Intraday Volatility Patterns Research Articles

High-frequency realized stochastic volatility model

A new high-frequency realized stochastic volatility model is proposed. Apart from the standard daily-frequency stochastic volatility model, the high-frequency stochastic volatility model is fit to intraday returns by extensively incorporating intraday volatility patterns. The daily realized volatility calculated using intraday returns is incorporated into the high-frequency stochastic volatility model by considering the bias in the daily realized volatility caused by microstructure noise. The volatility of intraday returns is assumed to consist of the autoregressive process, the seasonal component of the intraday volatility pattern, and the announcement component responding to macroeconomic announcements. A Bayesian method via Markov chain Monte Carlo is developed for the analysis of the proposed model. The empirical analysis using the 5-minute returns of E-mini S&P 500 futures provides evidence that our high-frequency realized stochastic volatility model improves in-sample model fit and volatility forecasting over the high-frequency stochastic volatility model.

Detection of a structural break in intraday volatility pattern

We develop theory leading to testing procedures for the presence of a change point in the intraday volatility pattern. The new theory is developed in the framework of Functional Data Analysis. It is based on a model akin to the stochastic volatility model for scalar point-to-point returns. In our context, we study intraday curves, one curve per trading day. After postulating a suitable model for such functional data, we present three tests focusing, respectively, on changes in the shape, the magnitude and arbitrary changes in the sequences of the curves of interest. We justify the respective procedures by showing that they have asymptotically correct size and by deriving consistency rates for all tests. These rates involve the sample size (the number of trading days) and the grid size (the number of observations per day). We also derive the corresponding change point estimators and their consistency rates. All procedures are additionally validated by a simulation study and an application to US stocks.

State-dependent intra-day volatility pattern and its impact on price jump detection - Evidence from international equity indices

Current price jump tests assume a constant intra-day volatility pattern (IVP) over sample period. We test this assumption by allowing IVP to depend on some state variables such as the sign of previous returns or the relative levels of volatility. Estimation results from 5-min GARCH model for four equity indices show that squared-return-based IVP weights increase in early morning hours when previous returns are negative, suggesting an asymmetric IVP. For a jump-robust IVP estimator, distinct responses are found for days with Realized Variance (RV) increasing from the previous day. Our results are consistent with and complement recent studies on time-varying IVP. Price jumps obtained using the state-dependent IVP are more prudent, show lower degree of clustering and are less concentrated over trading hours.

Intraday volatility patterns from short-dated options

We propose a nonparametric estimator for the deterministic periodic component of volatility from short-dated options within an in-fill asymptotic setting. The estimator uses options with zero and one day to expiration sampled at high-frequency during a trading day. At each point in time, we aggregate the options to form nonparametric estimates of conditional risk-neutral expectations of future integrated return variation for the two available option tenors. A suitable ratio of these estimates removes the stochastic components of the conditional expectations of future volatility, up to asymptotically higher-order terms, and allows to form estimates of the deterministic periodic component of volatility. We derive a Central Limit Theorem for the estimator, with its rate of convergence determined from the mesh of the strike grid and the length of the time to expiration of the options. The newly-developed estimation procedure is applied to S&P 500 index options data.

Robust estimation of integrated and spot volatility

We introduce a new method to estimate the integrated volatility (IV) and the spot volatility (SV) based on noisy high-frequency data. Our method employs the ReMeDI approach introduced by Li and Linton (2022) to estimate the moments of microstructure noise and thereby eliminate their influence, and the pre-averaging method to target the volatility parameter. The method is robust: it can be applied when the efficient price exhibits stochastic volatility and jumps, the observation times are random, and the noise process is nonstationary, autocorrelated, asymptotically vanishing and dependent on the efficient price. We derive the limit distributions for the proposed estimators under the infill asymptotics in a general setting. Our extensive simulation studies demonstrate the robustness, accuracy and computational efficiency of our estimators compared to several alternative estimators recently proposed in the literature. Empirically, we show that neglecting the complexities of noise and the random observation times generates substantial biases in volatility estimation and may yield a different intraday volatility pattern.

