Volatility Measures Research Articles

Modal volatility function

We in this article propose a novel non‐parametric estimator for the volatility function within a broad context that encompasses nonlinear time series models as a special case. The new estimator, built on the mode value, is designed to complement existing mean volatility measures to reveal distinct data features. We demonstrate that the suggested modal volatility estimator can be obtained asymptotically as well as if the conditional mean regression function were known, assuming observations are from a strictly stationary and absolutely regular process. Under mild regularity conditions, we establish that the asymptotic distributions of the resulting estimator align with those derived from independent observations, albeit with a slower convergence rate compared to non‐parametric mean regression. The theory and practice of bandwidth selection are discussed. Moreover, we put forward a variance reduction technique for the modal volatility estimator to attain asymptotic relative efficiency while maintaining the asymptotic bias unchanged. We numerically solve the modal regression model with the use of a modified modal‐expectation‐maximization algorithm. Monte Carlo simulations are conducted to assess the finite sample performance of the developed estimation procedure. Two real data analyses are presented to further illustrate the newly proposed model in practical applications. To potentially enhance the accuracy of the bias term, we in the end discuss the extension of the method to local exponential modal estimation. We showcase that the suggested exponential modal volatility estimator shares the same asymptotic variance as the non‐parametric modal volatility estimator but may exhibit a smaller bias.

Assessing volatility persistence in fractional Heston models with self-exciting jumps

We derive a new fractional Heston model with self-exciting jumps. We study volatility persistence and demonstrate that the quadratic variation necessarily exhibits less memory than the integrated variance, which preserves the degree of long-memory of the instantaneous volatility. Focusing on realized volatility measures, we find that traditional long-memory estimators are dramatically downward biased, in particular for low-frequency intraday sampling. Conveniently, our Monte Carlo experiments reveal that some noise-robust local Whittle-type estimators offer good finite sample properties. We apply our theoretical results in a risk forecasting study and show that our frequency-domain forecasting procedure outperforms the traditional benchmark models.

A long short-term memory enhanced realized conditional heteroskedasticity model

This paper examines the potential of using realized volatility measures for capturing financial markets’ uncertainty. Earlier studies show the usefulness of the high-frequency data based Generalized AutoRegressive Conditional Heteroskedasticity (RealGARCH) model for enhancing volatility forecasting accuracy; however, this model focuses only on linear and short-term dependencies of realized volatility measures on the underlying volatility. Recognizing the critical economic implications of this limitation, the long short-term memory neural network is integrated into RealGARCH, aiming to explore the full impact of realized volatility on volatility modeling and forecasting via capturing the nonlinear and long-term effects. A comprehensive empirical study using 31 indices from 2004 to 2021 is conducted. The results demonstrate that our proposed framework achieves superior in-sample and out-of-sample performance compared to several benchmark models. Importantly, it retains interpretability and effectively adapts to the stylized facts observed in volatility, emphasizing its significant potential for enhancing economic decision-making and risk management.

Investor attention and market activity: evidence from green cryptocurrencies

Purpose This paper aims to investigate the relationship between investor attention and market activity (return, volatility and volume) using a sample of 14 clean energy cryptocurrencies (hereafter green cryptocurrency), namely, Chia, Cardano, Stellar, Tron, Ripple, Nano, IOTA, EOS, Bitcoin Green, Alogrand, Hedara, Polkadot, FLOW and Tezos. Design/methodology/approach This paper use 26040 crypto-day observations and a range of econometric techniques, including Dynamic Granger causality, Panel vector autoregression (VAR), Impulse response function and the decomposition of forecast error variance. Findings Based on 26040 crypto-day observations, this paper finds a bidirectional Granger causal relationship between investor attention and all measures of market activity, namely, return, absolute volatility, squared volatility and volume. The panel VAR and impulse response function demonstrate that market activity in the green crypto ecosystem, especially volatility and volume, is considerably responsive to changes in investor attention proxied by Google search volume (hereafter Google search volume (GSV)). The findings also demonstrate a significant asymmetric effect of return and volume on investor attention since past negative shocks “or bad news” in return and volume are more likely to grab the investor’s attention. All in all, our study emphasizes the crucial role of investor attention in the green crypto ecosystem. Originality/value (i) The research is the first to shed light on investor attention in the green cryptocurrency market. (ii) The paper uses a wide range of green cryptocurrencies to offer a comprehensive picture of the green cryptocurrency ecosystem. (iii) This paper is the first to use the panel Granger causality to investigate investor attention in the cryptocurrency market which provides several advantages over the conventional Granger causality approach. (iv) This paper is the first to provide novel empirical evidence on the prevalent influence of investor attention in the green crypto market.

