Asymmetric Conditional Volatility Research Articles

Modelling the Growth and Volatility in Daily International Mass Tourism to Peru

Peru is a South American country that is divided into two parts by the Andes Mountains. The rich historical, cultural and geographic diversity has led to the inclusion of ten Peruvian sites on UNESCO's World Heritage List. For the potential negative impacts of mass tourism on the environment, and hence on future international tourism demand, to be managed appropriately require modelling growth rates and volatility adequately. The paper models the growth rate and volatility (or the variability in the growth rate) in daily international tourist arrivals to Peru from 1997 to 2007. The empirical results show that international tourist arrivals and their growth rates are stationary, and that the estimated symmetric and asymmetric conditional volatility models all fit the data extremely well. Moreover, the estimates resemble those arising from financial time series data, with both short and long run persistence of shocks to the growth rate in international tourist arrivals.

Modelling Short and Long Haul Volatility in Japanese Tourist Arrivals to New Zealand and Taiwan

This paper estimates the effects of short and long haul volatility (or risk) in monthly Japanese tourist arrivals to Taiwan and New Zealand, respectively. In order to model appropriately the volatilities of international tourist arrivals, we use symmetric and asymmetric conditional volatility models that are commonly used in financial econometrics, namely the GARCH (1,1), GJR (1,1) and EGARCH (1,1) models. The data series are for the period January 1997 to December 2007. The volatility estimates for the monthly growth in Japanese tourists to New Zealand and Taiwan are different, and indicate that the former has an asymmetric effect on risk from positive and negative shocks of equal magnitude, while the latter has no asymmetric effect. Moreover, there is a leverage effect in the monthly growth rate of Japanese tourists to New Zealand, whereby negative shocks increase volatility but positive shocks of very similar magnitude decrease volatility. These empirical results seem to be similar to a wide range of financial stock market prices, so that the models used in financial economics, and hence also the issues related to risk and leverage effects, are also applicable to international tourism flows.

Structure and Asymptotic Theory for Multivariate Asymmetric Conditional Volatility

Various univariate and multivariate models of volatility have been used to evaluate market risk, asymmetric shocks, thresholds, leverage effects, and Value-at-Risk in economics and finance. This article is concerned with market risk, and develops a constant conditional correlation vector ARMA–asymmetric GARCH (VARMA–AGARCH) model, as an extension of the widely used univariate asymmetric (or threshold) GJR model of Glosten et al. (1992), and establishes its underlying structure, including the unique, strictly stationary, and ergodic solution of the model, its causal expansion, and convenient sufficient conditions for the existence of moments. Alternative empirically verifiable sufficient conditions for the consistency and asymptotic normality of the quasi-maximum likelihood estimator are established under non-normality of the standardized shocks.

Volatility dynamics of the US business cycle: A multivariate asymmetric GARCH approach

Most empirical investigations of the business cycles in the United States have excluded the dimension of asymmetric conditional volatility. This paper analyses the volatility dynamics of the US business cycle by comparing the performance of various multivariate generalised autoregressive conditional heteroskedasticity (GARCH) models. In particular, we propose two bivariate GARCH models to examine the evidence of volatility asymmetry and time-varying correlations concurrently, and then apply the proposed models to five sectors of Industrial Production of the United States. Our findings provide strong evidence of asymmetric conditional volatility in all sectors, and some support of time-varying correlations in various sectoral pairs. This has important policy implications for government to consider the effective countercyclical measures during recessions.