Intraday Seasonality and Volatility Pattern: An Explanation with Recurrence Quantification Analysis

The Recurrence Quantification Analysis (RQA), a pattern recognition-based time series analysis method, can be successfully utilized for short, nonstationary, nonlinear, and chaotic time series. These RQA measures quantify several properties of time series, including predictability, regularity, stability, randomness, and complexity. In this regard, first, we analyzed the intraday seasonality with RQA and demonstrated how RQA measures change among the intraday periods by using 160 million row matched orders of 100 shares from Borsa Istanbul Equity Market between 2019M10 and 2020M02. We selected 50 stocks from the BIST50 Index group and 50 stocks from outside of the BIST100 Index group. Since these two share groups exhibit similar intraday RQA seasonality, our results are robust. Second, we explained intraday volatility with RQA measures and found a relationship between RQA measures and intraday volatility using a regression model.

Intraday Periodic Volatility Curves

The volatility of financial asset returns displays pronounced variation over the trading day. Our goal is nonparametric inference for the average intraday volatility pattern, viewed as a function of time-of-day. The functional inference is based on a long span of high-frequency return data. Our setup allows for general forms of volatility dynamics, including time-variation in the intraday pattern. The estimation is based on forming local volatility estimates from the high-frequency returns over overlapping blocks of asymptotically shrinking size, and then averaging these estimates across days in the sample. The block-based estimation of volatility renders the error in the estimation due to the martingale return innovation asymptotically negligible. As a result, the centered and scaled calendar volatility effect estimator converges to a Gaussian process determined by the empirical process error associated with estimating average volatility across the trading day. Feasible inference is obtained by consistently estimating the limiting covariance operator. Simulation results corroborate our theoretical findings. In an application to S&P 500 futures data, we find evidence for a shift in the intraday volatility pattern over time, including a more pronounced role for volatility outside U.S. trading hours in the latter part of the sample. Supplementary materials for this article are available online.

The Role of Jumps in Realized Volatility Modeling and Forecasting

Abstract Building on an extensive empirical analysis, I investigate the relevance of jumps and signed variations in predicting realized volatility. I show that properly accounting for intra-day volatility patterns and staleness sensibly reduces the identified jumps, in particular for low and moderate liquidity assets. Modeling realized variance using jumps and intra-day return sign improves the in-sample fit of commonly adopted specifications, irrespective of assets liquidity. From a forecasting perspective, the empirical evidence I report shows that most models, independently from their flexibility, are statistically equivalent in many cases. These results are confirmed with different samples, assets liquidity level, forecast horizons, and possible transformations of the dependent and explanatory variables.

Регулярные коммуникации Банка России и краткосрочные эффекты волатильности на финансовых рынках

This paper investigates the relationship between the volatility of various indicators of the Russia financial markets and the communication policy of the Bank of Russia, namely, regular communications channel – press releases and press conferences following the meetings of the Board of Directors of the Bank of Russia. The use of these two channels of regular verbal interventions aims not only to familiarize market participants with the decision on the key rate adopted during the meeting, but also to describe the reasons for this decision, along with a brief description of the current state of the economy in the way the regulator observes it. The results of econometric analysis using HAR‑models of high-frequency 5-minute volatility, taking into account intraday volatility patterns, show that regular communications of the Bank of Russia (namely, press releases following a meeting of the Bank of Russia Board of directors) really increase volatility in financial markets, while market participants cannot instantly estimate the significance of the new information, while this process takes about 15–20 minutes. However, the effect of increasing volatility is practically insignificant statistically when it comes to press conferences of the Governor Elvira Nabiullina. This result may indicate almost complete absence of new information for the market participants, disclosed during the opening speech at the press conference and the Q&A session. Also, within the framework of the study, recommendations were formulated for the Bank of Russia to change the format of regular communications.

Cross-Time-Frequency Analysis of Volatility Interdependence among Stock and Currency Markets

Volatility transmission between stock markets and currency markets is an ongoing debate in the pertinent literature. However, the majority of the previous studies have used only daily data with a limited sample. This study aims to fill this gap by identifying how sample stock markets and currencies play the role of volatility transmitter and receiver, particularly on an intraday basis. To this end, this research detects volatility interdependencies among various stock markets and currencies using five major stock indices and six major currency pairs. The results for daily and intraday frequencies are quite disparate. In particular, the results signify that the transmission of volatility from currency markets to stock markets is much stronger on an intraday basis. The results also indicate a strengthening of the volatility transmission and spillover interdependence among stock markets on a daily basis. These results may be ascribed to the continuous trading mechanism of these markets, which in turn allows the news to impact these markets first, which then transmit it to stock markets. The findings obtained also imply that intraday price fluctuations in major currencies should be closely tracked to monitor intraday volatility patterns in stock markets.

