An Improved Two‐step Regularization Scheme for Spot Volatility Estimation

We are concerned with the problem of spot volatility estimation in the presence of microstructure noise. We introduce an estimator based on the technique of multi‐step regularization. A preliminary form for such an estimator was proposed in Ogawa (2008) and was shown to work in a real‐time manner. However, the main drawback of this scheme is that it needs a lot of observation data. The aim of the present paper is to introduce an improvement to this scheme, such that the modified estimator can work more efficiently and with a data set of smaller size. The technical aspects of implementation of the proposed scheme and its performance on simulated data are analysed. The scheme is tested against other spot volatility estimators, namely a realized volatility type estimator, the Fourier estimator and three kernel estimators.     

ANALYTICAL EVALUATION OF VOLATILITY FORECASTS*

Estimation and forecasting for realistic continuous‐time stochastic volatility models is hampered by the lack of closed‐form expressions for the likelihood. In response, Andersen, Bollerslev, Diebold, and Labys (Econometrica, 71 (2003), 579–625) advocate forecasting integrated volatility via reduced‐form models for the realized volatility, constructed by summing high‐frequency squared returns. Building on the eigenfunction stochastic volatility models, we present analytical expressions for the forecast efficiency associated with this reduced‐form approach as a function of sampling frequency. For popular models like GARCH, multifactor affine, and lognormal diffusions, the reduced form procedures perform remarkably well relative to the optimal (infeasible) forecasts.     

ALLOWING FOR JUMP MEASUREMENTS IN VOLATILITY: A HIGH‐FREQUENCY FINANCIAL DATA ANALYSIS OF INDIVIDUAL STOCKS

Following recent advances in the non‐parametric realized volatility approach, we separately measure the discontinuous jump part of the quadratic variation process for individual stocks and incorporate it into heterogeneous autoregressive volatility models. We analyse the distributional properties of the jump measures vis‐à‐vis the corresponding realized volatility ones, and compare them to those of aggregate US market index series. We also demonstrate important gains in the forecasting accuracy of high‐frequency volatility models.     

OPTIMAL WEIGHT FOR REALIZED VARIANCE BASED ON INTERMITTENT HIGH‐FREQUENCY DATA*

Japanese stock markets have two types of breaks, overnight and lunch, during which no trading occurs, causing an inevitable increased variance in estimating daily volatility via a naive realized variance (RV). In order to perform a more stabilized estimation, we modify Hansen and Lunde's weighting technique. As an empirical study, we estimate optimal weights by using a particular approach for Japanese stock data listed on the Tokyo Stock Exchange, and then compare the forecast performance of weighted and non‐weighted RV through an autoregressive fractionally integrated moving average model. The empirical result indicates that the appropriate use of the optimally weighted RV can lead to remarkably smaller estimation variance compared with the naive RV, in many series. Therefore a more accurate forecasting of daily volatility data is obtained. Finally, we perform a Monte Carlo simulation to support the empirical result.     

Analysis of High Frequency Data in Finance: A Survey

This study examines the use of high frequency data in finance, including volatility estimation and jump tests. High frequency data allows the construction of model-free volatility measures for asset returns. Realized variance is a consistent estimator of quadratic variation under mild regularity conditions. Other variation concepts, such as power variation and bipower variation, are useful and important for analyzing high frequency data when jumps are present. High frequency data can also be used to test jumps in asset prices. We discuss three jump tests: bipower variation test, power variation test, and variance swap test in this study. The presence of market microstructure noise complicates the analysis of high frequency data. The survey introduces several robust methods of volatility estimation and jump tests in the presence of market microstructure noise. Finally, some applications of jump tests in asset pricing are discussed in this article.     

The High‐Frequency Responses of Australian Financial Futures to Unexpected Cash Rate Announcements*

This study examines the high‐frequency responses of Australian financial futures to monetary surprises using intra‐day futures data. Using the event window method with tick data to control for the endogeneity between market interest rates and the cash rate, our empirical findings support the following. First, monetary policy announcements significantly impact not only short‐term interest rate futures but also longer‐term treasury security future markets. Second, the most significant responses of these markets occur in the event window that contains the policy announcement. Third, we also find that the monetary policy is not well anticipated by market participants until the Reserve Bank of Australia’s policy release.     

QUANTILE FORECASTS OF FINANCIAL RETURNS USING REALIZED GARCH MODELS*

This article applies the realized generalized autoregressive conditional heteroskedasticity (GARCH) model, which incorporates the GARCH model with realized volatility, to quantile forecasts of financial returns, such as Value‐at‐Risk and expected shortfall. Student's t‐ and skewed Student's t‐distributions as well as normal distribution are used for the return distribution. The main results for the S&P 500 stock index are: (i) the realized GARCH model with the skewed Student's t‐distribution performs better than that with the normal and Student's t‐distributions and the exponential GARCH model using the daily returns only; and (ii) using the realized kernel to take account of microstructure noise does not improve the performance.     

