Currency futures market in India: an empirical analysis of market efficiency and volatility

As the Indian currency futures market has been in existence for over 7 years, this paper analyses the effectiveness of the 1-month USD/INR currency futures rates in predicting the expected spot rate. The volatility of the USD/INR spot returns was also analysed. Modelling volatility of the USD/INR spot rate using a generalized autoregressive conditional heteroskedasticity (GARCH) and exponential generalized autoregressive conditional heteroskedasticity (EGARCH) model indicated the presence of volatility clustering. Using multivariate GARCH models such as the constant conditional correlation and dynamic conditional correlation, signs of a volatility spillover between the USD/INR spot and currency futures market were also observed.     

Announcement Effects and Asymmetric Volatility in Industry Stock Returns: Evidence from Taiwan

This study employs financial econometric models to examine the asymmetric volatility of equity returns in response to monetary policy announcements in the Taiwanese stock market. The meetings of the board of directors at the Central Bank of the Republic of China (Taiwan) are considered for testing the announcement effects. The asymmetric generalized autoregressive conditional heteroskedasticity (GARCH) model and the smooth transition autoregression with GARCH model are used to measure equity returns' asymmetric volatility. We conclude that the asymmetric volatility of countercyclical equity returns can be identified. Our findings support the leverage effect of stock price changes for most industry equity returns in Taiwan.     

Testing For Threshold Nonlinearity in Short-Term Interest Rates

This article addresses some empirical problems in the term structureof interest rates using a threshold autoregressive frameworkwith GARCH errors. This framework provides a parsimonious representationof some stylized features of interest rate data and facilitatesstatistical inference in the presence of high persistence andconditional heteroskedasticity. We propose a bootstrap-basedLM test for linearity in the conditional mean and variance functions.The empirical results indicate a presence of threshold nonlinearitiesin the AR and GARCH representations of the conditional momentsof short-term rate. The explicit modeling of these nonlinearitiesappears to improve the stability properties of the process forspot rate. The article also reports that allowing for thresholdnonlinearities in conditional mean and variance leads to significantforecast improvements. The economic significance of these findingsis evaluated by the term structure implications of the estimatedTAR-GARCH model.     

A lattice model for option pricing under GARCH-jump processes

This study extends the GARCH pricing tree in Ritchken and Trevor (J Financ 54:366–402, 1999) by incorporating an additional jump process to develop a lattice model to value options. The GARCH-jump model can capture the behavior of asset prices more appropriately given its consistency with abundant empirical findings that discontinuities in the sample path of financial asset prices still being found even allowing for autoregressive conditional heteroskedasticity. With our lattice model, it shows that both the GARCH and jump effects in the GARCH-jump model are negative for near-the-money options, while positive for in-the-money and out-of-the-money options. In addition, even when the GARCH model is considered, the jump process impedes the early exercise and thus reduces the percentage of the early exercise premium of American options, particularly for shorter-term horizons. Moreover, the interaction between the GARCH and jump processes can raise the percentage proportions of the early exercise premiums for shorter-term horizons, whereas this effect weakens when the time to maturity increases.     

Regime switching correlation hedging

This paper investigates the hedging effectiveness of commodity futures when the correlations of spot and futures returns are subject to multi-state regime shifts. An independent switching dynamic conditional correlation GARCH (IS-DCC) which is free from the problems of path-dependency and recombining is applied to model multi-regime switching correlations. The results of hedging exercises indicate that state-dependent IS-DCC outperforms state-independent DCC GARCH and three-state IS-DCC exhibits superior hedging effectiveness, illustrating importance of modeling higher-state switching correlations for dynamic futures hedging.     

NONLINEAR DYNAMICS AND THE DISTRIBUTION OF DAILY STOCK INDEX RETURNS

Three alternative models of daily stock index returns are considered: (1) a diffusion-jump process; (2) an extended generalized autoregressive conditional heteroskedasticity (GARCH) process; and (3) a combination of the GARCH and jump processes. Non-nested tests between the diffusion-jump process and a GARCH(1.1) process with t-distributed errors reject the diffusion-jump process, but do not always reject the GARCH process. Kolmogorov-Smirnov tests of fit, however, reject the GARCH(1,1)-t process for all cases. Nonlinear dependence is not removed for the value-weighted index and the S&P 500 stock index; therefore, deterministic chaos cannot be dismissed.     

On the distribution and conditional heteroscedasticity in Taiwan stock prices

This paper studies the distribution and conditional heteroscedasticity in stock returns on the Taiwan stock market. Apart from the normal distribution, in order to explain the leptokurtosis and skewness observed in the stock return distribution, we also examine the Student-t, the Poisson–normal, and the mixed-normal distributions, which are essentially a mixture of normal distributions, as conditional distributions in the stock return process. We also use the ARMA (1,1) model to adjust the serial correlation, and adopt the GJR–generalized autoregressive conditional heteroscedasticity (GARCH (1,1)) model to account for the conditional heterscedasticity in the return process. The empirical results show that the mixed–normal–GARCH model is the most probable specification for Taiwan stock returns. The results also show that skewness seems to be diversifiable through portfolio. Thus the normal–GARCH or the Student-t–GARCH model which involves symmetric conditional distribution may be a reasonable model to describe the stock portfolio return process¹.     

