Conditional Volatility Models Research Articles

The Issues and Implications About the Volatility of the Stock and the Bond Prices and Their Returns and the Volatility of Interest Rates and Inflation - Which Are Being Researched in Finance and Macro-Monetary Economics Literature: A Survey

Volatility of returns of the financial assets, and the volatility of the inflation and aggregate demand, are important issues in the Financial markets, and the macro- monetary economics. In this article, the volatility in the stock and bond markets are surveyed and discussed in detail. Our view is that the higher volatility in the long-term rates than in the short-term rates, may be due to the higher leverage effect in the long-term markets and rates than in the short -term rates. In the previous century, last fifty years, the average stock returns were much higher and the expected return or the cost of capital was lower. The conditional volatility models and the volatility spill over between the spot and futures markets and their implications are deeply explored in this article along with the price discovery between spot and futures markets and the conditions for the efficiency in these markets. In our section dealing with Macro- monetary economics, the effect of the variability of inflation on the demand for money function, on the nominal rates of interest, and on the slope of the aggregate supply curve, are brought into sharp focus and is being discussed through the relevant literature survey.

Corporate Governance and Indian Stock Market: A Study with Asymmetric Conditional Volatility Models

An efficient capital market needs improved quality as well as the quantity of information available to investors, which is possible by raising the principles of good corporate governance. Numerous studies showed its importance in the development of the stock market. To strengthen the trust of investors in companies Securities Exchange Board of India (SEBI) revised Clause 49 of the Listing Agreement of the Indian Stock Market which gets operationalized in October 2014. This study investigates the impact of revised Clause 49 on Indian stock market volatility using asymmetric conditional volatility models. For analysis, author considered return pattern of five indexes; S P Pre-CG regulation period from January 1st, 2006 to September 30th, 2014 and Post-CG regulation period from October 1st, 2014 to March 31st, 2017. Results show that the revised Clause 49, 2013 helps to build the trust of investors for Small-Cap companies in Indian Stock Market.

Estimation of Conditional Volatility Models for Indian Stock Market

Estimation of Conditional Volatility Models for Indian Stock Market

Bootstrap Inference on the Boundary of the Parameter Space with Application to Conditional Volatility Models

It is a well-established fact that testing a null hypothesis on the boundary of the parameter space, with an unknown number of nuisance parameters at the boundary, is infeasible in practice in the sense that limiting distributions of standard test statistics are non-pivotal. In particular, likelihood ratio statistics have limiting distributions which can be characterized in terms of quadratic forms minimized over cones, where the shape of the cones depends on the unknown location of the (possibly mulitiple) model parameters not restricted by the null hypothesis. We propose to solve this inference problem by a novel bootstrap, which we show to be valid under general conditions, irrespective of the presence of (unknown) nuisance parameters on the boundary. That is, the new bootstrap replicates the unknown limiting distribution of the likelihood ratio statistic under the null hypothesis and is bounded (in probability) under the alternative. The new bootstrap approach, which is very simple to implement, is based on shrinkage of the parameter estimates used to generate the bootstrap sample toward the boundary of the parameter space at an appropriate rate. As an application of our general theory, we treat the problem of inference in finite-order ARCH models with coefficients subject to inequality constraints. Extensive Monte Carlo simulations illustrate that the proposed bootstrap has attractive finite sample properties both under the null and under the alternative hypothesis.

Estimation of Conditional Volatility Models for Indian Stock Market

The leverage effect or asymmetric effect is defined as the unequal influence of negative shock on volatility in comparison with positive shock. The negative shocks or the bad news seems to have larger influence on next period volatility. The objective of this study is to test the presence of volatility clustering and long-term memory features in Indian capital market and to compare the symmetric and asymmetric conditional models. The presence of asymmetric effect was tested with the help of conditional volatility models like TGARCH, EGARCH and PGARCH. These volatility models were applied to NSE broad indices and sectoral indices. The data for a period of 18 years was collected from PROWESS database. The results suggest that there is volatility clustering and long-term memory features in Indian capital market. Asymmetric volatility models performed better on all the indices tested. In selecting the best volatility models, AIC information criterion and log likelihood parameters were used. AIC selects PGARCH and TGARCH models as best performing model and log likelihood selects PGARCH model as the best model. Hence, it was concluded that PGARCH model performs better than other asymmetrical models for Indian capital market.