Do Jumps Matter in Realized Volatility Modeling and Forecasting? Empirical Evidence and a New Model

Building on an extensive empirical analysis I investigate the relevance of jumps and signed variations in predicting Realized Volatility. I show that properly accounting for intra-day volatility patterns and staleness sensibly reduces the identified jumps. Realized Variance decompositions based on intra-day return size and sign improve the in-sample fit of the models commonly adopted in empirical studies. I also introduce a novel specification based on a more informative decomposition of Realized Volatility, which offer improvements over standard models. From a forecasting perspective, the empirical evidence I report shows that most models, irrespective of their flexibility, are statistically equivalent in many cases. This result is confirmed with different samples, liquidity levels, forecast horizons and possible transformations of the dependent and explanatory variables.

Time-Varying Periodicity in Intraday Volatility

ABSTRACT We develop a nonparametric test for whether return volatility exhibits time-varying intraday periodicity using a long time series of high-frequency data. Our null hypothesis, commonly adopted in work on volatility modeling, is that volatility follows a stationary process combined with a constant time-of-day periodic component. We construct time-of-day volatility estimates and studentize the high-frequency returns with these periodic components. If the intraday periodicity is invariant, then the distribution of the studentized returns should be identical across the trading day. Consequently, the test compares the empirical characteristic function of the studentized returns across the trading day. The limit distribution of the test depends on the error in recovering volatility from discrete return data and the empirical process error associated with estimating volatility moments through their sample counterparts. Critical values are computed via easy-to-implement simulation. In an empirical application to S&P 500 index returns, we find strong evidence for variation in the intraday volatility pattern driven in part by the current level of volatility. When volatility is elevated, the period preceding the market close constitutes a significantly higher fraction of the total daily integrated volatility than during low volatility regimes. Supplementary materials for this article are available online.

Intraday return volatility in Saudi Stock Market: An evidence from Tadawul All Share Index

The association between risk and return is a significant concept in finance that has been studied in the past to a large extent. The stock market volatility is closely associated with the risk. The current study examines the intraday volatility pattern of stock market of Saudi Arabia by reviewing the stocks of Tadawul All Share Index (TASI). We obtain return data at 5-minute frequency from the SASEIDX starting on 25 October 2017 and ending on 9 May 2018. We examine the stock market volatility by using different symmetric and asymmetric GARCH models and observe that, the symmetric GARCH models showed a significant positive association between risk and return. Similarly, the asymmetric GARCH models show that the estimates were significant and the leverage estimate was negative and significant, indicating a no-leverage effect in the return series. Moreover, the asymmetric results suggest that negative shocks do not entail to future higher volatility than positive shocks. Therefore, the symmetric and asymmetric GARCH models are comfortable to capture the volatility of Saudi stock market from Intraday data.

Intraday volatility and the implementation of a closing call auction at Borsa Istanbul

The implementation of a closing call auction on market quality and volatility is examined at Borsa Istanbul in Turkey. Using 5- and 15-minute intervals, we document the accentuated volatility after the open and before the close during the morning and afternoon sessions. We show that the implementation of a closing call decreases volatility accentuation just prior to the market close, and increases market quality. We also document the evolution of intraday volatility patterns at Borsa Istanbul using the longest to date high frequency dataset available, and show that volatility has been increasing over time, especially at the close.

A Mixed Frequency Stochastic Volatility Model for Intraday Stock Market Returns

We propose a mixed frequency stochastic volatility (MFSV) model for the dynamics of intraday asset return volatility. In order to account for long-memory we separate stochastic daily and intraday volatility patterns by introducing a long-run component that changes at daily frequency and a short-run component that captures the remaining intraday volatility dynamics. An additional component captures deterministic intraday patterns. We analyze the stochastic properties of the resulting non-linear state-space model both on the daily and the intraday frequency and show how the model can be estimated in a single step using simulated maximum likelihood based on Efficient Importance Sampling (EIS). We apply the model to intraday returns of five New York Stock Exchange traded stocks. The estimation results indicate distinct dynamic patterns for daily and intradaily volatility components, where about 50% of intraday volatility dynamics are explained by the daily component. In-sample diagnostic tests and an out-of-sample forecasting experiment indicate that already the very basic model specification successfully accounts for the complex dynamic and distributional properties of asset returns both on the intraday and the daily frequency.

