Range-based Volatility Research Articles

Forecasting volatility of stock indices: Improved GARCH-type models through combined weighted volatility measure and weighted volatility indicators

This paper proposes an unbiased combined weighted (CW) volatility measure and weighted volatility indicators (WVI) that integrates the return- and range-based volatility measures to model the dynamics volatility of stock returns. The main feature of the CW measure is that it is formulated based on the weighted inter- and intra-price information to quantify the volatility directly, while the WVI effectively identifies signals on the shift of volatility. Empirical analysis using five stock indices demonstrates that the CW measure, utilising squared returns in combination with range-based Garman-Klass volatility measure, exhibits the lowest losses based on root mean squared error and quasi-likelihood when compared to 5-minute realised volatility as a proxy for true volatility. Furthermore, we investigate the feasibility of incorporating the CW measure and WVI as the exogenous variable(s) in the generalised autoregressive conditional heteroscedasticity (GARCH)-type models to enhance the forecasting performance. The findings indicate that the GARCH-CW-WVI and EGARCH-CW-WVI models exhibit superior in-sample model fit based on the Akaike information criterion than the existing GARCH and EGARCH models. Moreover, our proposed models also offer the best out-of-sample forecasts evaluated using various loss functions and further tested using Hansen’s model confidence set based on the mean squared error loss. Different risk levels of value-at-risk (VaR) and expected shortfall (ES) forecasts based on GARCH-CW-WVI and EGARCH-CW-WVI models are computed and examined with various backtests to confirm the accuracies of VaR and ES forecasts.

Range-Based Volatility Timing

Range-Based Volatility Timing

Improving volatility forecasts: Evidence from range-based models

Volatility models based on the daily high-low range have become increasingly popular. The high and low prices are easily available, yet the range contains very useful information about volatility. It has been established in the literature that range-based volatility models outperform standard volatility models based on closing prices. However, little is known about which range-based model performs the best. We therefore evaluate two range-based volatility models, i.e. CARR and Range-GARCH with the standard GARCH model and two asymmetric GARCH models, i.e., GJR and EGARCH, based on the Monte Carlo experiments and a wide sample of currencies and stock indices. For simulated time series, the range-based models outperform the standard GARCH model and asymmetric models, and the performance of the Range-GARCH model and the CARR model is similar. However, for real financial time series (six currency pairs and nine stock indices) the Range-GARCH model outperforms the standard GARCH, GJR, EGARCH, and CARR models, while ranking of the competing models is ambiguous. We argue that Range-GARCH is the best from the competing models.

An Empirical Investigation of Value at Risk (VaR) Forecasting Based on Range-Based Conditional Volatility Models

Value at Risk (VaR) is a widely used measure of market risk. Precision in the estimation of volatility leads to accurate VaR forecasts. As volatility is time-varying and has a clustering effect, GARCH class of volatility models is helpful in modeling volatility more precisely. Studies have also shown that range-based volatility estimates are more efficient than traditional models that use only closing prices. Therefore, this study uses the GARCH family of volatility models to model and forecast VaR. The study compares conventional models that use closing prices alone, like GARCH and TARCH, with range-based models like RGARCH and RTARCH models, where the range defined as daily high price minus low price is introduced as an exogenous variable, to explore if the latter provides better predictive accuracy. All the models are back-tested using the Kupiec (1995) unconditional coverage and Christoffersen (1998) conditional coverage tests. The data period in the study ranges from 2003-2021, and we consider five BRICS indices and three major developed economies, namely, the USA, the UK, and Germany. An empirical investigation shows that range-based models do a better job in VaR forecasting as it has more information content than daily closing prices, thereby giving more accurate VaR estimates. The study hopes this finding will greatly help stakeholders like financial institutions, regulators, and practitioners in more effective market risk management.

Range-based volatility modeling in financial markets using a family of scale mixtures of Birnbaum-Saunders distribution

We propose scale mixtures of Birnbaum-Saunders distributions as a new class of positive skewed and leptokurtic distributions and use it to model volatility in stock markets. To estimate the model parameters, we develop an Expectation-Conditional-Maximization algorithm. The numerical performance of the proposed methodology is evaluated by means of Monte Carlo simulations. Application of the new model in volatility modeling is illustrated with some real-life data.

