Conditional Variance Equation Research Articles

A Better Asymmetric Model of Changing Volatility in Stock and Exchange Rate Returns: Trend-GARCH

The impact of short run price trending on the conditional volatility is tested empirically. A new family of conditionally heteroscedastic models with a trend-dependent conditional variance equation: The Trend-GARCH model is described. Modern microeconomic theory often suggests the connection between the past behaviour of time series, the subsequent reaction of market individuals, and thereon changes in the future characteristics of the time series. Results reveal important properties of these models, which are consistent with stylized facts found in financial data sets. They can also be employed for model identification, estimation, and testing. The empirical analysis supports the existence of trend effects. The Trend-GARCH model proves to be superior to alternative models such as EGARCH, AGARCH, TGARCH OR GARCH-in-Mean in replicating the leverage effect in the conditional variance, in fitting the news impact curve and in fitting the volatility estimates from high frequency data. In addition, we show that the leverage effect is dependent on the current trend, i.e. it differentiates between bullish and bearish markets. Furthermore, trend effects can account for a significant part of the long memory property of asset price volatilities.

Uncovered Interest Parity (UIP) in the Mean and Variance of the ILS/USD Exchange Rate

This paper examines the simultaneous short-term relationships between the ILS/USD exchange rate and domestic interest rates, the foreign interest rates and the interest-rate differentials along the term structure of interest rates. The test is performed using the ARCH (autoregressive conditional heteroskedasticity) procedure of two variables with a bi-variate threshold ARCH (BV-TARCH) that incorporates a set of equations describing the short term relationship between the exchange rate and interest rates. This procedure enables us to analyze the effect of each of the variables on the other, both the first moment, i.e., the expectation, and the second moment, the conditional variance. It also enables us to identify asymmetry in the effects of shocks and their autoregressive effects. The second section of the paper examines the Uncovered Interest Parity (UIP) hypothesis along the interest-rate differential term structure. The analysis of the results of the procedure used on weekly data for the years 1999-2005 shows that in the mean equation the exchange rate has a positive effect on the long-term domestic interest rates and on the interest-rate differential, but the reverse relationship does not hold. On the other hand, in the conditional variance equation, no cross-relationship was found between the exchange rate and the interest rates or the interest-rate differential. The conditional correlation of the error matrix of these variables and its level of significance rose with the term structure. Examination of the UIP during the sample period shows that changes in the interest-rate differential, particularly for the long term, predicted the changes in the exchange rate better than did the differential itself. These findings can be explained by the significant contraction of the interest-rate differential that occurred during the sample period compared with the small depreciation reflected by the ILS/USD exchange rate in that period.

The asymmetric reactions of mean and volatility of stock returns to domestic and international information based on a four-regime double-threshold GARCH model

In this paper, we investigate the asymmetric reactions of mean and volatility of stock returns in five major markets to their own local news and the US information via linear and nonlinear models. We introduce a four-regime Double-Threshold GARCH (DTGARCH) model, which allows asymmetry in both the conditional mean and variance equations simultaneously by employing two threshold variables, to analyze the stock markets’ reactions to different types of information (good/bad news) generated from the domestic markets and the US stock market. By applying the four-regime DTGARCH model, this study finds that the interaction between the information of domestic and US stock markets leads to the asymmetric reactions of stock returns and their variability. In addition, this research also finds that the positive autocorrelation reported in the previous studies of financial markets may in fact be mis-specified, and actually due to the local market's positive response to the US stock market.

Modeling extinction and reignition in turbulent flames

The conditional moment closure method (CMC) has been extended to improve reactive species predictions in flames with significant local extinction and reignition. Simple first-order closure of the conditionally averaged reaction rate term does not give satisfactory results due to large fluctuations around the conditional mean and an alternative closure is suggested here. The new closure is based on a precomputed parameterized reference field that maps reactive species mass fractions as functions of mixture fraction and sensible enthalpy. During the computations, the reference field is continuously adjusted to ensure consistency with the CMC solution and doubly conditioned chemical source terms that are functions of time, space, mixture fraction, and sensible enthalpy can thus be obtained. Integration over sensible enthalpy space yields the improved singly conditioned chemical source term that can be used for the solution of the CMC equations. Full closure can be achieved by assuming a β-PDF for the probability distribution in sensible enthalpy space and an additional conditional variance equation needs to be solved. The overall agreement between the measured and the computed variance is satisfactory and the extended CMC model is applied to Sandia Flames D, E, and F. Excellent predictions of temperature, major species, intermediates, and NO are obtained in Flames D and E while temperature predictions can be significantly improved in Sandia Flame F.