Modelling risk in agricultural finance: Application to the poultry industry in Taiwan

The volatility in agricultural prices, such as for broiler and color broiler chickens in Taiwan, is similar in various aspects to financial volatility as it relates to the risk and returns associated with agricultural production. However, as the characteristics of agricultural markets may be different from financial markets, the results arising from empirical risk analysis need to be investigated. The broiler and color broiler industries are the second and third largest livestock industries in Taiwan. When Taiwan applied to join the World Trade Organization (WTO) in the 1990s, these two industries faced the threat of deregulation of chicken meat imports. However, developments in these two industries have not been the same under deregulation, with the level of competition in the broiler and color broiler industries being markedly different. The purpose of the paper is to model the prices, growth rates and their respective volatilities in weekly broiler and color broiler chicken prices in Taiwan from January 1995 to June 2007. The empirical results show that the time series of broiler and color broiler prices, their logarithms and their growth rates are stationary, and that the estimated symmetric and asymmetric conditional volatility models all fit the data extremely well. The empirical second moment and log-moment conditions also support the statistical adequacy of the estimated volatility models. The empirical results have significant implications for risk management and policy considerations in the agricultural production industry in Taiwan.

An Analysis of the Conditional Volatility Dynamics of the Australian Business Cycle

In this paper, we analyse the conditional variance of the Australian real gross domestic product (GDP) and the expenditure components by a variety of generalised autoregressive conditional heteroskedasticity (GARCH) models. First, we test the plausibility of the constant-correlation assumption by employing Tsei¯s (2000) Lagrange Multiplier (LM) test and the Bera and Kimi¯s (2002) Information Matrix (IM) test. Our results indicate that the correlations among the shocks to real GDP and its various expenditure components are invariant over time. In addition, these shocks are not highly correlated with one another. Second, we examine if volatility asymmetry exists in the Australian business cycle by proposing four bivariate asymmetric GARCH specifications. Except for the case of gross fixed capital formation, the evidence of asymmetric conditional volatility in the growth rates of the Australian real GDP and the other components is weak. Despite the weak evidence of asymmetric volatility, higher volatility is generally associated with the contractionary phase of the Australian business cycle. This finding has important implications for macroeconomic policy and forecasting for business cycle.

Exchange rate exposure of sectoral returns and volatilities: Evidence from Japanese industrial sectors

Most studies of exchange rate exposure of stock returns do not address three relevant aspects simultaneously. They are, namely: sensitivity of stock returns to exchange rate changes; sensitivity of volatility of stock returns to volatility of changes in foreign exchange market; and the correlation between volatilities of stock returns and exchange rate changes. In this paper, we employ a bivariate GJR-GARCH model to examine all such aspects of exchange rate exposure of sectoral indexes in Japanese industries. Based on a sample data of fourteen sectors, we find significant evidence of exposed returns and its asymmetric conditional volatility of exchange rate exposure. In addition, returns in many sectors are correlated with those of exchange rate changes. We also find support for the “averaged-out exposure and asymmetries” argument. Our findings have direct implications for practitioners in formulating investment decisions and currency hedging strategies.

Asymmetric conditional volatility in international stock markets

Recent studies show that a negative shock in stock prices will generate more volatility than a positive shock of similar magnitude. The aim of this paper is to appraise the hypothesis under which the conditional mean and the conditional variance of stock returns are asymmetric functions of past information. We compare the results for the Portuguese Stock Market Index PSI 20 with six other Stock Market Indices, namely the SP 500, FTSE 100, DAX 30, CAC 40, ASE 20, and IBEX 35. In order to assess asymmetric volatility we use autoregressive conditional heteroskedasticity specifications known as TARCH and EGARCH. We also test for asymmetry after controlling for the effect of macroeconomic factors on stock market returns using TAR and M-TAR specifications within a VAR framework. Our results show that the conditional variance is an asymmetric function of past innovations raising proportionately more during market declines, a phenomenon known as the leverage effect. However, when we control for the effect of changes in macroeconomic variables, we find no significant evidence of asymmetric behaviour of the stock market returns. There are some signs that the Portuguese Stock Market tends to show somewhat less market efficiency than other markets since the effect of the shocks appear to take a longer time to dissipate.