VOLATILITY MODELS*

Models for estimating the volatility of financial assets are reviewed in this paper. The volatility can be estimated by the univariate GARCH family of models, or stochastic volatility models. These univariate models are developed intomultivariate models. Finally, the search for an adequate framework for the estimation has led to the analysis of high frequency intraday data. The variance over a fixed interval can be estimated accurately as the sum of squared realizations, provided the data are available at sufficiently high sampling frequencies. The future of this new area is wide open for theoretical developments and for applied studies.     

Non‐discriminatory Trade Policies in Panel Structural Gravity Models: Evidence from Monte Carlo Simulations

This paper provides Monte Carlo (MC) simulation evidence on the performance of methods used for identifying the effects of nondiscriminatory trade policy (NDTP) variables in panel structural gravity models. The benchmarked methods include a fixed effect (FE) estimator that utilizes data on intra national trade flows, the bonus‐vetus (BV) and the two‐stage fixed effect (FE‐2S) estimator. The results indicate that only the FE estimates are unbiased and consistent under very general assumptions of the data generating process. The favourable asymptotic properties of the FE estimator unfold as the number of period T increases.     

Does measurement error matter in volatility forecasting? Empirical evidence from the Chinese stock market

Based on methods developed by Bollerslev et al. (2016), we explicitly accounted for the heteroskedasticity in the measurement errors and for the high volatility of Chinese stock prices; we proposed a new model, the LogHARQ model, as a way to appropriately forecast the realized volatility of the Chinese stock market. Out-of-sample findings suggest that the LogHARQ model performs better than existing logarithmic and linear forecast models, particularly when the realized quarticity is large. The better performance is also confirmed by the utility based economic value test through volatility timing.     

Pricing Nikkei 225 Options Using Realized Volatility

This article examines option pricing performance using realized volatilities with or without handling microstructure noise, non‐trading hours and large jumps. The dynamics of realized volatility is specified by ARFIMA(X) and HAR(X) models. The main results using put options on the Nikkei 225 index are that: (i) the ARFIMAX model performs best; (ii) the Hansen and Lunde (2005a) adjustment for non‐trading hours improves the performance; (iii) methods for reducing microstructure noise‐induced bias yield better performance, while if the Hansen–Lunde adjustment is used, the other methods are not necessarily needed; and (iv) the performance is unaffected by removing large jumps from realized volatility.     

Empirical Evidence of the Leverage Effect in a Stochastic Volatility Model: A Realized Volatility Approach

Increasing attention has been focused on the analysis of the realized volatility, which can be treated as a proxy for the true volatility. In this paper, we study the potential use of the realized volatility as a proxy in a stochastic volatility model estimation. We estimate the leveraged stochastic volatility model using the realized volatility computed from five popular methods across six sampling-frequency transaction data (from 1-min to 60- min) based on the trust region method. Availability of the realized volatility allows us to estimate the model parameters via the MLE and thus avoids computational challenge in the high dimensional integration. Six stock indices are considered in the empirical investigation. We discover some consistent findings and interesting patterns from the empirical results. In general, the significant leverage effect is consistently detected at each sampling frequency and the volatility persistence becomes weaker at the lower sampling frequency.     

Robust Volatility Estimation with and Without the Drift Parameter

We find the closed form solution for the joint probability of the running maximum and the drawdown of the Brownian motion with a non-zero drift parameter at a random time that is exponentially distributed and independent of the Brownian motion. This characterization leads us to come up with a robust method of estimating volatility using open, high, low and closing prices. We rigorously show the independence of robust volatility estimators based on extreme values of asset prices relative to the standard robust volatility estimator based on closing price alone. We further prove that the proposed robust volatility ratio is unbiased with no drift parameter. Moreover, we find that the robust volatility ratio with a non-zero drift parameter has only a second order effect. We have shown that our proposed extreme value robust volatility estimator is 2–3 times relatively more efficient when compared to the classical robust volatility estimator based on Monte Carlo simulation experiment. On the empirical side, we test the proposed robust volatility ratio based on high and low prices on different asset classes like stock indices, exchange rate and precious metals.

     

A study of Shanghai fuel oil futures price volatility based on high frequency data: Long-range dependence,modeling and forecasting

In existing researches, the investigations of oil price volatility are always performed based on daily data and squared daily return is always taken as the proxy of actual volatility. However, it is widely accepted that the popular realized volatility (RV) based on high frequency data is a more robust measure of actual volatility than squared return. Due to this motivation, we investigate dynamics of daily volatility of Shanghai fuel oil futures prices employing 5-minute high frequency data. First, using a nonparametric method, we find that RV displays strong long-range dependence and recent financial crisis can cause a lower degree of long-range dependence. Second, we model daily volatility using RV models and GARCH-class models. Our results indicate that RV models for intraday data overwhelmingly outperform GARCH-class models for daily data in forecasting fuel oil price volatility, regardless the proxy of actual volatility. Finally, we investigate the major source of such volatile prices and found that trader activity has major contribution to fierce variations of fuel oil prices.     