BIVARIATE ARCH MODELS: FINITE-SAMPLE PROPERTIES OF QML ESTIMATORS AND AN APPLICATION TO AN LM-TYPE TEST

At the present time, there exists an important and growing econometric literature that deals with the application of multivariate-ARCH models to a variety of economic and financial data. However, the properties of the estimation procedures that are used have not yet been fully explored. This paper provides two main new results: the first concerns the large biases and variances that can arise when the ML estimation method is employed in a simple bivariate structure under the assumption of conditional heteroscedasticity; and the second examines how to use these analytical theoretical results to improve the size and the power of a test for multivariate ARCH effects. We analyse two models: one proposed in Wong and Li (1997) (where the disturbances are dependent but uncorrelated) and another proposed by Engle and Kroner (1995) and Liu and Polasek (1999, 2000) (where conditional correlation is allowed through a diagonal representation). We prove theoretically that a relatively large difference between the intercepts in the two conditional variance equations produces, in the first model, very large variances in some of the ML estimators and, in the second, very severe biases in some of the ML estimators of the parameters. Later we use our bias expressions to propose an LM type test of multivariate ARCH effects, showing that the size and the power of the test improve when we allow for bias correction in the estimators, and that the best recommendation in practical applications is always to use the expected hessian version of the LM. We address as well some constraints that should be included in the estimation of the models but which have so far been ignored. Finally, we present a SUR (seemingly unrelated) specification in both models, that provides an alternative way to retrieve the information matrix. We also extend Lumsdaine (1995) results in multivariate framework.

Time-varying hedge ratios for non-ferrous metals prices

This paper examines the effectiveness of time-varying bivariate GARCH and GARCH-X determined hedge ratios for six non-ferrous metals cash-futures portfolios against time-invariant alternatives. The results suggest that the GARCH-X model, which incorporates the (squared) short-run deviation from a long-run cointegrating relationship in the conditional variance and covariance equations, provides the most effective hedge in five of the six cases. Thus, the results presented here strongly support the view that incorporating time-variation into the hedge ratio improves the performance of the hedge in terms of risk reduction.

Non-linear dependence and conditional heteroscedasticity in stock returns evidence from the norwegian thinly traded equity market

The paper investigates the presence of non-linear dependencies in stock returns for the Norwegian equity market as it is very difficult to interpret the unconditional distribution of stock returns and its economic implications if the i.i.d. assumption is violated. Standard tests of non-linear dependence give strong evidence for the presence of non-linearity in raw returns. Modelling non-linear dependence must distinguish between models that are non-linear in mean and hence depart from the Martingale hypothesis, and models that are non-linear in variance and hence depart from independence but not from the Martingale hypothesis. Therefore, three non-linear models of asset returns are formulated applying ARMA-GARCH specifications for the conditional mean and variance equations. The paper goes on to answer which model has the necessary characteristics that are sufficient to account for most of the non-linear dependence. In the Norwegian equity market most of the non-linear dependence seems to be conditional heteroscedasticity. However, the most thinly traded assets still report significant non-linear dependence for all non-linear specifications. These results imply that the independence hypothesis can be rejected for all assets, portfolios and indices. Moreover, for thinly traded assets the Martingale hypothesis can also be rejected. The economic implications from the unconditional distributions of thinly traded assets are therefore very difficult to interpret and are unfamiliar territory for those who are accustomed to thinking analytically, intuitively and linearly.

Second-order conditional moment closure modeling of a turbulent CH 4/H 2/N 2 jet diffusion flame

The second-order CMC model for a detailed chemical mechanism is used to model a turbulent CH 4/H 2/N 2 jet diffusion flame. Second-order corrections are made to the three rate limiting steps of methane–air combustion, while first-order closure is employed for all the other steps. Elementary reaction steps have a wide range of timescales with only a few of them slow enough to interact with turbulent mixing. Those steps with relatively large timescales require higher-order correction to represent the effect of fluctuating scalar dissipation rates. Results show improved prediction of conditional mean temperature and mass fractions of OH and NO. Major species are not much influenced by second-order corrections except near the nozzle exit. A parametric study is performed to evaluate the effects of the variance parameter in log-normal scalar dissipation PDF and the constants for the dissipation term in conditional variance and covariance equations.

