Mike K. P. So

Asymmetrical reaction to US stock-return news: evidence from major stock markets based on a double-threshold model

Abstract This paper examines the hypothesis that both stock returns and volatility are asymmetrical functions of past information from the US market. By employing a double-threshold GARCH model to investigate six major index-return series, we find strong evidence supporting the asymmetrical hypothesis of stock returns. Specifically, negative news from the US market will cause a larger decline in a national stock return than an equal magnitude of good news. This holds true for the volatility series. The variance appears to be more volatile when bad news impacts the market than when good news does.

Comparison of nonnested asymmetric heteroskedastic models

The GJR-GARCH model is a popular choice among nonlinear models of the well-known asymmetric volatility phenomenon in financial market data. However, recent work employs double threshold nonlinear models to capture both mean and volatility asymmetry. A Bayesian model comparison procedure is proposed to compare the GJR-GARCH with various double threshold GARCH specifications, by designing a reversible jump Markov chain Monte Carlo algorithm. A simulation experiment illustrates good performance in estimation and model selection over reasonable sample sizes. In a study of seven markets strong evidence is found that the DTGARCH, with US market news as threshold variable, outperforms the GJR-GARCH and traditional self-exciting DTGARCH models. This result was consistent across six markets, excluding Canada.

Bayesian mixture of autoregressive models

An infinite mixture of autoregressive models is developed. The unknown parameters in the mixture autoregressive model follow a mixture distribution, which is governed by a Dirichlet process prior. One main feature of our approach is the generalization of a finite mixture model by having the number of components unspecified. A Bayesian sampling scheme based on a weighted Chinese restaurant process is proposed to generate partitions of observations. Using the partitions, Bayesian prediction, while accounting for possible model uncertainty, determining the most probable number of mixture components, clustering of time series and outlier detection in time series, can be done. Numerical results from simulated and real data are presented to illustrate the methodology.

Multivariate modelling of the autoregressive random variance process

The autoregressive random variance (ARV) model proposed by Taylor (Financial returns modelled by the product of two stochastic processes, a study of daily sugar prices 1961–79. In Time Series Analysis: Theory and Practice 1 (ed. O. D. Anderson). Amsterdam: North-Holland, 1982, pp. 203–26) is useful in modelling stochastic changes in the variance structure of a time series. In this paper we focus on a general multivariate ARV model. A traditional EM algorithm is derived as the estimation method. The proposed EM approach is simple to program, computationally efficient and numerically well behaved. The asymptotic variance--covariance matrix can be easily computed as a by-product using a well-kno wn asymptotic result for extremum estimators. A result that is of interest in itself is that the dimension of the augmented state space form used in computing the variance–covariance matrix can be shown to be greatly reduced, resulting in greater computational efficiency . The multivariate ARV model considered here is useful in studying the lead–lag (causality) relationship of the variance structure across different time series. As an example, the leading effect of Thailand on Malaysia in terms of vari ance changes in the stock indices is demonstrated.

Volatility Forecasting with Double Markov Switching GARCH Models

This paper investigates inference and volatility forecasting using a Markov switching heteroscedastic model with a fat-tailed error distribution to analyze asymmetric effects on both the conditional mean and conditional volatility of financial time series. The motivation for extending the Markov switching GARCH model, previously developed to capture mean asymmetry, is that the switching variable, assumed to be a first-order Markov process, is unobserved. The proposed model extends this work to incorporate Markov switching in the mean and variance simultaneously. Parameter estimation and inference are performed in a Bayesian framework via a Markov chain Monte Carlo scheme. We compare competing models using Bayesian forecasting in a comparative value-at-risk study. The proposed methods are illustrated using both simulations and eight international stock market return series. The results generally favor the proposed double Markov switching GARCH model with an exogenous variable. Copyright

Long-term memory in stock market volatility

The modified rescaled range test proposed by Lo (1991) and the semiparametric test proposed by Geweke and Porker-Hudak (1983) are applied to detect the existence of long-term dependence in volatility for S & P 500 index, Dow Jones Industrial Average index and its constituent stocks. Three proxies of the variability of returns: the absolute mean deviation, the squared mean deviation and the logarithm of the absolute mean deviation are adopted in this study. Strong evidence of long-term dependence in volatility is found in nearly all cases. This suggests that it is important to incorporate the long memory feature in the modelling of volatility in order to produce good volatility forecasts and derivative pricing formulas.

Bayesian Unit-Root Testing in Stochastic Volatility Models

This article discusses the use of Integrated Nested Laplace Approximations (INLA) in inference procedures and construction of unit root tests in stochastic volatility models. This approach allows to obtain accurate analytical approximations for the parameters and latent volatities, representing an alternative to methods based on Markov Chain Monte Carlo.

Estimation of Multiple Period Expected Shortfall and Median Shortfall for Risk Management

With the regulatory requirements for risk management, Value at Risk (VaR) has become an essential tool in determining capital reserves to protect the risk induced by adverse market movements. The fact that VaR is not coherent has motivated the industry to explore alternative risk measures such as expected shortfall. The first objective of this paper is to propose statistical methods for estimating multiple-period expected shortfall under GARCH models. In addition to the expected shortfall, we investigate a new tool called median shortfall to measure risk. The second objective of this paper is to develop backtesting methods for assessing the performance of expected shortfall and median shortfall estimators from statistical and financial perspectives. By applying our expected shortfall estimators and other existing approaches to seven international markets, we demonstrate the superiority of our methods with respect to statistical and practical evaluations. Our expected shortfall estimators likely provide an unbiased reference for setting the minimum capital required for safeguarding against expected loss.

An empirical evaluation of fat-tailed distributions in modeling financial time series

There is substantial evidence that many financial time series exhibit leptokurtosis and volatility clustering. We compare the two most commonly used statistical distributions in empirical analysis to capture these features: the t distribution and the generalized error distribution (GED). A Bayesian approach using a reversible-jump Markov chain Monte Carlo method and a forecasting evaluation method are adopted for the comparison. In the Bayesian evaluation of eight daily market returns, we find that the fitted t error distribution outperforms the GED. In terms of volatility forecasting, models with t innovations also demonstrate superior out-of-sample performance.

Vine-copula GARCH model with dynamic conditional dependence

Constructing multivariate conditional distributions for non-Gaussian return series has been a major research agenda recently. Copula GARCH models combine the use of GARCH models and a copula function to allow flexibility on the choice of marginal distributions and dependence structures. However, it is non-trivial to define multivariate copula densities that allow dynamic dependent structures in returns. The vine-copula method has been gaining attention recently in that a multi-dimensional density can be decomposed into a product of conditional bivariate copulas and marginal densities. The dependence structure is interpreted individually in each copula pair. Yet, most studies have only focused on time varying correlation. A vine-copula GARCH model with dynamic conditional dependence is proposed. A generic approach to specifying dynamic conditional dependence using any dependence measures is developed. The characterization also induces multivariate conditional dependence dynamically through vine decomposition. The main idea is to incorporate dynamic conditional dependence, such as Kendalls tau and rank correlation, not to mention linear correlation, in each bivariate copula pair. The estimation is conducted through a sequential approach. Simulation experiments are performed and five Hong Kong blue chip stock data from January 2004 to December 2011 are studied. Using t and two Archimedean copulas, it is revealed that Kendalls tau and linear correlation of the stock returns vary over time, indicating the presence of time varying properties in dependence.