Volatility Equation Research Articles

Can asymmetry, long memory, and current return information improve crude oil volatility prediction? ——Evidence from ASHARV-MIDAS model

We propose an ASHARV-MIDAS model that incorporates the asymmetric and long-memory characteristics of financial asset returns, while integrating current return information into the volatility equation to enhance prediction accuracy. Additionally, we derive the lag order expression and conditional variance of short-term volatility in the novel model to analyze its distinction from the classical GARCH-MIDAS model that does not consider current return information. Empirical and robustness tests demonstrate superior in-sample parameter estimation performance and more precise out-of-sample volatility prediction capabilities of our proposed model.

Estimation of Realized Asymmetric Stochastic Volatility Models Using Kalman Filter

Despite the growing interest in realized stochastic volatility models, their estimation techniques, such as simulated maximum likelihood (SML), are computationally intensive. Based on the realized volatility equation, this study demonstrates that, in a finite sample, the quasi-maximum likelihood estimator based on the Kalman filter is competitive with the two-step SML estimator, which is less efficient than the SML estimator. Regarding empirical results for the S&P 500 index, the quasi-likelihood ratio tests favored the two-factor realized asymmetric stochastic volatility model with the standardized t distribution among alternative specifications, and an analysis on out-of-sample forecasts prefers the realized stochastic volatility models, rejecting the model without the realized volatility measure. Furthermore, the forecasts of alternative RSV models are statistically equivalent for the data covering the global financial crisis.

The Impacts of Terrorist Events on Stock Market Volatility

Acts of terrorism have increased markedly in recent decades. Social analyses have found terror-related events to be associated with nationwide increases in fear, panic, and uncertainty amongst individuals and businesses who play a major role in the stock market. The current paper intends to contribute to the established literature by quantitatively examining the impacts of terrorist attacks on financial market volatility by conducting an in-depth case study of the Sri Lankan stock market during and after the civil war (1986–2017). Sri Lanka serves as an excellent natural experiment for the current study due to the sustained length and severity of the terrorist attacks between 1983 and 2009. Five forms of terror variables: (i) cumulative number of deaths; (ii) cumulative number of victims injured; (iii) number of fatalities; (iv)number of injured, and (v) a terror dummy variable were utilized in modeling the stock market volatility. This paper uses autoregressive conditionally heteroscedastic (ARCH), and generalized autoregressive conditionally heteroscedastic (GARCH) methods to model the stock market volatility. The method is consistent with the assumption that the innovations from stock returns models contain a fixed unconditional variance, but the conditional variance varies. The findings of this paper suggest that terror attacks, in general, have exerted a significant effect on stock market volatility in Sri Lanka during the conflict period. Surprisingly, extrinsic factors of terror-related events such as the number of people injured or killed due to terrorist attacks were not found to be statistically significant jointly or separately in the conditional volatility equation, thus making it difficult to form a clear interaction among the variables. Investors seem to concern themselves more about the risk of instability which manifests as a result of terror-related events rather than the human cost of such events. The findings of this paper may be useful in improving the accuracy of future volatility prediction models. They could also be relevant in evaluating military sector projects that aim to boost investor confidence.

On improving GARCH volatility forecasts for Bitcoin via a meta-learning approach

Modelling the volatility of Bitcoin, the cryptocurrency with the largest market share, has recently attracted considerable attention from researchers, practitioners and investors in financial markets and portfolio management. For this purpose, a wide variety of GARCH-type models have been employed. However, there is no consensus in the literature on which specification arising from the volatility equation and the assumed error distribution is better in an out-of-sample performance. This study tries to fill this gap by comparing the forecasting performances of 110 GARCH-type models for Bitcoin volatility. Furthermore, it proposes a new combining method based on support vector machines (SVM). This method effectively selects the set of superior models to perform meta-learning. The results indicate that the best performing GARCH specification depends on the loss function chosen, and the proposed method leads to more accurate volatility forecasts than those of the best GARCH-type models and other combining methods investigated.