Long Memory, Spurious Memory: Persistence in Range-Based Volatility of Exchange Rates

This study considers the long memory and fractional integration in the range-based volatilities across 30 currencies against USD. Graphical analysis of the autocorrelation function at long lags and pole near zero frequencies in the periodogram suggests the existence of fractional integration. We apply semi-parametric methods to measure long-range dependence. We find a decrease in the memory estimates with an increase in the bandwidth, which indicates the presence of spurious memory rather true long memory. The hypothesis of long memory against the alternative of spurious memory is also tested by applying the different semi-parametric methods. Empirical results confirm the presence of spurious memory that may be a result of some shocks to the volatility estimator. Furthermore, the reduced memory estimates obtained by utilising an estimator accounting for level shifts also explains the inconsistency of the Local Whittle estimator. We also estimate the number of breaks for each series.

The comparison of range-based volatility estimators and an application of TVP-VARbased connectedness

This paper aims to show the application of range-based volatility in connectedness analysis. For this purpose, we compare the volatility estimators Parkinson, Yang-Zhang, Garman-Klass, Rogers-Satchell, and modified Garman- Klass by Yang and Zhang methods. As an example, we calculated the range-based stock prices’ volatility of four defense industry companies quoted in Borsa Istanbul. We compared the forecast performance of volatility against Heteroskedastic Root Mean Square Error statistics. We include the best performing volatility series in the spillover analysis. Instead of the Cholesky decomposition VAR and generalized VAR approaches used in the calculation of the Diebold-Yılmaz connectedness index, we apply the TVP-VAR-based connectedness approach. The comparison results show that Rogers-Satchell for ASELSAN, KATMERLER, and PAPIL, and Parkinson volatility estimator for OTOKAR have the smallest error, respectively. The empirical findings of TVP-VAR connectedness show that the average forecast error variance of the network is 34.35%.

Volatility Co-Movement between Bitcoin and Stablecoins: BEKK–GARCH and Copula–DCC–GARCH Approaches

This paper aims to investigate and measure Bitcoin and the five largest stablecoin market volatilities by incorporating various range-based volatility estimators to the BEKK- GARCH and Copula-DCC-GARCH models. Specifically, we further measure Bitcoins’ volatility related to five major stablecoins and examine the connectedness between Bitcoin and the stablecoins. Our empirical findings document that the connectedness between Bitcoin and stablecoin market volatility behaviors exhibits the presence of stable interconnection. This study is of particular importance since it is crucial for market participation in the ongoing crypto assets to be informed about both the volatility patterns of major cryptocurrencies and the relative volatility of Bitcoin against the stablecoin markets. Eventually, we find that there is no systematic evidence for the various parity deviations of the stablecoins that are profoundly impacted by Bitcoin volatility. Thus, Bitcoin and the largest stablecoin Tether could stabilize together. However, Bitcoin shall not be generalized to other stablecoins in terms of stability results.

Time-varying risk aversion and renminbi exchange rate volatility: Evidence from CARR-MIDAS model

In this paper, we investigate the relation between time-varying risk aversion and renminbi exchange rate volatility using the conditional autoregressive range-mixed-data sampling (CARR-MIDAS) model. The CARR-MIDAS model is a range-based volatility model, which exploits intraday information regarding the intraday trajectory of the price. Moreover, the model features a MIDAS structure allowing for time-varying risk aversion to drive the long-run volatility dynamics. Our empirical results show that time-varying risk aversion has a significantly negative effect on the long-run volatility of renminbi exchange rate. Moreover, we observe that both intraday ranges and time-varying risk aversion contain important information for forecasting renminbi exchange rate volatility. The range-based CARR-MIDAS model incorporating time-varying risk aversion provides more accurate out-of-sample forecasts of renminbi exchange rate volatility compared to a variety of competing models, including the return-based GARCH, GARCH-MIDAS and GARCH-MIDAS incorporating time-varying risk aversion as well as range-based CARR, CARR-MIDAS and heterogeneous autoregressive (HAR), for forecast horizons of 1 day up to 3 months. This result is robust to alternative risk aversion measure, alternative MIDAS lags as well as alternative out-of-sample periods. Overall, our findings highlight the value of incorporating intraday information and time-varying risk aversion for forecasting the renminbi exchange rate volatility.

News-based sentiment and bitcoin volatility

In this work, I studied whether news media sentiments have an impact on Bitcoin volatility. In doing so, I applied three different range-based volatility estimates along with two different sentiments, namely psychological sentiments and financial sentiments, incorporating four various sentiment dictionaries. By analyzing 17,490 news coverages by 91 major English-language newspapers listed in the LexisNexis database from around the globe from January 2012 until August 2021, I found news media sentiments to play a significant role in Bitcoin volatility. Following the heterogeneous autoregressive model for realized volatility (HAR-RV)—which uses the heterogeneous market idea to create a simple additive volatility model at different scales to learn which factor is influencing the time series—along with news sentiments as explanatory variables, showed a better fit and higher forecasting accuracy. Furthermore, I also found that psychological sentiments have medium-term and financial sentiments have long-term effects on Bitcoin volatility. Moreover, the National Research Council Emotion Lexicon showed the main emotional drivers of Bitcoin volatility to be anticipation and trust.

