Forecasting conditional correlations in stock,bond and foreign exchange markets

The paper forecasts conditional correlations between three classes of international financial assets, namely stock, bond and foreign exchange. Two countries are considered, namely Australia and New Zealand. Forecasting will be conducted using three multivariate GARCH models, namely the CCC model [T. Bollerslev, Modelling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model, Rev. Econ. Stat. 72 (1990) 498–505], VARMA-GARCH model [S. Ling, M. McAleer, Asymptotic theory for a vector ARMA-GARCH model, Econometric Theory 19 (2003) 280–310], and VARMA-AGARCH model [M. McAleer, S. Hoti, F. Chan, Structure and asymptotic theory for multivariate asymmetric volatility, Econometric Rev., in press]. A rolling window technique is used to forecast 1-day ahead conditional correlations. To evaluate the impact of model specification on conditional correlations forecasts, this paper calculates and compares the correlations between conditional correlations forecasts resulted from the three models. The paper finds the evidence of volatility spillovers and asymmetric effect of negative and positive shock on the conditional variance in most pairs of series. However, it suggests that incorporating volatility spillovers and asymmetric do not contribute to better conditional correlations forecasts.     

Fat tails and asymmetry in financial volatility models

Although the generalised autoregressive conditional heteroskedasticity (GARCH) model has been quite successful in capturing important empirical aspects of financial data, particularly for the symmetric effects of volatility, it has had far less success in capturing the effects of extreme observations, outliers and skewness in returns. This paper examines the GARCH model under various non-normal error distributions in order to evaluate skewness and leptokurtosis. The empirical results show that GARCH models estimated using asymmetric leptokurtic distributions are superior to their counterparts estimated under normality, in terms of: (i) capturing skewness and leptokurtosis; (ii) the maximized log-likelihood values; and (iii) isolating the ARCH and GARCH parameter estimates from the adverse effects of outliers. Overall, the flexible asymmetric Student’s t-distribution performs best in capturing the non-normal aspects of the data.     

Modelling conditional correlations in the volatility of Asian rubber spot and futures returns

Asia is presently the most important market for the production and consumption of natural rubber. World prices of rubber are subject to not only to changes in demand, but also speculation regarding future markets. Japan and Singapore are the major future markets for rubber, while Thailand is one of the world's largest producers of rubber. As rubber prices are influenced by external markets, it is important to analyse the relationship between the relevant markets in Thailand, Japan and Singapore. The analysis is conducted using several alternative multivariate GARCH models. The empirical results indicate that the constant conditional correlations arising from the CCC model lie in the low to medium range. The results from the VARMA-GARCH model and the VARMA-AGARCH model suggest the presence of volatility spillovers and asymmetric effects of positive and negative return shocks on conditional volatility. Finally, the DCC model suggests that the conditional correlations can vary dramatically over time. In general, the dynamic conditional correlations in rubber spot and futures returns shocks can be independent or interdependent.     

Generalised long-memory GARCH models for intra-daily volatility

The class of fractionally integrated generalised autoregressive conditional heteroskedastic (FIGARCH) models is extended for modelling the periodic long-range dependence typically shown by volatility of most intra-daily financial returns. The proposed class of models introduces generalised periodic long-memory filters, based on Gegenbauer polynomials, into the equation describing the time-varying volatility of standard GARCH models. A fitting procedure is illustrated and its performance is evaluated by means of Monte Carlo simulations. The effectiveness of these models in describing periodic long-memory volatility patterns is shown through an empirical application to the Euro-Dollar intra-daily exchange rate.     

Bayesian changepoint and time-varying parameter learning in regime switching volatility models

This paper proposes a combined state and piecewise time-varying parameter learning technique in regime switching volatility models using multiple changepoint detection. This approach is a Sequential Monte Carlo method for estimating GARCH & EGARCH based volatility models with an unknown number of changepoints. Modern auxiliary particle filtering techniques are used to calculate the posterior densities and online forecasts. This approach also automatically deals with the common ancestral path dependence problem faced in these type volatility models. The model is tested on Borsa Istanbul (BIST) formerly known as Istanbul Stock Exchange (ISE) market data using daily log returns. A full structural changepoint specification is defined in which all parameters of the conditional variance of the volatility models are dynamic. Finally, it is shown with simulation experiments that the proposed approach partitions the series into several regimes and learns the parameters of each regime's volatility model in parallel with the multiple changepoint detection process.     