Entropy-Based Volatility Analysis of Financial Log-Returns Using Gaussian Mixture Models

Volatility in financial markets refers to the variation in asset prices over time. High volatility indicates increased risk, making its evaluation essential for effective risk management. Various methods are used to assess volatility, with the standard deviation of log-returns being a common approach. However, this implicitly assumes that log-returns follow a Gaussian distribution, which is not always valid. In this paper, we explore the use of (differential) entropy to evaluate the volatility of financial log-returns. Estimation of entropy is obtained using a Gaussian mixture model to approximate the underlying density of log-returns. Following this modeling approach, popular risk measures such as Value at Risk and Expected Shortfall can also be computed. By integrating Gaussian mixture modeling and entropy into the analysis of log-returns, we aim to provide a more accurate and robust framework for assessing financial volatility and risk measures.

In-situ online investigation of biogenic volatile organic compounds emissions from tropical rainforests in Hainan, China

Biogenic volatile organic compounds (BVOCs) emitted by tropical plants represent a significant proportion of global emissions, but the in-situ BVOC measurements in tropical rainforests are extremely sparse. Herein, a vehicle-mounted mobile monitoring system was developed for in-situ online investigations of BVOC emissions from thirty representative tree species in the tropical rainforests of Hainan Island, southern China. The results showed that monoterpenes were the primary BVOCs emitted from most broadleaf trees. Isoprene, sabinene, γ-terpinene and β-ocimene were the most abundant BVOCs. Localized canopy-scale emission factors (EFs) exhibited notable discrepancies with the defaults in the Model of Emissions of Gases and Aerosols from Nature (MEGAN), specifically with isoprene EFs being slightly lower than the model, while the EFs for monoterpenes and sesquiterpenes were 1 to 27 times higher than those in MEGAN. The BVOC emission inventory for the predominant mature forest species in Hainan Island in 2023 was further estimated to be 244.43 Gg C·yr−1, with isoprene and monoterpenes accounting for 74 % and 16 %, respectively. Additionally, unimodal monthly variation patterns were revealed, with BVOC emissions peaked in July (30.08 Gg C·yr−1) and bottomed in January (8.84 Gg C·yr−1). This study demonstrates the potential and versatility of the applied mobile platform for in-situ online measurements of plant volatiles. Our findings provide important data support for reducing uncertainties in BVOC emission estimations in tropical rainforests and for evaluating their health benefits in the context of forest therapy.

Methods for estimating integrated variance: Jump robustness issues in high frequency time series

Integrated variance is a volatility measure of a process in continuous time, which is applicable in financial mathematics as a means to optimize a portfolio, project dynamics of a price of a financial asset. The consistency of an estimator for integrated variance of a random process is at the core of this article. A fundamental diffusion process is extended by adding a jump component as a means of improving the descriptive function of the process. It is activity of jumps that is a factor subject to which is the consistency of the estimator for integrated variance. Due to this fact, consistency is defined as an extent to which the estimator at hand is jump robust. Two main methods for estimating integrated variance are considered and the capacity of corresponding estimators to withstand the effect of jumps while converging is briefly analyzed. The arguments indicating a necessity for further research of the effect of jumps with reference to works of the authors who have established a ground for analysis of integrated variance and those works containing main asymptotic results for consistency of integrated variance estimators are elaborated. Based on this, avenue for further research and development of asymptotic theory for consistency of an estimator for integrated variance is identified.