Price volatility of south-east fishery's quota species: an empirical analysis

This study investigates the autoregressive conditional heteroscedasticity (ARCH) and generalized-ARCH (GARCH) effects in the price series of Australian South-East Fishery's quota species. It is found that in all cases significant ARCH and/or GARCH effects are present. To search for the origins of these effects a weakly exogenous variable (trading volume) is introduced to the conditional variance equation of the ARCH and GARCH models, provided that such effects are observed in the first stage of investigation. It is found that in 14 cases the estimated coefficients of the trading volume are negative. In all cases, the 'trading volume' variable does not contribute to the removal of the ARCH and/or GARCH effects. Finally, the policy implications of the findings are discussed.

An analytical approximation to the option formula for the GARCH model

This article derives an analytical approximation to the option formula for a spot asset price whose conditional variance equation follows a nonlinear asymmetric GARCH (NGARCH) process. The approximate option formula, which is just a volatility adjustment in comparison to the Black–Scholes (BS) formula, is very simple and provides the volatility term structure of spot asset prices. Also, the formula shows that the most characteristic feature of an NGARCH model appears in the vega of a European option, which depends on both the spread between the long-run variance and the current one and a parameter reproduced from the stationary property of the conditional variance. This methodology can be easily extended to an option formula for the generalized GARCH process.

An Empirical Examination of the Relationship Between Central Bank Intervention and Exchange Rate Volatility: Some Australian Evidence

Arguably, market stability is one of the primary reasons behind government intervention in the foreign exchange market. Whether or not the authorities achieve this goal is an empirical matter and testing of this issue is made difficult by the fact that government intervention and exchange rate volatility may be jointly determined. In this paper, the extent to which volatility drives intervention is considered using PROBIT analysis. The results suggest that while support for the hypothesis exists, volatility on its own does not to provide enough information to allow us to accurately forecast government intervention. A modified GARCH model is then tested which incorporates the impact of government intervention in the mean and conditional variance equation. The evidence presented suggest that the dynamics of market are different on the days where the central bank is active in the market.

Likelihood inference in BL-GARCH models

The paper presents a procedure based on the EM algorithm for the indirect estimation of the parameters of BiLinear GARCH (BL-GARCH) models. BL-GARCH generalize the class of GARCH models by considering interactions of past shocks and volatilities in the conditional variance equation. In this way the response of the conditional variance to past information becomes asymmetric allowing to account for the so called leverage effect, typically characterizing the behaviour of financial time series. The results of an application to a time series of stock market returns are presented.

Public information arrival and volatility of intraday stock returns

This study employs firm-specific announcements as a proxy for information flows and investigates the information–volatility relation using high-frequency data from the Australian Stock Exchange. Our analysis reveals a positive and significant impact of the arrival rate of the selected news variable on the conditional variance of stock returns, even after controlling for the potential effects of trading volume and high opening volatility. Furthermore, the inclusion of the news variable in the conditional variance equation of the generalized autoregressive conditional heteroscedastic model also reduces volatility persistence, especially with intraday data. Combined with the evidence that news arrivals display a very strong pattern of autocorrelation, our results are consistent with the Mixture of Distribution Hypothesis, which attributes conditional heteroscedasticity of stock returns to time-dependence in the news arrival process.

Maturity Effects in Futures Markets: Evidence from Eleven Financial Futures Markets

This essay examines the volatility dynamics of the financial futures returns. Samuelson (1965) demonstrated theoretically that the conditional variance of changes in futures prices should increase as the time-to-maturity decreases. Interestingly, the empirical evidence on the Samuelson hypothesis is mixed. This essay revisits that issue, applying a unified GARCH framework to a unique data set of daily data, spanning 19 years up to 2000, and eleven types of financial contracts (currencies, S&P500, Nikkei 225, Eurodollar, Treasury Bills). The conditional variance equation is augmented by time-to-maturity, open interest and trading volume variables. I detect evidence for a role of the time-to-maturity in currency futures, and mixed evidence in equity index and interest rate futures. Lagged trading volume and open interest are positively related to volatility in most of these financial futures but they do not fully account for the estimated conditional variance.