A Fuzzy Asymmetric GARCH model applied to stock markets

In this paper, we derive a new class of flexible threshold asymmetric Generalized Autoregression Conditional Heteroskedasticity (GARCH) models. We use this tool for analysis and modeling of the properties that are apparent in many financial time series. In general, the transmission of volatility in the stock market is time-varying, nonlinear, and asymmetric with respect to both positive and negative results. Given this fact, we adopt the method of fuzzy logic systems to modify the threshold values for an asymmetric GARCH model. Our simulations use stock market data from the Taiwan weighted index (Taiwan), the Nikkei 225 index (Japan), and the Hang Seng index (Hong Kong) to illustrate the performance of our proposed method. From the simulation results, we have determined that the forecasting of volatility performance is significantly improved if the leverage effect of clustering is considered along with the use of expert knowledge enabled by the GARCH model.     

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.     

Intraday dynamic relationships between CSI 300 index futures and spot markets: a high-frequency analysis

Based on intraday 5-min high-frequency dataset, this paper empirically analyzes the intraday dynamic relationships between China’s CSI 300 index futures and spot markets with vector autoregression (VAR) and multivariate GARCH (MGARCH) models. By comparing four VAR–MGARCH models (dynamic conditional correlation, constant conditional correlation, diagonal and BEKK), the VAR–DCC–MGARCH model is found to fit the data the best and be preferred over the other models. The results of this model show that although there are bidirectional price causal relationships between the CSI 300 index futures and spot markets, the index futures return shock affects the spot market more severely than the spot return shock affects the futures market, indicating that the index futures market dominates the price discovery process between the two markets. There are bidirectional volatility spillovers effects between the CSI 300 index futures and spot markets, and the spillovers effects from index futures to spot almost equal to that from index spot to futures. The time-varying conditional correlations between the CSI 300 index futures and spot markets change from 0.4787 to 0.9594 across time, showing there is a strong positive correlation and linkage effect between the two markets. These results indicate that after a period of time of development, the price discovery performance of the CSI 300 index futures market has begun to function well, and the impact of the CSI 300 index futures market on its underlying spot market has strengthened.     

GARCH,jumps and permanent and transitory components of volatility: the case of the Taiwan exchange rate

This paper investigates whether there are three distinctive features in financial asset prices, that is, time-varying conditional volatility, jumps and the component factors of volatility. It adopts a component-GARCH-Jump, which can efficiently capture the three features simultaneously. Our results demonstrate that the three features exist in the Taiwan exchange rate. Besides time-varying conditional volatility, our model identifies 172 jumps between 5 January 1988 and 21 March 2003. The empirical evidence shows that the permanent component of the conditional variance is a relatively smooth movement except for a fairly sharp shift which began in 1997. This means that the effect of the Asian crisis shock might very well have exerted not only a transitory jump effect, but also a permanent effect on Taiwan’s exchange rate.     

Heavy-tailed mixture GARCH volatility modeling and Value-at-Risk estimation

This paper presents a heavy-tailed mixture model for describing time-varying conditional distributions in time series of returns on prices. Student-t component distributions are taken to capture the heavy tails typically encountered in such financial data. We design a mixture MT(m)-GARCH(p, q) volatility model for returns, and develop an EM algorithm for maximum likelihood estimation of its parameters. This includes formulation of proper temporal derivatives for the volatility parameters. The experiments with a low order MT(2)-GARCH(1, 1) show that it yields results with improved statistical characteristics and economic performance compared to linear and nonlinear heavy-tail GARCH, as well as normal mixture GARCH. We demonstrate that our model leads to reliable Value-at-Risk performance in short and long trading positions across different confidence levels.     