Beyond GARCH: Intraday Insights Into the Exchange Rate and Stock PriceVolatility Dynamics in Borsa Istanbul Sectors

This study investigated the impact of exchange rate volatility on sectoral stockvolatility by employing the intraday volatility measure directly calculated fromthe original data, using daily data from 27 Borsa Istanbul sectors between April 29, 2003, and April 25, 2023. In the literature, GARCH models are commonly usedtostudy the volatility spillovers between exchange rates and stock prices, typicallyusing aggregate data. However, the GARCH family models provide inefficient andbiased estimates if they are misspecified. Moreover, using aggregate-level data maylead to biased and misleading conclusions. The research used intraday volatilitymeasures to overcome the shortcomings of GARCH models. The ordinary least squares (OLS), GARCH (1,1) methods, and Garman and Klass (1980) volatilityestimator are used. The empirical results showed that the estimates fromeachmethod vary significantly, and these disparities in the results might be due tomisspecification in GARCH (1,1) models. The intraday volatility model estimationresults showed that although stock price volatilities in all sectors are positively andsignificantly affected by exchange rate volatility, their magnitudes varysignificantly. Taken together, this implies the presence of vast heterogeneities inthe responses of sectoral stock price volatilities to exchange rate volatility. The results encourage policymakers to pay special attention to these heterogeneities toprevent capital flights and underinvestment. Additionally, the findings assist investors in making more effective decisions by helping themadapt their investment strategies to factor in exchange rate fluctuations and mitigate the impact of unexpected events in the exchange rate market

COVID-19 and Uncertainty Effects on Tunisian Stock Market Volatility: Insights from GJR-GARCH, Wavelet Coherence, and ARDL

This study rigorously investigates the impact of COVID-19 on Tunisian stock market volatility. The investigation spans from January 2020 to December 2022, employing a GJR-GARCH model, bias-corrected wavelet analysis, and an ARDL approach. Specific variables related to health measures and government interventions are incorporated. The findings highlight that confirmed and death cases contribute significantly to the escalation in TUNINDEX volatility when using both the conditional variance and the realized volatility. Interestingly, aggregate indices related to government interventions exhibit substantial impacts on the realized volatility, indicating a relative resilience of the Tunisian stock market amidst the challenges posed by COVID-19. However, the application of the bias-corrected wavelet analysis yields more subtle outcomes in terms of the correlations of both measures of volatility to the same metrics. Our econometric implications bear on the application of such a technique, as well as on the use of the realized volatility as an accurate measure of the “true” value of volatility. Nevertheless, the measures and actions undertaken by the authorities do not exclude fear and insecurity from investors due to another virus or any other crisis. The positive and long-term impact on the volatility of US equity market uncertainty, VIX, economic policy uncertainty (EPU), and the infectious disease EMV tracker (IDEMV) is obvious through the autoregressive distributed lag model (ARDL). A potential vulnerability of the Tunisian stock market to future shocks is not excluded. Government and stock market authorities should grapple with economic and financial fallout and always instill investor confidence. Importantly, our results put mechanisms such as overreaction to public news and (in)efficient use of information under test. Questioning the accuracy of announcements is then recommended.

Crystals and melt inclusions record deep storage of superhydrous magma prior to the largest known eruption of Cerro Machín volcano, Colombia