Asymmetry and Leverage with News Impact Curve Perspective in Australian Stock Returns’ Volatility during COVID-19

This paper studies the effect of COVID-19 on the volatility of Australian stock returns and the effect of negative and positive news (shocks) by investigating the asymmetric nature of the shocks and leverage impact on volatility. We employ a generalised autoregressive conditional heteroskedasticity (GARCH) model and extend the analysis using the exponential GARCH (EGARCH) model to capture asymmetry and allegedly leverage. We proxy the news related to the negative effect of COVID-19 on the Australian health system and its economy as bad news, and on the other hand, measures taken by government economic stimulus packages through their monetary and fiscal policies as good news. The S&P ASX200 (ASX-200) index is used as a proxy to the Australian stock market, and we use value-weighted returns of the stocks listed on ASX-200 for the period 27 January 2020 to 29 December 2020. The empirical results suggest the EGARCH model fits better in capturing asymmetry and leverage than the GARCH model in estimating the volatility of the Australian stock returns. However, another interesting finding is that the EGARCH model with volatility equation without news demonstrates a larger (smaller) leverage effect of the negative (positive) shocks on the conditional volatility compared to its variant with the news.

Emerging stock market volatility and economic fundamentals: the importance of US uncertainty spillovers, financial and health crises

This paper studies the US and global economic fundamentals that exacerbate emerging stock markets volatility and can be considered as systemic risk factors increasing financial stability vulnerabilities. We apply the bivariate HEAVY system of daily and intra-daily volatility equations enriched with powers, leverage, and macro-effects that improve its forecasting accuracy significantly. Our macro-augmented asymmetric power HEAVY model estimates the inflammatory effect of US uncertainty and infectious disease news impact on equities alongside global credit and commodity factors on emerging stock index realized volatility. Our study further demonstrates the power of the economic uncertainty channel, showing that higher US policy uncertainty levels increase the leverage effects and the impact from the common macro-financial proxies on emerging markets’ financial volatility. Lastly, we provide evidence on the crucial role of both financial and health crisis events (the 2008 global financial turmoil and the recent Covid-19 pandemic) in raising markets’ turbulence and amplifying the volatility macro-drivers impact, as well.

An Exceedance Probability of Financial Return and Its Application to the Risk Analysis

This paper studies a new specification of the autoregressive binary choice model for estimating the exceedance probability of return and its application to the risk management tasks, especially for Value-at-Risk calculation. The author proposed a new parametrization of the volatility equation, which implies the presence of an additional random term. Such a model could not be estimated using the methods of classical statistics; therefore the Bayesian NUTS algorithm was chosen as an appropriate toolkit. Estimated exceedance probabilities were applied in calculating VaR. As a data set, it was taken the daily return of PAO «Sberbank» shares and the one-minute return of the USD-RUB currency pair. The results of VaR estimation were tested for asymptotic convergence to the true value by Engle and Manganelli’s dynamic quantile test.

A Stochastic Volatility Model With a General Leverage Specification

We introduce a new stochastic volatility model that postulates a general correlation structure between the shocks of the measurement and log volatility equations at different temporal lags. The resulting specification is able to better characterize the leverage effect and propagation in financial time series. Furthermore, it nests other asymmetric volatility models and can be used for testing and diagnostics. We derive the simulated maximum likelihood and quasi maximum likelihood estimators and investigate their finite sample performance in a simulation study. An empirical illustration shows that the postulated correlation structure improves the fit of the leverage propagation and leads to more precise volatility predictions.

Exponential GARCH Model with Exogenous Covariate for South Sudanese Pounds—USD Exchange Rate Volatility: On the Effects of Conflict on Volatility

The empirical models that explain the variation in exchange rate on the ground of macroeconomic fundamentals only are usually bias on the account of omitted variable hence, they cannot decently explain variations in exchange rate. However, if socio-political determinants, like civil wars, violence are incorporated in simple time series specification, the variations of exchange rate can be understood better. Apparently in developing countries like South Sudan where socio-political problems like conflict are most prevalent, the subject remains largely under-explored. This paper therefore, applies ARMA (p, q)-EGARCH (p, q) model with exogenous covariate for SSP-USD exchange rate volatility to examine the effect of conflict as an exogenous variable on exchange rate volatility. The proposed model is ARMA (1, 2)-EGARCH (1, 1) class of models with exogenous covariate in both mean and volatility equations. An empirical application of the proposed model is demonstrated by incorporating the conflict index as covariate in both mean and volatility equations of the proposed model. Parameter estimation was performed using maximum likelihood estimation method. The estimation results with classical maximum likelihood estimation method suggested that exchange rate volatility was persistent as evidenced by higher values of the coefficient of the parameter that accounts for persistence (β) in conditional volatility. Furthermore, the parameter for leverage effect in our models was found to be significant. The results showed that the effects of conflict on volatility of SSP-USD was found positive and statistically significant in both equations indicating that higher prevalence of conflict makes the exchange rate to be more volatile.