Return and volatility spillovers across the Western and MENA countries

We use weekly data on returns and range-based volatility over 2005–2017 to examine the degree of interconnectedness in financial markets of eleven MENA and four Western economies using the methodology proposed by Diebold and Yilmaz (2009, 2012, 2014). Our findings suggest (a) similar patterns of dynamic spillovers in both returns and in volatility. Both return and volatility spillover indices experienced significant bursts from 2008 to 2011 coinciding with the U.S. financial crisis. (b) Financial markets of Israel, Saudi Arabia and the UAE are more closely integrated with Westerns markets and may serve as primary channels for transmission of Western shocks to the region. Also, shocks to these three markets have noticeable impacts on other MENA markets. (c) Shocks to the U.S. financial markets play a critical role in return and volatility of MENA markets. (d) These findings are robust to alterations in window size and forecast horizon.

Investor sentiment and predictability for volatility on energy futures Markets: Evidence from China

This research specifically reveals the predictability for the volatility on energy futures markets when involving investor sentiment, using the newly launched China’s INE crude oil futures as an incremental evidence. First, we propose a novel investor sentiment index captures the feature of instant sentiment conversion and the internet attention for energy futures markets. Second, we present the nexus between the proposed novel investor sentiment and conditional volatility, which shows that the proposed investor sentiment significantly impacts on return and volatility. It indicates that the emerging markets filled with noise traders like China are more deeply influenced by investor sentiment and bring about more volatility. Third, the results of dual leverage effects in modeling energy futures volatility shows that the optimistic (pessimistic) sentiment shift has negative(positive) effects on volatility, and downward (upward) shocks from bad news (good news) are followed by greater volatility. Fourth, incorporating the novel investor sentiment into models can significantly improve volatility forecasting accuracy because of its smaller loss function results compared with the benchmark models without sentiment. Moreover, high frequency realized volatility and range-based volatility are regarded as real volatility to examine the predictability, and Diebold Mariano test is used to present the difference of forecasting ability. Our results are robust by using the data from China’s Thermal Coal Futures. Overall, we present that the novel investor sentiment can be utilized for monitoring and predicting volatility shocks for emerging markets with lots of noise traders.

Volatility Forecasting Based on Cyclical Two-Component Model: Evidence from Chinese Futures Markets and Sector Stocks

This article aims to study the schemes of forecasting the volatilities of Chinese futures markets and sector stocks. An improved method based on the cyclical two-component model (CTCM) introduced by Harris et al. in 2011 is provided. The performance of CTCM is compared with the benchmark model: Heterogeneous Autoregressive model of Realized Volatility type (HAR-RV type). The impact of open interest for futures market is included in HAR-RV type model. We employ 3 different evaluation rules to determine the most efficient models when the results of different evaluation rules are inconsistent. The empirical results show that CTCM is more accurate than HAR-RV type in both estimation and forecasting. The results also show that the realized range-based tripower volatility (RTV) is the most efficient estimator for both Chinese futures markets and sector stocks.

The use of range-based volatility estimators in testing for Granger causality in risk on international capital markets

This study utilizes the extreme value theory (EVT) approach to compare the performance of a wide variety of range-based volatility estimators in the analysis of causality in risk between emerging and developed markets. The AR(1)-GARCH(1,1) model with t-distribution is used as a benchmark. Regulator and firm loss functions are used to select the best volatility model. Two tests of causality in risk are used in our empirical study. The AR-GARCH model with EVT outperforms the other approaches in the case of huge risk. Among the most likely risk-taking markets are Standard & Poor's 500, CAC 40, Nikkei 225, Nasdaq and FTSE 100.

Range-based volatility forecasting: a multiplicative component conditional autoregressive range model

To capture the effect in volatility, a multiplicative component conditional autoregressive range (MCCARR) model is proposed. We show theoretically that the MCCARR model can capture the long-memory effect well. An empirical study is performed on the Standard & Poor's 500 index, and the results show that the MCCARR model outperforms both conditional autoregressive range and heterogeneous autoregressive models for in-sample and out-of-sample volatility forecasting.