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.     

PREDICTING STOCK RETURNS AND VOLATILITY WITH INVESTOR SENTIMENT INDICES: A RECONSIDERATION USING A NONPARAMETRIC CAUSALITY‐IN‐QUANTILES TEST

Evidence of monthly stock returns predictability based on popular investor sentiment indices, namely S^BW and S^PLS as introduced by Baker and Wurgler (2006, 2007) and Huang et al. (2015) respectively are mixed. While, linear predictive models show that only S^PLS can predict excess stock returns, nonparametric models (which accounts for misspecification of the linear frameworks due to nonlinearity and regime changes) finds no evidence of predictability based on either of these two indices for not only stock returns, but also its volatility. However, in this paper, we show that when we use a more general nonparametric causality‐in‐quantiles model of Balcilar et al., (forthcoming), in fact, both S^BW and S^PLS can predict stock returns and its volatility, with S^PLS being a relatively stronger predictor of excess returns during bear and bull regimes, and S^BW being a relatively powerful predictor of volatility of excess stock returns, barring the median of the conditional distribution.     

Systemic risk contagion in FX market: A frequency connectedness and network analysis

In this study, we analyse systemic risk contagion between a set of most actively traded currencies (EURO, JPY, GBP, AUD, CAD and CHF) by application of VAR based frequency connectedness proposed by Baruník and K?ehlík. By using this novel approach, we gauge foreign exchange (FX) market connectedness in 200‐day frequency band using spectral representation of variance decompositions of VAR and identify directional spillovers between the most actively traded foreign exchange rates. Dynamics of the overall spillover index reveals that the index capture well‐known financial stress incidents properly. Finally, network topology of directional spillovers between currency pairs is provided for visulalization interconnectedness between them.     

“Expiration hour effect of futures and options markets on stock market” — A case study on NSE (National Stock Exchange of India)

This paper studies the effect of expiration day of the Index futures and Options on the trading volume, variance and price of the underlying shares. The impact of derivatives trading on the underlying stock market has been widely documented in the Finance literature. In particular, significant differences in the statistical properties of asset returns (for instance, mean and variance) during expiration and non-expiration days have been advanced as an evidence for the destabilization effect (or lack there of) of derivative instruments. The earlier studies have, however, drawn their conclusions without rigorously modelling the underlying stochastic data generation process. Given that the statistical properties mentioned before are merely traits of the asset returns, this approach can lead to spurious results if analyzed in isolation of the underlying process. We propose to address this crucial shortcoming by examining the expiration day effect from a GARCH (Generalized Auto Regressive Conditional Heteroskedastic) framework. We use both daily and high frequency (5 min and 10 min) data on S&P CNX Nifty Index. Our central finding using intra-day data is that while there is no pressure – downward or upward – on index returns, the volatility is indeed significantly affected by the expiration of contracts. This effect, however, doesn’t show up in daily data.     

Shall One Sit “Longer” for a Free Lunch? Impact of Trading Durations on the Realized Variances and Volatility Spillovers

This study examines the effect of trading durations on the realized variance of rupee futures traded in national stock exchange (NSE), India and Dubai Gold & Commodities Exchange (DGCX), Dubai as there exists a difference in the trading durations at these exchanges, where DGCX has longer trading duration. The empirical results suggest that longer trading duration has significantly higher realized variance, and also non-trading durations at NSE account for higher overall realized variance of Rupee Futures. We model the impact of trading durations on intraday and overnight realized variance for rupee futures and estimate a reduced realized volatility of 40–70 bps due to shorter trading duration. We find that non-trading durations at National Stock Exchange account for 60–70% of the overall realized variance of rupee futures. Using MGARCH model with BEKK parameterization, we find evidence of bidirectional volatility spillover from Offshore to Onshore Rupee markets.

     

Dynamic frequency connectedness between oil and natural gas volatilities

The goal of this paper is twofold. First, we study dynamic volatility connectedness between oil and natural gas over the period 1994 to 2018. Second, we examine the frequency dynamics of the transmission mechanism arising from frequency-specific responses to volatility shocks. To do so, we adopt a newly introduced approach that decomposes connectedness measures based on variance decompositions into their components at different frequency ranges. Our results summarize as follows: (a) there is a substantial variation in volatility spillovers over time; (b) the natural gas market was a net transmitter during the central part of our sample period; (c) the magnitude of spillovers was smaller after the financial crisis, but volatilities are not decoupled. (d) The volatility propagation mechanism is frequency dependent. Connectedness is typically created at low-frequencies, with volatility shocks across markets having long-lasting effects. However, during some specific periods, such as after Katrina, volatility was transmitted much faster, with shocks dissipating in the short-run.