Abstract Cerro Machín, a volcano located in the northern segment of the Andes, is considered one of the most dangerous volcanoes in Colombia with an explosive record that involves at least five plinian events. Prior studies focused on the last dome-building eruption have suggested the presence of a water-rich mid-crustal magma reservoir. However, no direct volatile measurements have been published and little work has been completed on the explosive products of the volcano. Here, we study the largest known eruption of Cerro Machín volcano which occurred 3600 yr BP producing dacitic pyroclastic fall deposits that can be traced up to 40 km from the vent. Lapilli pumice clasts have a mineral assemblage of plagioclase, amphibole, quartz, and biotite phenocrysts, with accessory olivine, Fe-Ti oxides, and apatite. The occurrence of Fo89-92 olivine rimmed by high Mg# amphibole and the established high-water contents in the magma imply the presence of magma near or at water saturation at pressures >~500 MPa. Measurements of up to 10.7 wt% H2O in melt inclusions hosted in plagioclase and quartz in the 3600 years BP eruption products support the idea that Cerro Machín is a remarkably water-rich volcanic system. Moreover, this is supported by measurements of ~103 – 161 ppm H2O in plagioclase phenocrysts. The application of two parameterizations of water partitioning between plagioclase and silicate melt allows us to use our water in plagioclase measurements to estimate equilibrium melt water contents of 5 ± 1 – 11 ± 2 wt% H2O, which are in good agreement with the water contents we measured in melt inclusions. Results of amphibole geobarometry are consistent with a magma reservoir stored in the mid-to-lower crust at a modal pressure of 700 ± 250 MPa, corresponding to a depth of ~25 km. Minor crystallization in the shallow crust is also recorded by amphibole barometry and calculated entrapment pressures in melt inclusions. Amphibole is present as unzoned and zoned crystals. Two populations of unzoned amphibole crystals are present, the most abundant indicate crystallization conditions of 853 ± 26 °C (1 se; standard error), and the less abundant crystallized at an average temperature of 944 ± 24 °C (1 se). Approximately 18% of the amphibole crystals are normally or reversely zoned, providing evidence for a minor recharge event that could have been the trigger mechanism for the explosive eruption. Plagioclase crystals also show normal and reverse zoning. The moderate Ni concentrations (<1600 μg/g) in the high-Fo olivine xenocrysts suggest that Cerro Machín primary magmas are generated by inefficient interaction of mantle peridotite with a high-silica melt produced by slab melting of basaltic material. Some sediment input is also suggested by the high Pb/Th (>2.2), Th/La (0.3 – 0.4), and low La/Th (<13; relative to mantle array) ratios. Whole rock chemistry reveals heavy rare earth element (HREE) depletion and Sr enrichment that likely formed during the crystallization of garnet and amphibole in the upper part of the mantle or lower portion of the crust, promoting the formation of water-rich dacitic magma that was then injected into the middle-to-lower crust. Textural and compositional differences in the crystal cargo that erupted during dome-building and plinian events support the idea that large volumes of magma recharge lead to effusive eruptions, while only small recharge events are needed to trigger plinian eruptions at Cerro Machín.

The Dissimilar Market Volatility in Neighboring Financial Markets: An Empirical Study Using A Multivariate Garch Model

ABSTRACT: Conventional knowledge of market volatility represents that two proximate financial markets operated in the same country would display a similar pattern in their time-varying volatility. In this paper, we propose that the heterogeneity in financial policy orientation of stock markets creates significant inter-market differences in terms of the volatility of stock returns, even if they are culturally and geographically linked to each other. For the empirical investigation of our proposition, the volatility data from two major stock exchanges in the Middle East, the Abu Dhabi Securities Exchange (ADX) and the Dubai Financial Market (DFM) are used. Both the ADX and DFM stock exchanges operate in the same country, the United Arab Emirates (UAE). The ADX is based in Abu Dhabi, the administrative capital, while the DFM is based in Dubai, the commercial and business hub of the UAE. They were both established in the year 2000, and their operational headquarters are located about 150 km from each other. This paper uses a multivariate GARCH model, in particular a diagonal VECH GARCH (1, 1) model to estimate volatility measures for stock returns between ADX-listed and DFM-listed stocks. The paper finds that the stock returns are significantly less volatile in the ADX compared to those in the DFM suggesting that the volatility transmission is incomplete between these two neighboring financial markets. This difference in volatility can potentially be attributed to the relatively conservative financial policies adopted by the oil-rich emirate of Abu Dhabi compared to the more market-oriented economic policies of Dubai, the country’s financial and commercial hub. Our findings have considerable implications for portfolio managers in ascertaining risk premiums when allocating investments across the two stock exchanges. For instance, this disparity in volatility should be taken into account by investors and policymakers when designing risk management strategies because it suggests that investors in the DFM may be exposed to higher levels of risk and uncertainty compared to their counterparts in the ADX. Investors operating in the DFM may require more robust risk management strategies, such as asset diversification and hedging, compared to their ASX counterparts.