Holidays, weekends and range-based volatility

This study analyses the effect of non-trading periods on the forecasting ability of S&P500 index range-based volatility models. We find that volatility significantly diminishes on the first trading day after holidays and weekends, but not after long weekends. Our findings indicate that models that include autoregressive terms that interact with dummies that allow us to capture changes in volatility levels after interrupting periods provide greater explanatory power than simple autoregressive models. Therefore, the shorter the length of the non-trading periods between two trading days, the higher the overestimation of the volatility if this effect is not considered in volatility forecasting.

ОЦІНЮВАННЯ РІВНЯ ФІНАНСОВОЇ СТІЙКОСТІ БАНКІВСЬКОГО СЕКТОРУ УКРАЇНИ НА ОСНОВІ Z-ІНДЕКСУ

Проаналізовано динаміку фінансової стійкості банківського сектору України на основі побудови квартальних часових рядів агрегованого і зваженого Z-індексів для вибірки українських банків за період 2010—2017 років. Виявлено доцільність використання медіани як міри центральної тенденції та розмаху як міри мінливості для розрахунку Z-індексів українських банків. Порівняння зваженого за ринковими частками Z-індексу з іншими індикаторами стійкості банківської системи підтвердило можливість його трактування як агрегованого показника стійкості системи банків. Отримані оцінки агрегованого і зваженого Z-індексів показали, що фінансова стійкість української банківської системи досягла критичного рівня. Груповий аналіз вказує на першочергове зниження стійкості державних банків із 2014 року, що підтверджує негативний вплив монополізації державою банківського сектору. Низькі показники стійкості банків з іноземним капіталом можуть свідчити про невисоку зацікавленість іноземних інвесторів вкладати в банківський бізнес в Україні в сучасних умовах. Найкращими з трьох груп виявились показники фінансової стійкості банків з українським капіталом, що зберегли свою присутність на ринку після очищення банківського сектору у 2015—2017 роках і демонструють стабілізацію своєї діяльності.

Forecast the realized range-based volatility: The role of investor sentiment and regime switching

In this study, we first investigate the impacts of investor sentiment on the realized range-based volatility in the framework of regime switching model. Out-of-sample results show that investor sentiment can significantly improve the forecasting performance of volatility models. Moreover, the results further find that combining the regime switching of those models with investor sentiment can substantially gain higher forecasting accuracy. Our conclusions are robust to different forecasting windows.

Nonlinear high-frequency stock market time series: Modeling and combine forecast evaluations

This study intends to examine two major challenges in high-frequency (intraday) volatility analysis: first, the selection of a suitable realized volatility and second, the appropriate statistical model for the intraday volatility analysis. In order to address the first challenge, the multiple power variation volatility, nearest neighboring truncated volatility and range-based volatility have been included in the volatility selections. For the intraday volatility modeling, a skewed heterogeneous autoregressive (HAR) model with the features of leverage effect and structural break has been used to improve the standard HAR model specifications. Various volatility representation forecasts using the individual improved-HAR models as well as the combined models are evaluated under the combine forecast evaluations. The Dow Jones Industrial Average (DJIA) and MERVAL Argentina stock indexes have been selected for the empirical study. The empirical results showed that the mixture of best performing forecast models are relying on the type of volatility representation and also the selected proxy for the latent volatility.

Liquidity and realized range-based volatility forecasting: Evidence from China

This paper examines the dynamical impact of market wide liquidity on the volatility by using the Markov switching-regime approach on the Heterogeneous Autoregressive model of the realized range-based volatility (MS-HAR-RRV-LIQ). First, based on the simple partition of the liquidity measures by their historical means, we find the impact of the market liquidity on the realized range-based volatility (RRV) is non-linear with significantly stronger when the market is fluctuating. Second, by utilizing the method of Markov regimes switching, we find that in sample results, the impact of market liquidity on RRV is dynamics with much stronger when the market is fluctuating. In addition, the impact of liquidity on RRV are persistent for both the fluctuating state and the stable state, which indicate that the impact of liquidity on volatility would remain in its original state unless there are major economic events. Third, in order to eliminate the hidden information of volatility in liquidity measures, we further decompose the liquidity measures to obtain the volatility-adjusted liquidity, and find that the impact of liquidity driven by the component of liquidity uncorrelated with volatility on market volatility is also dynamics with much stronger when the market is fluctuating. Finally, out-of-sample results suggest that the models of HAR-RRV-LIQ and their corresponding volatility-adjusted liquidity models with regimes switching can increase the forecasting ability significantly than those without regime switching.