Asymmetric Risk Impacts of Chinese Tourists to Taiwan

Since 2008, when Taiwan’s President Ma Ying-Jeou relaxed the Cross-Strait policy, China has become Taiwan’s largest source of international tourism. In order to understand the risk persistence of Chinese tourists, the paper investigates the short-run and long-run persistence of shocks to the change rate of Chinese tourists to Taiwan. The daily data used for the empirical analysis is from 1 January 2013 to 28 February 2018. McAleer’s (2015) fundamental equation in tourism finance is used to link the change rate of tourist arrivals and the change in tourist revenues. Three widely-used univariate conditional volatility models, namely GARCH(1,1), GJR(1,1) and EGARCH(1,1), are used to measure the short-run and long-run persistence of shocks, as well as symmetric, asymmetric and leverage effects. Three different Heterogeneous AutoRegressive (HAR) models, HAR(1), HAR(1,7) HAR(1,7,28), are considered as alternative mean equations for capturing a variety of long memory effects. The mean equations associated with GARCH(1,1), GJR(1,1) and EGARCH(1,1) are used to analyse the risk persistence of the change in Chinese tourists. The exponential smoothing process is used to adjust the seasonality around the trend in Chinese tourists. The empirical results show asymmetric impacts of positive and negative shocks on the volatility of the change in the number of Group-type and Medical-type tourists, while Individual-type tourists display a symmetric volatility pattern. Somewhat unusually, leverage effects are observed in EGARCH for Medical-type tourists, which shows a negative correlation between shocks in tourist numbers and the subsequent shocks to volatility. For both Group-type and Medical-type tourists, the asymmetric impacts on volatility show that negative shocks have larger effects than do positive shocks. The leverage effect in EGARCH for Medical-type tourists implies that larger shocks would decrease volatility in the change in the numbers of Medical-type tourists. These results suggest that Taiwan tourism authorities should act to prevent the negative shocks for the Group-type and Medical-type Chinese tourists to dampen the shocks that arise from having fewer Chinese tourists to Taiwan.

An Econometric Analysis of ETF and ETF Futures in Financial and Energy Markets Using Generated Regressors

It is well known that there is an intrinsic link between the financial and energy sectors, which can be analysed through their spillover effects, which are measures of how the shocks to returns in different assets affect each other’s subsequent volatility in both spot and futures markets. Financial derivatives, which are not only highly representative of the underlying indices, but can also be traded on both the spot and futures markets, include Exchange Traded Funds (ETFs), a tradable spot index whose aim is to replicate the return of an underlying benchmark index. When ETF futures are not available to examine spillover effects, “generated regressors” are useful for constructing both financial ETF futures and energy ETF futures. The purpose of the paper is to investigate the co-volatility spillovers within and across the U.S. energy and financial sectors in both spot and futures markets, by using “generated regressors” and a multivariate conditional volatility model, namely diagonal BEKK. The daily data used are from 23 December 1998–22 April 2016. The dataset is analysed in its entirety and is also subdivided into three distinct subsets. The empirical results show there is a significant relationship between the financial ETF and energy ETF in the spot and futures markets. Therefore, financial and energy ETFs are suitable for constructing a financial portfolio from an optimal risk management perspective and also for dynamic hedging purposes.

Value-at-risk modeling and forecasting with range-based volatility models: empirical evidence

ABSTRACT This article considers range-based volatility modeling for identifying and forecasting conditional volatility models based on returns. It suggests the inclusion of range measuring, defined as the difference between the maximum and minimum price of an asset within a time interval, as an exogenous variable in generalized autoregressive conditional heteroscedasticity (GARCH) models. The motivation is evaluating whether range provides additional information to the volatility process (intraday variability) and improves forecasting, when compared to GARCH-type approaches and the conditional autoregressive range (CARR) model. The empirical analysis uses data from the main stock market indexes for the U.S. and Brazilian economies, i.e. S&P 500 and IBOVESPA, respectively, within the period from January 2004 to December 2014. Performance is compared in terms of accuracy, by means of value-at-risk (VaR) modeling and forecasting. The out-of-sample results indicate that range-based volatility models provide more accurate VaR forecasts than GARCH models.