Testing for constant hedge ratios in commodity markets: a multivariate GARCH approach

We develop a new multivariate generalized ARCH (GARCH) parameterization suitable for testing the hypothesis that the optimal futures hedge ratio is constant over time, given that the joint distribution of cash and futures prices is characterized by autoregressive conditional heteroskedasticity (ARCH). The advantage of the new parameterization is that it allows for a flexible form of time-varying volatility, even under the null of a constant hedge ratio. The model is estimated using weekly corn prices. Statistical tests reject the null hypothesis of a constant hedge ratio and also reject the null that time variation in optimal hedge ratios can be explained solely by deterministic seasonality and time to maturity effects.     

The intertemporal relation between expected returns and risk

This paper explores the time-series relation between expected returns and risk for a large cross section of industry and size/book-to-market portfolios. I use a bivariate generalized autoregressive conditional heteroskedasticity (GARCH) model to estimate a portfolio's conditional covariance with the market and then test whether the conditional covariance predicts time–variation in the portfolio's expected return. Restricting the slope to be the same across assets, the risk-return coefficient is highly significant with a risk–aversion coefficient (slope) between one and five. The results are robust to different portfolio formations, alternative GARCH specifications, additional state variables, and small sample biases. When conditional covariances are replaced by conditional betas, the risk premium on beta is estimated to be in the range of 3% to 5% per annum and is statistically significant.     

Asian Pacific Stock Market Volatility Modeling and Value at Risk Analysis

The potential for stock market growth in Asian Pacific countries has attracted foreign investors. However, higher growth rates come with higher risk. We apply value at risk (VaR) analysis to measure and analyze stock market index risks in Asian Pacific countries, exposing and detailing both the unique risks and system risks embedded in those markets. To implement the VaR measure, it is necessary to perform "volatility modeling" by mixture switch, exponentially weighted moving average (EWMA), or generalized autoregressive conditional heteroskedasticity (GARCH) models. After estimating the volatility parameters, we can calibrate the VaR values of individual and system risks. Empirically, we find that, on average, Indonesia and Korea exhibit the highest VaRs and VaR sensitivity, and currently, Australia exhibits relatively low values. Taiwan is liable to be in high-state volatility. In addition, the Kupiec test indicates that the mixture switch VaR is superior to delta normal VaR; the quadratic probability score (QPS) shows that the EWMA is inclined to underestimate the VaR for a single series, and GARCH shows no difference from GARCH t and GARCH generalized error distribution (GED) for a multivariate VaR estimate with more assets.     

The Dynamics of Short-Term Interest Rate Volatility Reconsidered

In this paper we present and estimate a model of short-term interest rate volatility that encompasses both the level effect of Chan, Karolyi, Longstaff and Sanders (1992) and the conditional heteroskedasticity effect of the GARCH class of models. This flexible specification allows different effects to dominate as the level of the interest rate varies. We also investigate implications for the pricing of bond options. Our findings indicate that the inclusion of a volatility effect reduces the estimate of the level effect, and has option implications that differ significantly from the Chan, Karolyi, Longstaff and Sanders (1992) model.     

The Determinants of Conditional Autocorrelation in Stock Returns

We investigate whether return volatility, trading volume, return asymmetry, business cycles, and day‐of‐the‐week are potential determinants of conditional autocorrelation in stock returns. Our primary focus is on the role of feedback trading and the interplay of return volatility. We present empirical evidence using conditional autocorrelation estimates generated from multivariate generalized autoregressive conditional heteroskedasticity (M‐GARCH) models for individual U.S. stock and index data. In addition to return volatility, we find that trading volume and market returns are important in explaining the time‐varying patterns of return autocorrelation.     

Modeling Conditional Skewness in Stock Returns

Abstract

In this paper, we propose a new GARCH-in-Mean (GARCH-M) model allowing for conditional skewness. The model is based on the so-called z distribution capable of modeling skewness and kurtosis of the size typically encountered in stock return series. The need to allow for skewness can also be readily tested. The model is consistent with the volatility feedback effect in that conditional skewness is dependent on conditional variance. Compared to previously presented GARCH models allowing for conditional skewness, the model is analytically tractable, parsimonious and facilitates straightforward interpretation.Our empirical results indicate the presence of conditional skewness in the monthly postwar US stock returns. Small positive news is also found to have a smaller impact on conditional variance than no news at all. Moreover, the symmetric GARCH-M model not allowing for conditional skewness is found to systematically overpredict conditional variance and average excess returns.     

Positivity constraints on the conditional variances in the family of conditional correlation GARCH models

In this article, we derive a set of necessary and sufficient conditions for positivity of the vector conditional variance equation in multivariate GARCH models with explicit modelling of conditional correlation. These models include the constant conditional correlation GARCH model of Bollerslev [1990. Review of Economics and Statistics 72, 498–505] and its extensions. Under the new conditions, it is possible to introduce negative volatility spillovers in the model. An empirical example illustrates usefulness of having such conditions in practice.     