Cybersecurity strategies for protecting big data in business intelligence systems: Implication for operational efficiency and profitability

The alarming increase in consumers goods and services with concurrent devaluations of naira have necessitated the need to examine the effects of NUSX(Nigerian naira/1 US dollar), NFX (Nigerian naira/1 France franc) and NCX (Nigerian naira/1 Chinese yuan) rates on inflation(measured by CPI) and its volatility in Nigeria using data sets spanning from 2008 to 2022. The auxiliary autoregressive AAR(3) order of integration test specify that all the variables are stationary at first difference. Adopting multiple regression model with least square method of estimation and generalized autoregressive conditional heteroskedasticity (GARCH(1, 1)) as measure of volatility, the results indicate that NCX (Nigerian naira/1 Chinese yuan), NFX (Nigerian naira/1 France franc) and NUSX(Nigerian naira/1 US dollar) have no influence on both inflation and its volatility in Nigeria. This implies that variation in exchange rates system is not sufficient to explain the sudden increase in the prices of goods and services in Nigeria. Therefore, the government should look beyond exchange rates in finding solution to rising inflation phenomenon in Nigeria’s economic space.

The Impact of Stochastic Volatility on Option Pricing Using the Black-Scholes Model: Empirical Evidence from NVIDIA

This paper investigates the impact of volatility on option pricing using the Black-Scholes model. Utilizing historical stock and option data from NVIDIA, this study demonstrates the limitations of the Black-Scholes model in capturing dynamic market conditions. The empirical analysis reveals significant discrepancies between model predictions and actual market prices, highlighting the importance of accurate volatility estimation. The findings suggest that incorporating better volatility measures can improve the accuracy of option pricing models. Additionally, the implications of these findings for traders and risk managers are discussed, emphasizing the need for more sophisticated approaches to volatility estimation in financial markets. This study adds to the body of knowledge by presenting actual data regarding the efficiency of different volatility metrics in option pricing. Moreover, it underscores the necessity of continuous improvement in financial modeling techniques to adapt to changing market dynamics. The study's results align with previous research that has shown the limitations of the Black-Scholes model and the benefits of alternative volatility estimation methods. This paper also discusses the potential application of these findings to improving trading strategies and risk management practices. The practical implications are significant, suggesting that traders and risk managers should consider incorporating advanced volatility measures into their models to enhance decision-making processes and financial outcomes. The conclusions drawn from this study highlight the critical role of accurate volatility estimation in achieving more reliable option pricing and underscore the need for ongoing research and innovation in this field.

Heterogeneous Volatility Information Content for the Realized GARCH Modeling and Forecasting Volatility

Abstract As the demand for accuracy in volatility modeling and forecasting increases, the literature tends to incorporate different volatility measures with heterogeneous information content to construct the hybrid volatility model. This study focuses on one of the popular hybrid volatility models: the Realized Generalized Autoregressive Heteroskedasticity (Realized GARCH) and embeds various volatility measures, including the CBOE VIX, VIX1D, Realized Volatility, and Daily Range to examine their heterogeneous impact on the conditional volatility estimation and forecasting. To evaluate the impact of the volatility measures, we first construct a volatility response function. This involves calculating the difference in one-step-ahead conditional volatility forecasts that incorporate information from both return and volatility measures against the forecasts based on return innovations only. Subsequently, the variance share is calculated to evaluate its role in explaining future variations in the Realized GARCH. Our results show that among these four volatility measures, VIX is the most informative volatility. Although VIX1D is overemphasized by the literature, its significance in volatility forecasting remains substantial, confirming that risk-neutral volatility measures are generally more informative than physical measures. Finally, we also find that incorporating multiple risk-neutral volatility measures does not improve forecasting performance compared to using a single measure due to overlapping information.