The correct regularity condition and interpretation of asymmetry in EGARCH

In the class of univariate conditional volatility models, the three most popular are the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten et al. (1992), and the exponential GARCH (or EGARCH) model of Nelson (1990, 1991). For purposes of deriving the mathematical regularity properties, including invertibility that relates the standardized residuals to the returns shocks, to determine the likelihood function for estimation, and the statistical conditions to establish asymptotic properties, it is essential to understand the stochastic properties underlying the three univariate models. The random coefficient autoregressive process was used to obtain GARCH by Tsay (1987), an extension of which was used by McAleer (2014) to obtain GJR. A random coefficient complex nonlinear moving average process was used by McAleer and Hafner (2014) to obtain EGARCH. These models can be used to capture asymmetry, which denotes the different impacts on conditional volatility of positive and negative shocks of equal magnitude, and possibly also leverage, which is the negative correlation between returns shocks and subsequent shocks to volatility (see Black 1976). McAleer (2014) showed that asymmetry was possible for GJR, but not leverage. McAleer and Hafner (2014) showed that leverage was not possible for EGARCH. Surprisingly, the condition for asymmetry in EGARCH seem to have been ignored in the literature, or has concentrated on the incorrect parametric condition, with no clear explanation, and hence with associated unclear and misleading interpretations. The purpose of the paper is to derive the regularity condition for asymmetry in EGARCH, and to provide the correct interpretation. It is shown that, in practice, EGARCH always displays asymmetry, though not leverage.

Asymptotic Theory for Extended Asymmetric Multivariate GARCH Processes

The paper considers various extended asymmetric multivariate conditional volatility models, and derives appropriate regularity conditions and associated asymptotic theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical estimation. For this purpose, we use an underlying vector random coefficient autoregressive process, for which we show the equivalent representation for the asymmetric multivariate conditional volatility model, to derive asymptotic theory for the quasi-maximum likelihood estimator. As an extension, we develop a new multivariate asymmetric long memory volatility model, and discuss the associated asymptotic properties.

Realized stochastic volatility with general asymmetry and long memory

The paper develops a novel realized stochastic volatility model of asset returns and realized volatility that incorporates general asymmetry and long memory (hereafter the RSV-GALM model). The contribution of the paper ties in with Robert Basmann’s seminal work in terms of the estimation of highly non-linear model specifications (Basmann, 1988), especially for specifying causal effects from returns to future volatility. This paper discusses asymptotic results of a Whittle likelihood estimator for the RSV-GALM model and a test for general asymmetry, and analyzes the finite sample properties. The paper also develops an approach to obtain volatility estimates and out-of-sample forecasts. Using high frequency data for three US financial assets, the new model is estimated and evaluated. The paper compares the forecasting performance of the new model with a realized conditional volatility model.

Realized Stochastic Volatility with General Asymmetry and Long Memory

The paper develops a novel realized stochastic volatility model of asset returns and realized volatility that incorporates general asymmetry and long memory (hereafter the RSV-GALM model). The contribution of the paper ties in with Robert Basmann’s seminal work in terms of the estimation of highly non-linear model specifications (“Causality tests and observationally equivalent representations of econometric models”, Journal of Econometrics, 1988), especially for specifying causal effects from returns to future volatility. This paper discusses asymptotic results of a Whittle likelihood estimator for the RSV-GALM model and a test for general asymmetry, and analyses the finite sample properties. The paper also develops an approach to obtain volatility estimates and out-of-sample forecasts. Using high frequency data for three US financial assets, the new model is estimated and evaluated. The paper compares the forecasting performance of the new model with a realized conditional volatility model.

The Information Environment, Informed Trading, and Volatility

ABSTRACTThe relation between informed trading and volatility is analyzed using the change in the proportion of informed transactions calculated through the probability of informed trading variable. The analysis relates to the Spanish market during 1997–2010, given that the Spanish market covers a very diverse range of listed companies. Some companies are comparable to companies listed on U.S. markets while others are smaller in size and have a lower trading volume and inferior quality of information. The methodology is based on a modification of the model proposed by Avramov, Chordia, and Goyal [2006]. The authors’ proposal incorporates the change in the proportion of informed transactions, calculated with intraday data, into the volatility model. The results are also presented using a conditional volatility model in which the change in the proportion of informed transactions is incorporated. These results attest to the influence of informed trading as a price-stabilizing factor in heavily traded and highly capitalized stocks (familiar stocks). Informed trading leads to a marked decrease in volatility for these particular stocks both in periods of calm and crisis.