A three‐dimensional asymmetric power HEAVY model

AbstractThis article proposes the three‐dimensional HEAVY system of daily, intra‐daily, and range‐based volatility equations. We augment the bivariate model with a third volatility metric, the Garman–Klass estimator, and enrich the trivariate system with power transformations and asymmetries. Most importantly, we derive the theoretical properties of the multivariate asymmetric power model and explore its finite‐sample performance through a simulation experiment on the size and power properties of the diagnostic tests employed. Our empirical application shows that all three power transformed conditional variances are found to be significantly affected by the powers of squared returns, realized measure, and range‐based volatility as well. We demonstrate that the augmentation of the HEAVY framework with the range‐based volatility estimator, leverage and power effects improves remarkably its forecasting accuracy. Finally, our results reveal interesting insights for investments, market risk measurement, and policymaking.

Genelleştirilmiş Otoregresif Koşullu Değişen Varyans Modelleri İle Bitcoin Volatilitesinin Analizi (Analysis of Bitcoin Volatility with Generalized Autoregressive Conditional Heteroskedastic Models)

Purpose – In the last decade, digital innovations in the field of finance emerge mainly due to Blockchain technology. The most widely used product of Blockchain technology in the world is cryptocurrencies. Bitcoin draws attention to both market capitalization and transaction volume. The analysis of the volatility of Bitcoin has great significance both theoretically and practically. Therefore, the research aims to determine the most suitable volatility model in Bitcoin investment analysis and present a model suggestion that can be used for predicting the future. Design/methodology/approach – In this study, daily logarithmic return series between 29.04.2013-17.04.2019 are used to analyze Bitcoin volatility. While calculating the return series, daily closing prices of Bitcoin are based on. As a research method, generalized autoregressive conditional heteroskedastic (GARCH) models are tested. In this study, ARCH, GARCH, GJR / TARCH, EGARCH, APARCH, and CGARCH type models are compared for volatility modeling of Bitcoin logarithmic return series. Findings – The study found that the best method for the analysis of Bitcoin volatility is the EGARCH model. Another important finding of the study is that negative shocks are more effective on Bitcoin returns than positive shocks. Discussion – The study contributes to the literature in terms of analyzing the dynamics of Bitcoin volatility, which is a new and digital product, with various models and current data set. Bitcoin investors and researchers can predict returns by using the volatility equation in result of this research. Another output of the study is that negative news effects Bitcoin returns more than positive news. Using this information, traders will be able to take positions on Bitcoin prices.

On the macro-drivers of realized volatility: the destabilizing impact of UK policy uncertainty across Europe

ABSTRACTThis paper studies the bivariate HEAVY system of daily and intra-daily volatility equations and its macro-augmented asymmetric power extension. We focus on economic drivers that exacerbate stock market volatility and can be proved to be major threats for financial stability. Our study proves the inflammatory effects of UK Policy Uncertainty alongside global credit and commodity factors that spread across European financial markets. This UK-led spillover phenomenon should be considered by world market participants and recognized, monitored and mitigated by policymakers amid the Brexit fears and the associated highly probable harm for Europe. Other findings are as follows. First, once we allow for power transformations, asymmetries, and macro-effects in the benchmark specification, it is found that both powered conditional variances are significantly affected by the powers of squared negative returns and realized measure, further improving the HEAVY framework's forecasting accuracy. Second, the structural breaks applied to the bivariate system capture the time-varying behavior of the parameters, in particular during the global financial crisis of 2007/08. Third, higher UK uncertainty levels increase the leverage and global macro-effects from credit and commodity markets on all European stock markets' realized volatilities.

Dynamics of a mean-reverting stochastic volatility equation with regime switching

In this paper, we consider a mean-reverting stochastic volatility equation with regime switching, and present some sufficient conditions for the existence of global positive solution, asymptotic boundedness in pth moment, positive recurrence and existence of stationary distribution of this equation. Some results obtained in this paper extend the ones in literature. Example is given to verify the results by simulation.

A Testing Procedure for Constant Parameters in Stochastic Volatility Models

This paper proposes a two-step method for an omnibus misspecification test for constant parameters in the volatility equation of stochastic volatility models. The proposed test has a well-known null asymptotic distribution free of nuisance parameters. It is easy to implement and has low computational cost. Monte Carlo simulations support the relevance of the proposed method, evaluate the performance of the procedure, and highlight its small computational load. An empirical application shows the relevance of the procedure.