Conditional Dependence in Precious Metal Prices

This study investigates the time-series properties of gold and silver spot prices. Both precious metal price series are found to exhibit time dependence and pronounced generalized autoregressive conditional heteroscedastic (GARCH) effects. Splitting the data into similar economic subperiods provides superior explanation of these effects because of the observed long-run nonconstancy of the unconditional variance. Further, the power exponential distribution, as opposed to the Student-t, is found to portray accurately the thick-tailed conditional variance that remains after the GARCH effects are removed. These findings imply that constant variance pricing models are inappropriate for securities that are based on precious metal prices.     

Long-Range Dependence in U.S. Home Price Volatility

The existence of GARCH effects in a financial price series means that the probability of large losses is much higher than standard mean-variance analysis suggests. Accordingly, several recent papers have investigated whether GARCH effects exist in the U.S. housing market, as changes in house prices can have far-ranging impacts on defaults, foreclosures, tax revenues and the values of mortgage-backed securities. Some research in finance indicates that the conditional variance of some assets exhibits far greater persistence, or even “long memory”, than is accounted for in standard GARCH models. If house prices do indeed have this very persistent volatility, properly estimating the conditional variance to allow for such persistence is crucial for optimal portfolio management. We examine a number of U.S. metropolitan areas, and find that, for those with significant GARCH effects, more than half indeed exhibit the very high persistence found in other assets such as equities. We also find that, for those markets exhibiting such persistent volatility, C-GARCH models typically do a better job in forecasting than standard GARCH models. Moreover, there is some tentative evidence that metro areas with the fastest appreciation may be most likely to have such long memory conditional variance. These findings should help in improving risk management, through, for instance the construction of better-specified value-at-risk models.     

Re-examining the asymmetric predictability of conditional variances: The role of sudden changes in variance

The existence of “spillover effects” in financial markets is well documented and multivariate time series techniques have been used to study the transmission of conditional variances among large and small market value firms. Earlier research has suggested that volatility surprises to large capitalization firms are a reliable predictor of the volatility of small capitalization firms. A related line of research has examined how regime shifts in volatility may account for a considerable amount of the persistence in volatility. However, these studies have focused on univariate modeling and many have imposed regime changes on a priori grounds. This paper re-examines the asymmetry in the predictability of the volatilities of large versus small market value firms allowing for sudden changes in variance. Our method of analysis extends the existing literature in two important ways. First, recent advances in time series econometrics allow us to detect the time periods of sudden changes in volatility of large cap and small cap stocks endogenously using the iterated cumulated sums of squares (ICSS) algorithm. Second, we directly incorporate the information obtained on sudden changes in volatility in a Bivariate GARCH model of small and large cap stock returns. Our findings indicate that accounting for volatility shifts considerably reduces the transmission in volatility and, in essence, removes the spillover effects. We conclude that ignoring regime changes may lead one to significantly overestimate the degree of volatility transmission that actually exists between the conditional variances of small and large firms.     

Heteroskedasticity in Stock Returns

We use predictions of aggregate stock return variances from daily data to estimate time-varying monthly variances for size-ranked portfolios. We propose and estimate a single factor model of heteroskedasticity for portfolio returns. This model implies time-varying betas. Implications of heteroskedasticity and time-varying betas for tests of the capital asset pricing model (CAPM) are then documented. Accounting for heteroskedasticity increases the evidence that risk-adjusted returns are related to firm size. We also estimate a constant correlation model. Portfolio volatilities predicted by this model are similar to those predicted by more complex multivariate generalized-autoregressive-conditional-heteroskedasticity (GARCH) procedures.     

Common stochastic trends and volatility in Asian-Pacific equity markets

This paper uses Johansen's cointegration test and a modified cointegration test with generalized autoregressive conditional heteroskedasticity (GARCH) effects to examine linkages between the U.S. and five Asian-Pacific stock markets (Australia, Hong Kong, Japan, Malaysia, and Singapore) during the period from 1988 to 1994. The modified cointegration test with GARCH effects is used to assess whether these stock price series share common time-varying volatility. The results indicate that the six stock markets are highly integrated through the second moments of stock returns but not the first moments.     

Dynamic relationship between exchange rate and stock price: Evidence from China

The paper empirically analyzes the dynamic relationship between Renminbi (RMB) real effective exchange rate and stock price with VAR and multivariate generalized autoregressive conditional heteroskedasticity (GARCH) models using monthly data from January 1991 to June 2009. The results show that there is not a stable long-term equilibrium relationship between RMB real effective exchange rate and stock price. There are also not mean spillovers between the foreign exchange and stock markets. Furthermore, the paper examines the cross-volatility effects between foreign exchange and stock markets using likelihood ratio statistic. There exist the bidirection volatility spillovers effects between the two markets, indicating the past innovations in stock market have the great effect on future volatility in foreign exchange market, and vice versa.