Bayesian Dynamic Modeling of High-Frequency Integer Price Changes

We investigate high-frequency volatility models for analyzing intra-day tick by tick stock price changes using Bayesian estimation procedures. Our key interest is the extraction of intra-day volatility patterns from high-frequency integer price changes. We account for the discrete nature of the data via two different approaches: ordered probit models and discrete distributions. We allow for stochastic volatility by modeling the variance as a stochastic function of time, with intra-day periodic patterns. We consider distributions with heavy tails to address occurrences of jumps in tick by tick discrete prices changes. In particular, we introduce a dynamic version of the negative binomial difference model with stochastic volatility. For each model we develop a Markov chain Monte Carlo estimation method that takes advantage of auxiliary mixture representations to facilitate the numerical implementation. This new modeling framework is illustrated by means of tick by tick data for several stocks from the NYSE and for different periods. Different models are compared with each other based on predictive likelihoods.We find evidence in favor of our preferred dynamic negative binomial difference model.

Risk and Return Around the Clock

We investigate price discovery over the 24-hour trading day for equities, currencies, bonds, and commodities. Sizable price discovery occurs around the clock for most assets. For a given asset, intraday risk and return distributions are fairly similar, indicating a broadly constant risk-return-relationship during the day. Although the amount of price discovery varies signi cantly during the day and di ers across assets, price discovery is generally e cient around the clock. Most assets do not exhibit the U-shaped intraday volatility pattern that has been documented for US equities, even if only main trading hours are considered. Intraday spikes in volatility are driven by the open or close of the market for the respective asset or other assets and by macroeconomic announcements. Both di usion and jump risk are important drivers of intraday volatility patterns, and US macroeconomic news account for a sizable fraction of jump-driven volatility. For some { but not all { assets, the relationship between volume and volatility that can generally be observed during the trading day does not hold at the time of jumps, suggesting that traders anticipate large price moves at the time of scheduled announcements and market depth falls accordingly.

Monitoring the Intraday Volatility Pattern

AbstractA functional time series consists of curves, typically one curve per day. The most important parameter of such a series is the mean curve. We propose two methods of detecting a change in the mean function of a functional time series. The change is detected on line, as new functional observations arrive. The general methodology is motivated by, and applied to, the detection of a change in the mean intraday volatility pattern. The methodology is asymptotically justified by applying a new notion of weak dependence for functional time series. It is calibrated and validated by simulations based on real intraday volatility curves.

Intraday Stealth Trading and Volatility: The Evidence from the Warsaw Stock Exchange

The intraday volatility and volume U-shape pattern is well documented in the literature. It describes the common pattern of investor’s behavior on the stock markets: investors trade in the beginning and the end of the day more intensive than in the lunch time. However that pattern does not differentiate between trades’ sizes and investors characteristics. The stealth trading hypothesis states that informed traders tend to hide their information. There is a need for such behavior at the time of low volatility and they may achieve this by breaking up their trades into smaller parts. At the time of high volatility informed traders are willing to place large orders at the beginning and the end of the trading day because high volatility provides a sufficient camouflage for their information. We examine volatility pattern for small, medium and large trades and consider how durations between trades and spreads differ between trade size categories. Our sample consists of the data from the Warsaw Stock Exchange, which is organized as an order driven market. We show that medium-size trades are associated with relative large cumulative stock price changes, however these results are not robust when liquidity measures and durations between the consecutive trades are taken into account.

Do Intraday Volatility Patterns Follow a ‘U’ Curve? Evidence from the Indian Market

This study examines the ‘intraday’ volatility patterns of NSE’s Nifty Index from August 2000 to December 2003. The tick by tick index returns are categorized into three groups – opening price to thirty minutes after opening price (morning sample), thirty minutes after opening price to fifteen minutes before closing price (mid-day sample) and fifteen minutes before closing price to closing price (evening sample). Defining the tick by tick index returns as a measure of deviation between successive prices, new volatility estimates are constructed to compute intraday volatility. The volatility patterns across the samples suggest high volatility during the initial trading period which sustains till 30 opening minutes and further increasing volatility during the last 15 minutes of a trading day. Information bunching and presence of private information are attributed to morning and evening period volatilities respectively. The volatility of intraday index prices of Nifty follows a crude U shaped curve.