Non‐trading day effects in asymmetric conditional and stochastic volatility models

Summary It is well known that non-trading days (or holidays) can have significant effectson the returns in financial series. In this paper, we analyze three models of non-trading dayeffects in stochastic volatility models with leverage effects, namely (i) the approach basedon the dummy variable in conditional volatility models; (ii) the approach based on a discretetime approximation of a continuous time stochastic volatility model and (iii) the twin non-trading day stochastic volatility model which nests the above two models. The three modelsare also estimated and tested within the asymmetric and exponential conditional volatilityframeworks. All the models within the stochastic, asymmetric conditional and exponentialconditional volatility frameworks are estimated and compared using a selection of financialreturns series. Key words: Symmetric and asymmetric conditional volatility , Exponential conditionalvolatility , Stochastic volatility , Non-trading day , Non-nested , Monte Carlo likelihood

Clarifications on the Asymmetric Volatility Effect and Foreign Investors' Destabilizing Influence: Agents' Information Perception

In this paper, the relation of asymmetric conditional volatility to market agents' information perception ability is built and positively tested. Liquidity dry-ups during extreme market conditions, that, due to investors' risk aversion, are more pronounced during negative than positive news result in asymmetric volatility. The well known volatility feedback effect assures that the short term effect of liquidity dry-ups troubles a financial market for an extended period. An explanation for the perceived liquidity dry-ups is found in market microstructure theory; adverse information cost. The propositions are then tested using a well documented phenomenon; Home Bias. The positive relation of relative foreign investors' exposure to the German DAX to volatility levels in general and the asymmetry specifically is documented with high statistical significance. The results are far reaching; on the one hand trading mechanism can be better understood. On the other hand, capital flow regulations are illuminated.

Conditional heteroscedasticity of exchange rates: further results based on the fractionally integrated approach

AbstractA recent article (Tse, 1998) published in this journal analysed the conditional heteroscedasticity of the yen–dollar exchange rate based on the fractionally integrated asymmetric power ARCH model. In this paper, we present replication results using Tse's (1998) yen–dollar series. We also examine the robustness of Tse's (1998) findings across different currencies, sample periods and non‐nested GARCH‐type models. Unlike Tse (1998), we find some evidence of asymmetric conditional volatility for daily returns of currencies measured against the dollar or the yen. Copyright © 2004 John Wiley & Sons, Ltd.

Forecasting Exchange Rate Volatility

The relative out-of-sample forecasting quality of symmetric and asymmetric conditional volatility models of an exchange rate differs according to the symmetric and asymmetric evaluation criteria. Both symmetric and asymmetric forecast competitors of currency volatility are biased and systematically overpredict volatility.

Comparative forecasting performance of symmetric and asymmetric conditional volatility models of an exchange rate

The relative out-of-sample forecasting quality of symmetric and asymmetric conditional volatility models of an exchange rate differs according to the symmetric and asymmetric evaluation criteria. Both symmetric and asymmetric forecast competitors of currency volatility are biased and systematically over-predict volatility.

Analysis of real GDP growth rates of greater China: An asymmetric conditional volatility approach

Most empirical studies of real gross domestic product (GDP) growth rates exclude the dimension of conditional volatility shocks. In this paper, we search for evidence of conditional volatility in the quarterly real GDP of greater China, which comprises the economies of Mainland China, the Hong Kong Special Administrative Region (SAR), and Taiwan. The widely accepted exponential GARCH model of Nelson [ Econometrica 59 (1991) 347–370] is employed to capture the possible existence of asymmetric conditional volatility in real GDP. It is found that negative real GDP shocks may induce a greater impact on future volatilities compared with positive shocks of the same magnitude. Policy implications from our findings are discussed.

Can the Random Walk Model be Beaten in Out-of-Sample Density Forecasts: Evidence from Intraday Foreign Exchange Rates