An alternative method for forecasting price volatility by combining models

ABSTRACTIn this article, we study the volatility in the monthly price series of edible oils in domestic and international markets using the two popular family of nonlinear time-series models, viz, Generalized autoregressive conditional heteroscedastic (GARCH) models and Stochastic volatility (SV) models. To improve the forecasts of the volatility process, we also propose a new method of combining the volatility of these two competing models using the powerful technique of Kalman filter. The individual models as well as the combined models are assessed on their ability to predict the correct directional change (CDC) in future values as well as other goodness-of-fit statistics. Further, forecasting performance are also evaluated by computing various measures to validate the proposed methodology.

Dynamic factor long memory volatility

In this paper, we develop a long memory orthogonal factor (LMOF) multivariate volatility model for forecasting the covariance matrix of financial asset returns. We evaluate the LMOF model using the volatility timing framework of Fleming et al. [J. Finance, 2001, 56, 329–352] and compare its performance with that of both a static investment strategy based on the unconditional covariance matrix and a range of dynamic investment strategies based on existing short memory and long memory multivariate conditional volatility models. We show that investors should be willing to pay to switch from the static strategy to a dynamic volatility timing strategy and that, among the dynamic strategies, the LMOF model consistently produces forecasts of the covariance matrix that are economically more useful than those produced by the other multivariate conditional volatility models, both short memory and long memory. Moreover, we show that combining long memory volatility with the factor structure yields better results than employing either long memory volatility or the factor structure alone. The factor structure also significantly reduces transaction costs, thus increasing the feasibility of dynamic volatility timing strategies in practice. Our results are robust to estimation error in expected returns, the choice of risk aversion coefficient, the estimation window length and sub-period analysis.

Stationarity and Invertibility of a Dynamic Correlation Matrix

One of the most widely-used multivariate conditional volatility models is the dynamic conditional correlation (or DCC) specification. However, the underlying stochastic process to derive DCC has not yet been established, which has made problematic the derivation of asymptotic properties of the Quasi-Maximum Likelihood Estimators (QMLE). To date, the statistical properties of the QMLE of the DCC parameters have purportedly been derived under highly restrictive and unverifiable regularity conditions. The paper shows that the DCC model can be obtained from a vector random coefficient moving average process, and derives the stationarity and invertibility conditions of the DCC model. The derivation of DCC from a vector random coefficient moving average process raises three important issues, as follows: (i) demonstrates that DCC is, in fact, a dynamic conditional covariance model of the returns shocks rather than a dynamic conditional correlation model; (ii) provides the motivation, which is presently missing, for standardization of the conditional covariance model to obtain the conditional correlation model; and (iii) shows that the appropriate ARCH or GARCH model for DCC is based on the standardized shocks rather than the returns shocks. The derivation of the regularity conditions, especially stationarity and invertibility, should subsequently lead to a solid statistical foundation for the estimates of the DCC parameters. Several new results are also derived for univariate models, including a novel conditional volatility model expressed in terms of standardized shocks rather than returns shocks, as well as the associated stationarity and invertibility conditions.

Multivariate Stochastic Volatility-Double Jump Model: An Application for Oil Assets

We propose a new multivariate model to capture the presence of jumps in mean and conditional variance in the returns of oil prices and companies in this sector. The model is based on the presence of common factors associated with jumps in mean and variance, as it performs a decomposition of the conditional variance of each asset as the sum of the common factor plus a specific transitory factor in a multivariate stochastic volatility structure. The estimation is made through Bayesian methods using Markov Chain Monte Carlo. The model allows recovering the changes in prices and volatility patterns observed in this sector, relating the jumps with the events observed in the period 2000-2015. We apply the model to estimate risk management measures, hedging and portfolio allocation and performing a comparison with other multivariate models of conditional volatility. Based on the results, we may conclude that the proposed model has a better performance when used to calculate portfolio VaR, since it does not reject the hypothesis of correct nominal coverage with certain specifications presented in this work. Furthermore, we conclude that the model can be used to hedge oil price risks, through the optimal hedge ratio for a portfolio containing an oil company as-set (stock) and the oil price contract. When compared to the standard methodology based on GARCH models, our model performs well in this application.