Over-the-Counter Forward Contracts and Spot Price Volatility

The purpose of the paper is to investigate the impact of the introduction of Forward Freight Agreement (FFA) trading on spot market price volatility in panamax 1, 1A, 2, and 2A trading routes of the dry-bulk shipping industry. The main concern about the impact of derivatives trading emanates from the results of studies that have found that the activities of speculators may destabilise (or stabilise) prices in the spot market. The proposed methodology is considering the link between volatility and information, and of possible asymmetric effects in the conditional volatilities. A GJR-GARCH (Glosten, et al., 1993) process is found to be the most appropriate specification. The results suggest that the onset of FFA trading has had (a) a stabilising impact on the spot price volatility in all investigated routes, (b) an impact on the asymmetry of volatility in routes 2 and 2A, and (c) substantially improved the quality and speed of information flow in routes 1, 1A and 2. However, after including in the conditional variance equation other explanatory variables that may affect spot volatility, the results indicate that only in voyage routes 1 and 2 the reduction in volatility may be a direct consequence of FFA trading. The results suggest that the introduction of FFA trading has not had a detrimental effect on the spot market. It appears that there has been an improvement in the way that information is transmitted into spot prices following the onset of FFA trading.

The impacts of Hong Kong’s Currency Board reforms on the interbank market

Among the economies with a Currency Board System (CBS), Hong Kong (HK) is probably the one with the largest and most developed financial sector, as well as the highest capital mobility. Hence, studying HK’s CBS is not only crucial to HK, but also important for the understanding of the modern CBS. This paper outlines the major monetary reforms in HK since the late 1980s. The impacts of these reforms and the 1997–1998 Asian Financial Crisis are then examined empirically. We focus on the differentials between the US and HK interbank interest rates. We assume the conditional-mean equation follows an autoregressive process and the conditional-variance equation follows a generalized autoregressive conditional heteroscedasticity process. This model captures the time-varying level and volatility of the differential. In light of the empirical results we provide an assessment of the reforms in HK.

Trading volume and stock market volatility: The Polish case

Relying on the mixture of distributions hypothesis (MDH), this paper investigates the relationship between daily returns and trading volume for 20 Polish stocks. Our empirical results show that in the majority of cases volatility persistence tends to disappear when trading volume is included in the conditional variance equation, which is in agreement with the findings of studies on developed stock markets. However, we cannot confirm the testable implications of the MDH in all cases, which indicates that future research on the causes and modeling of Polish stock market volatility is necessary.

Return predictability in African stock markets

This paper models weekly index returns adjusted for thin trading as a nonlinear autoregressive process with conditional heteroscedasticity to investigate the weak-form pricing efficiency of 11 African stock markets. Specifically, the use of the EGARCH-M model allows us to capture how conditional volatility affects the pricing process without imposing undue restrictions on the parameters of the conditional variance equation. On the basis of such a robust model, we are able to reject the evidence in prior studies that the Nigerian stock market is weak-form efficient. On the other hand, we confirm extant results that the markets in Egypt, Kenya, and Zimbabwe are efficient while that of South Africa is not weak-form efficient. We also generate new results, which point to the efficiency of the stock markets in Mauritius and Morocco, while the markets in Botswana, Ghana, Ivory Coast, and Swaziland are not consistent with weak-form efficiency.

An empirical examination of the relation between futures spreads volatility, volume, and open interest

AbstractThis study investigates the relation between petroleum futures spread variability, trading volume, and open interest in an attempt to uncover the source(s) of variability in futures spreads. The study finds that contemporaneous (lagged) volume and open interest provide significant explanation for futures spreads volatility when entered separately. The study also shows that lagged volume and lagged open interest, when entered in the conditional variance equation simultaneously, have greater effect on volatility and substantially reduce the persistence of volatility. This finding seems to support the sequential information arrival hypothesis of Copeland (1976). Finally, the findings of this study also suggest a degree of market inefficiency in petroleum futures spreads. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:1083–1102, 2002

Black’s hypothesis and developed economies

This paper examines the relationship between the volatility of output growth and the average growth rate of output in developed economies using the Generalized Auto-Regressive Conditional Hetereoskedasticity-in-mean (GARCHM) framework. The results indicate that that volatility is correlated with output growth for half of the countries and that the correlation is negative for some countries and positive for others. This finding is consistent with models that suggest country characteristics are important for determining the growth-volatility ralationship. However, the estimated correlation between volatility and the average growth rate is sensitive to the specification of the conditional variance equation.