Numerous studies have shown that the simple random walk model outperforms all structural and time series models in forecasting the conditional mean of exchange rate changes. However, in many important applications, such as risk management, forecasts of the probability distribution of exchange rate changes are often needed. In this paper, we develop a nonparametric portmanteau evaluation procedure for out-of-sample density forecast and provide a comprehensive empirical study on the out-of-sample performance of a wide variety of time series models in forecasting the intraday probability density of two major exchange rates - Euro/Dollar and Yen/Dollar. We find that some nonlinear time series models provide better density forecast than the simple random walk model, although they underperform in forecasting the conditional mean. For Euro/Dollar, it is important to model heavy tails through a Student-t innovation and asymmetric timevarying conditional volatility through a regime-switching GARCH model for both insample and out-of-sample performance; modeling conditional mean and serial dependence in higher order moments (e.g., conditional skewness), although important for in-sample performance, does not help out-of-sample density forecast. For Yen/Dollar, it is also important to model heavy tails and volatility clustering, and the best density forecast model is a RiskMetrics model with a Student-t innovation. As a simple application, we find that the models that provide good density forecast generally provide good forecast of Value-at-Risk.

Comparative Forecasting Performance of Symmetric and Asymmetric Conditional Volatility Models of an Exchange Rate

The relative out-of-sample forecasting quality of symmetric and asymmetric conditional volatility models of an exchange rate differs according to the symmetric and asymmetric evaluation criteria as well as a regression-based test of efficiency. Both symmetric and asymmetric forecast competitors of currency volatility are biased and systematically overpredict volatility.

Stock returns, seasonality and asymmetric conditional volatility in world equity markets

The paper tests four hypotheses at the same time using an autoregressive return-generating process and an asymmetric conditional variance specification, both also including deterministic day of the week dummies. The daily stock index returns from 19 countries are employed to test: (H1) predictable time variation in conditional volatility; (H2) asymmetry in volatility and leverage effect; (H3) effects of estimated volatility on returns; and (H4) day of the week effects on both returns and their volatility. Evidence is provided for predictable time varying daily volatility in all markets among which eight also exhibit a significant leverage effect. There is a significantly positive relationship between returns and their conditional volatility in only three countries. The nature of the day of the week effects on returns and their conditional volatility differs greatly among countries and across days. Thirteen countries exhibit seasonality in either mean returns (seven countries) or volatility (eight countries) or both (two countries). Each day is at least once reported to exhibit significant positive and negative effects in both mean and volatility with the exception that there is no negative effect on mean returns and no positive effect in volatility on Wednesdays.

Estimating non-linear ARMA models using Fourier coefficients

Linear time-series models are often inadequate to capture the presence of asymmetric adjustment and/or conditional volatility. Parametric models of asymmetric adjustment and ARCH-type models necessitate specifying the nature of the non-linear coefficient. If there is little a priori information concerning the actual form of the non-linearity, the estimated model can suffer from a misspecification error. We show that a non-linear time-series can be represented by a deterministic time-dependent coefficient model without first specifying the nature of the non-linearity. The methodology is applied to real GDP and the NYSE Transportation Index.

Asymmetric Conditional Volatility and Firm Size: Evidence from Australian Equity Portfolios

This paper examines the relationship between firm size and equity volatility for two portfolios of Australian equities. Univariate and Multivariate GARCH models are used to demonstrate that conditional variance is related to firm size. There is strong evidence to suggest that the variance‐covariance matrix of returns is time varying and asymmetric. A negative innovation to the return of the large firm portfolio results in higher levels of conditional volatility in the small firm portfolio than would be the case for a positive innovation of equal magnitude. News about own returns appears to determine the conditional variance of the portfolio of large firms. The conditional covariance between the two portfolios also displays evidence of asymmetry.

Some exotic options under symmetric and asymmetric conditional volatility of returns

For a plain vanilla call and three of the more popular exotic (path-dependent) types of options, this study examines the impact of symmetric and asymmetric GARCH processes in returns. The price, delta and gamma of European call options, Black–Scholes implied volatilities and convergence of these factors are all studied, through a simulation of price paths. For comparison, we ensure that the unconditional volatility of each process is identical. The impact of a standard symmetric GARCH volatility structure on the option parameters is usually to bias price and delta downwards, but to bias gamma upwards, sometimes quite considerably. Asymmetric GARCH effects exacerbate this effect, and it varies across the different options. GARCH effects appear not to induce a smile. Finally, as time to maturity shortens, at-the-money call prices and deltas converge slowly but gammas can change wildly when GARCH effects are added.