The Correct Regularity Condition and Interpretation of Asymmetry in EGARCH

In the class of univariate conditional volatility models, the three most popular are the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten, Jagannathan and Runkle (1992), and the exponential GARCH (or EGARCH) model of Nelson (1990, 1991). For purposes of deriving the mathematical regularity properties, including invertibility, to determine the likelihood function for estimation, and the statistical conditions to establish asymptotic properties, it is convenient to understand the stochastic properties underlying the three univariate models. The random coefficient autoregressive process was used to obtain GARCH by Tsay (1987), an extension of which was used by McAleer (2004) to obtain GJR. A random coefficient complex nonlinear moving average process was used by McAleer and Hafner (2014) to obtain EGARCH. These models can be used to capture asymmetry, which denotes the different effects on conditional volatility of positive and negative effects of equal magnitude, and possibly also leverage, which is the negative correlation between returns shocks and subsequent shocks to volatility (see Black 1979). McAleer (2014) showed that asymmetry was possible for GJR, but not leverage. McAleer and Hafner showed that leverage was not possible for EGARCH. Surprisingly, the conditions for asymmetry in EGARCH seem to have been ignored in the literature, or have concentrated on the incorrect conditions, with no clear explanation, and hence with associated misleading interpretations. The purpose of the paper is to derive the regularity condition for asymmetry in EGARCH to provide the correct interpretation. It is shown that, in practice, EGARCH always displays asymmetry, though not leverage.

An Empirical Investigation on Iron-Ore Price volatility with special reference to Dindigul Lock makers

Iron-ore is the staple raw material required for manufacturing locks. Iron ore price contributes to the cost of raw material for Dindigul lock makers. High volatility has been widely observed in the prices of Indian iron ore market. Irrefutably, the Lock maker's optimism has been battered by volatility and thus critically has an effect on their economic growth. This study develops and examines the conditional volatility model in an attempt to confine the prominent features of volatility in iron ore prices prevailing in Indian market confining to the benefit of Dindigul Lock makers. Results of the study exhibit that the high volatility of iron ore price is expected when the negative shocks are present. The Centre and State government are accountable in steering rural development through adequate disbursement of credit in the form of incentives to the lock makers to buy raw materials at an affordable cost.

Modelling, forecasting and trading with a new sliding window approach: the crack spread example

The scope of this analysis is the modeling and the tracking of the crack spread with a sophisticated new non-linear approach. The selected trading period covers 2087 trading days starting on 09/05/2005 and ending on 21/12/2015. The proposed model is a combined particle swarm optimiser (PSO) and a radial basis function (RBF) neural network which is trained using sliding windows of 300 and 400 days. This is benchmarked against a multilayer perceptron (MLP) neural network and higher order neural network using the same data-set. Outputs from the neural networks provide forecasts for 5 days ahead trading simulations. To model the spread an expansive universe of 250 inputs across different asset classes is also used. Included in the input data-set are 20 Autoregressive Moving Average models and 10 Generalized Autoregressive Conditional Heteroscedasticity volatility models. Results reveal that the sliding window approach to modelling the crack spread is effective when using 300 and 400 days training periods. Sliding windows of less than 300 days were found to produce unsatisfactory trading performance and reduced statistical accuracy. The PSO RBF model which was trained over 300 is superior in both trading performance and statistical accuracy when compared to its peers. As each of the unfiltered models’ volatility and maximum drawdown were unattractive, a threshold confirmation filter is employed. The threshold confirmation filter only trades when the forecasted returns are greater than an optimized threshold of forecasted returns. As a consequence, only forecasted returns of stronger conviction produce trading signals. This filter attempts to reduce maximum drawdowns and volatility by trading less frequently and only during times of greater predicted change. Ultimately, the confirmation filter improves risk return profiles for each model and transaction costs were also significantly reduced.