On evaporation kinetics of multicomponent aerosols: Characteristic times and implications for volatility measurements

On evaporation kinetics of multicomponent aerosols: Characteristic times and implications for volatility measurements

Factor timing in the Chinese stock market

AbstractI conduct an exploratory study about the feasibility of factor timing in the Chinese stock market, covering 24 representative and well‐identified risk factors in 10 categories from the literature. The long–short portfolio of short‐term reversal exhibits strong out‐of‐sample predictability, which is robust across various models and all types of predictors. This predictability is significant both statistically and economically, with a simple investment strategy obtaining its return three times higher than the buy‐and‐hold return in the sample period and a significant annualized 20.4% CH‐3 alpha. Portfolio historical volatility and market volatility measurement predictors play crucial roles in the reversal factor premium's robust predictability. However, such results are not evident in predicting all other factors' long–short portfolios as well as all factors' long‐wing and short‐wing portfolios, and this failure cannot be attributed to their exposure to unpredictable market returns.

Crude oil price volatility and environmental performance

We study the relationship between crude oil price volatility and corporate environmental performance. Using an extensive dataset from 32 countries consisting of 18,464 firm-year observations, we provide strong evidence that oil price volatility significantly increases firms' environmental performance. Our main inference is robust when using alternative measures of oil price volatility and environmental performance, alternative econometric specifications and samples, and several approaches to control for endogeneity. In a set of additional analyses, we first conduct a difference-in-differences analysis that exploits the Arab Spring as an exogenous oil price volatility increase and document a stronger relationship between oil price volatility and environmental performance in the aftermath of the Arab Spring. We second identify (i) capital expenditures and (ii) alternative energy importation as two mechanisms through which oil price volatility influences environmental performance. We finally show that national culture plays a significant role in moderating the relationship between oil price volatility and environmental performance. Taken together, our empirical findings highlight the role of economic uncertainty in affecting firms’ environmental performance and provide significant contributions to management and policymakers.

Predicting oil prices: A comparative analysis of machine learning and image recognition algorithms for trend prediction

This paper investigates the effectiveness of machine learning algorithms, including logistic regression, artificial neural networks, support vector machines, gradient boosting algorithms (XGBoost, ExtraTrees), random forests, and convolutional neural network (CNN) for trend prediction of daily spot oil prices across horizons of 1 to 8 days. We utilize a comprehensive set of features, including technical indicators, financial data, and volatility measures, to predict trends in closing prices. Our results reveal that the CNN model significantly outperforms other algorithms. This superior performance likely stems from CNN’s ability to capture visual patterns in price movements, potentially mimicking how traders identify trends.

A rational finance explanation of the stock predictability puzzle

AbstractWe address the stock predictability puzzle, a challenge in the stock market often discussed in behavioral finance. Our approach formulates a statistical model within rational finance, avoiding reliance on behavioral finance assumptions, and integrates stock return predictability into the Black–Scholes option pricing framework. Empirical analysis focuses on the predictability of stock prices by option and spot traders, introducing a forward‐looking measure we term “implied excess predictability.” Results show that option traders' predictability of stock returns positively correlates with moneyness, whereas for spot traders, this relationship is inverse. These findings suggest a potential asymmetry in stock price predictability between spot and option traders. Additionally, we demonstrate the importance of incorporating stock return predictability into option pricing formulas, particularly for options with strike prices significantly different from the stock price. Conversely, when moneyness is close to unity, predictability is not integrated into option pricing, indicating equal information among spot and option traders. Comparison of volatility measures reveals the difference between implied and realized variances or variance risk premia as potential predictors of stock returns.

Return volatility and trading volume of GameFi

Focusing on GameFi, we test theories regarding the relationship between return volatility and trading volume. These theories include the Mixture of Distribution Hypothesis (MDH) and the Sequential Information Arrival Hypothesis (SIAH). Empirical results indicate rejection of MDH and support for SIAH. These results are robust to alternative measurements of trading volume and return volatility. Subperiod analysis further reveals that SIAH is more pronounced during periods of high investor attention and low economic uncertainty. The results will be of interest to scholars interested in the robustness of established financial theories for revolutionary financial products.