatility series are systematically more volatile in high volatility periods. Returns in this framework display time varying volatility, skewness and kurtosis. We provide a detailed account of the empirical advantages of the model using data on the S&P 500 index and eight other indexes and stocks.Realized volatility; volatility of volatility; volatility risk; value-at-risk; forecasting; conditional heteroskedasticity

Realized Volatility Risk

In this paper we document that realized variation measures constructed from high-frequency returns reveal a large degree of volatility risk in stock and index returns, where we characterize volatility risk by the extent to which forecasting errors in realized volatility are substantive. Even though returns standardized by ex post quadratic variation measures are nearly gaussian, this unpredictability brings considerably more uncertainty to the empirically relevant ex ante distribution of returns. Carefully modeling this volatility risk is fundamental. We propose a dually asymmetric realized volatility (DARV) model, which incorporates the important fact that realized volatility series are systematically more volatile in high volatility periods. Returns in this framework display time varying volatility, skewness and kurtosis. We provide a detailed account of the empirical advantages of the model using data on the S&P 500 index and eight other indexes and stocks.

"Realized Volatility Risk"

In this paper we document that realized variation measures constructed from high-frequency returns reveal a large degree of volatility risk in stock and index returns, where we characterize volatility risk by the extent to which forecasting errors in realized volatility are substantive. Even though returns standardized by ex post quadratic variation measures are nearly gaussian, this unpredictability brings considerably more uncertainty to the empirically relevant ex ante distribution of returns. Carefully modeling this volatility risk is fundamental. We propose a dually asymmetric realized volatility (DARV) model, which incorporates the important fact that realized volatility series are systematically more volatile in high volatility periods. Returns in this framework display time varying volatility, skewness and kurtosis. We provide a detailed account of the empirical advantages of the model using data on the S&P 500 index and eight other indexes and stocks.

DSLOB: A Synthetic Limit Order Book Dataset for Benchmarking Forecasting Algorithms under Distributional Shift

In electronic trading markets, limit order books (LOBs) provide information about pending buy/sell orders at various price levels for a given security. Recently, there has been a growing interest in using LOB data for resolving downstream machine learning tasks (e.g., forecasting). However, dealing with out-of-distribution (OOD) LOB data is challenging since distributional shifts are unlabeled in current publicly available LOB datasets. Therefore, it is critical to build a synthetic LOB dataset with labeled OOD samples serving as a testbed for developing models that generalize well to unseen scenarios. In this work, we utilize a multi-agent market simulator to build a synthetic LOB dataset, named DSLOB, with and without market stress scenarios, which allows for the design of controlled distributional shift benchmarking. Using the proposed synthetic dataset, we provide a holistic analysis on the forecasting performance of three different state-of-the-art forecasting methods. Our results reflect the need for increased researcher efforts to develop algorithms with robustness to distributional shifts in high-frequency time series data.Comment: 11 pages, 5 figures, already accepted by NeurIPS 2022 Distribution Shifts Worksho

Pricing Options by Simulation Using Realized Volatility

A growing literature advocates the use of high-frequency data for the purpose of volatility estimation. However, despite the successes in modeling the conditional mean of realized volatility empirical evaluations of this class of models outside the realm of short run forecasting is limited. How can realized volatility be used for pricing options? What are the modeling qualities introduced by realized volatility models for pricing derivatives? In this short paper, we propose an option pricing framework based on a new realized volatility model that captures all the relevant empirical regularities of the realized volatility series of the S&P 500 index. We emphasize two main empirical regularities for our volatility model and that are potentially very relevant for option pricing purposes. First, realized variation measures constructed from high-frequency returns reveal a large degree of time series unpredictability in the volatility of asset returns. Even though returns standardized by (ex-post) quadratic variation measures are nearly gaussian, this unpredictability brings substantially more uncertainty to the empirically relevant (ex-ante) distribution of returns. In this setting carefully modeling the stochastic structure of the time series disturbances of realized volatility is fundamental. Second, there is evidence of very large leverage effects; large falls (rises) in prices being associated with persistent regimes of high (low) variance in the index returns. We propose a model for the conditional volatility, skewness and kurtosis of daily index and stocks returns. The main new feature of this model is to recognize that volatility is itself more volatile and more persistent in high volatility periods. Contrary to "peso problem" considerations, we show that when volatility is (nearly) observable it is not necessary to rely on rare realizations on past return data to learn about the tails of the return distribution, an unexplored and large modeling gain enabled by high frequency data. We conduct a brief empirical illustration analysis of the pricing performance of this approach against some benchmark models using data from the S&P 500 options in the 2001-2004 period. The results indicate that as expected the superior forecasting accuracy of realized volatility translates into significantly smaller pricing errors when compared to models of the GARCH family. More significantly, our results indicate that modeling leverage effects and the volatility of volatility are paramount reducing common pricing anomalies.Volatility, Option pricing, Volatility of volatility, Forecasting

REALIZED VOLATILITY RISK

In this paper we show that realized variation measures constructed from high- frequency returns reveal a large degree of volatility risk in stock and index returns, where we characterize volatility risk by the extent to which forecasting errors in realized volatility are substantive. Even though returns standardized by ex post quadratic variation measures are nearly Gaussian, this unpredictability brings greater uncertainty to the empirically relevant ex ante distribution of returns. Explicitly modeling this volatility risk is fundamental. We propose a dually asymmetric realized volatility model, which incorporates the fact that realized volatility series are systematically more volatile in high volatility periods. Returns in this framework display time varying volatility, skewness and kurtosis. We provide a detailed account of the empirical advantages of the model using data on the S&P 500 index and eight other indexes and stocks.Realized volatility, volatility of volatility, volatility risk, value-at-risk, forecasting, conditional heteroskedasticity.