A FORWARD EQUATION FOR COMPUTING DERIVATIVES EXPOSURE

We derive a forward equation for computing the expected exposure of financial derivatives. Under general assumptions about the underlying diffusion process, we give an explicit decomposition of the exposure into an intrinsic value which can be directly deduced from the term structure of the forward mark-to-market, and a time value which expresses the variability of the future mark-to-market. Our approach is inspired by Dupire’s equation for local volatility and leads to an ordinary differential equation qualifying the evolution of the expected exposure with respect to the observation dates. We show how this approach can be linked with local times theory in dimension one and to the co-area formula in a higher dimension. As for numerical considerations, we show how this approach leads to an efficient numerical method in the case of one or two risk factors. The accuracy and time-efficiency of this forward representation in small dimension are of special interest in benchmarking XVA valuation adjustments at trade level.

Bayesian semiparametric Markov switching stochastic volatility model

AbstractThis paper proposes a novel Bayesian semiparametric stochastic volatility model with Markov switching regimes for modeling the dynamics of the financial returns. The distribution of the error term of the returns is modeled as an infinite mixture of Normals; meanwhile, the intercept of the volatility equation is allowed to switch between two regimes. The proposed model is estimated using a novel sequential Monte Carlo method called particle learning that is especially well suited for state‐space models. The model is tested on simulated data and, using real financial times series, compared to a model without the Markov switching regimes. The results show that including a Markov switching specification provides higher predictive power for the entire distribution, as well as in the tails of the distribution. Finally, the estimate of the persistence parameter decreases significantly, a finding consistent with previous empirical studies.

Stock Price Reactions to Wire News from the European Central Bank: Evidence from Changes in the Sentiment Tone and International Market Indexes

This paper examines the link between changes in the sentiment tone with respect to the European Central Bank’s (ECB) announcements and stock returns. The analysis constructs a new index that describes the tone of the sentiment derived from these announcements, spanning the period January 2002 to June 2016. The novelty of this work relies on the development of a unique sentiment index associated with the messages conveyed by the ECB’s activities and the effect of this index on both the mean and the volatility of certain major international stock markets. In this context, the sentiment index is present in both the conditional mean and the volatility equations. The findings indicate a significant impact on both the mean and the volatility of returns, whereas the news sentiment/stock returns association increases in strength during the crisis period. The findings survive a robustness check based on the characteristics of the ECB governor’s personality.

Bayesian Analysis of Extended Auto Regressive Model with Stochastic Volatility

This paper proposes an extension of the autoregressive model with stochastic volatility error. The Bayes analysis of the proposed model using vague priors for the parameters of the conditional mean equation and informative prior for the parameters of conditional volatility equation is done. The Gibbs sampler with intermediate Metropolis steps is used to find out posterior inferences for the parameters of autoregressive model and independent Metropolis–Hastings algorithm is used to simulate the volatility of the mean equation. The two data sets in the form of gross domestic product growth rate of India at constant prices and exchange rate of Indian rupees relative to US dollar are considered for numerical illustration. These data are used after assuring the stationarity by differencing the data once. The retrospective as well as prospective short term predictions of the data are provided based on the two simple components of the general autoregressive process. The findings based on the real data are expected to assist the policy makers and managers to make economic and business strategies more precisely.

Shape-constrained semiparametric additive stochastic volatility models

ABSTRACTNonparametric stochastic volatility models, although providing great flexibility for modelling the volatility equation, often fail to account for useful shape information. For example, a model may not use the knowledge that the autoregressive component of the volatility equation is monotonically increasing as the lagged volatility increases. We propose a class of additive stochastic volatility models that allow for different shape constraints and can incorporate the leverage effect – asymmetric impact of positive and negative return shocks on volatilities. We develop a Bayesian fitting algorithm and demonstrate model performance on simulated and empirical datasets. Unlike general nonparametric models, our model sacrifices little when the true volatility equation is linear. In nonlinear situations we improve the model fit and the ability to estimate volatilities over general, unconstrained, nonparametric models.

Macro-Financial Linkages in the High-Frequency Domain: The Effects of Uncertainty on Realized Volatility

This paper estimates a bivariate HEAVY system including daily and intra-daily volatility equations and its macro-augmented asymmetric power extension. It focuses on economic factors that exacerbate stock market volatility and represent major threats to financial stability. In particular, it extends the HEAVY framework with powers, leverage, and macro effects that improve its forecasting accuracy significantly. Higher uncertainty is found to increase the leverage and macro effects from credit and commodity markets on stock market realized volatility. Specifically, Economic Policy Uncertainty is shown to be one of the main drivers of US and UK financial volatility alongside global credit and commodity factors.