Forecasting large scale conditional volatility and covariance using neural network on GPU

Forecasting volatility is an important issue in financial econometric analysis. This paper aims to seek a computationally feasible approach for predicting large scale conditional volatility and covariance of financial time series. In the case of multi-variant time series, the volatility is represented by a Conditional Covariance Matrix (CCM). Traditional models for predicting CCM such as GARCH models are incapable of dealing with high-dimensional cases as there are O(N ²) parameters to be estimated in the case of N-variant asset return, and it is difficult to accelerate the computation of estimating these parameters by utilizing modern multi-core architecture. These GARCH models also have difficulties in modeling non-linear properties. The widely used Restricted Boltzmann Machine (RBM) is an energy-based stochastic recurrent neural network and its extended model, Conditional RBM (CRBM), has shown its capability in modeling high-dimensional time series. In this paper, we first propose a CRBM-based approach to forecast CCM and show how to capture the long memory properties in volatility, and then we implement the proposed model on GPU by using CUDA and CUBLAS. Experiment results indicate that the proposed CRBM-based model obtains better forecasting accuracy for low-dimensional volatility and it also shows great potential in modeling for large-scale cases compared with traditional GARCH models.     

Nonlinear neural network forecasting model for stock index option price: Hybrid GJR–GARCH approach

This study integrated new hybrid asymmetric volatility approach into artificial neural networks option-pricing model to improve forecasting ability of derivative securities price. Owing to combines the new hybrid asymmetric volatility method can be reduced the stochastic and nonlinearity of the error term sequence and captured the asymmetric volatility simultaneously. Hence, in the ANNS option-pricing model, the results demonstrate that Grey-GJR–GARCH volatility provides higher predictability than other volatility approaches.     

Testing for expected return and market price of risk in Chinese A and B share markets: A geometric Brownian motion and multivariate GARCH model approach

There exist dual listed stocks which are issued by the same company in some stock markets. Although these stocks bare the same firm-specific risks and enjoy identical dividends and voting policies, they are priced differently. Some previous studies show this seeming deviation from the law of one price can be solved by allowing different expected returns and market prices of risk for investors holding heterogeneous beliefs. This paper provides empirical evidence for that argument by testing the expected return and market price of risk between Chinese A and B shares listed in Shanghai and Shenzhen stock markets. Models with dynamic of Geometric Brownian Motion are adopted. Multivariate GARCH models are also introduced to capture the feature of time-varying volatility in stock returns. The results suggest that the different pricing can be explained by the difference in expected returns between A and B shares. However, the difference between market price of risk is insignificant for both markets if GARCH models are adopted.     

A risk map of international tourist regions in Spain

This paper presents a different approach to tourism research at the regional level. Financial econometric techniques are applied to international tourist arrivals, as well as their volatilities, in the five main tourist regions in Spain, using monthly international tourist arrivals during 1997–2007. Univariate time series models are estimated for the conditional means of monthly international tourist arrivals and their volatilities. The estimated conditional volatility models are GARCH(1,1), GJR(1,1) and EGARCH(1,1). Both the second moment and log-moment conditions are calculated to provide diagnostic checks of the estimated models. The conditional mean estimates are generally statistically adequate, and the inferences are valid.     

A double-threshold GARCH model of stock market and currency shocks on stock returns

International integration of financial markets provides a channel for currency movements to affect stock prices. This paper applies a four-regime double-threshold GARCH (DTGARCH) model of stock market returns to investigate empirically the effects of daily currency movements on five stock market returns, namely in Taiwan, Singapore, South Korea, Japan and the USA. The asymmetric reactions of the mean and volatility stock returns in five markets to stock market and foreign exchange news are investigated using linear and nonlinear models. We discuss a four-regime DTGARCH model, which allows for asymmetry in both the conditional mean and conditional variance simultaneously by using two threshold variables to analyze stock market reactions to different types of information (that is, positive and negative news) that are generated from stock and foreign exchange markets. By applying the four-regime DTGARCH model, this paper finds that the interactions between the information of stock and foreign exchange markets lead to asymmetric reactions of stock returns and their associated variability. The empirical results show that international fund managers who invest in newly emerging stock markets need to evaluate the value and stability of domestic currencies as part of their stock market investment decisions.     

An algorithm for nonparametric GARCH modelling

A simple iterative algorithm for nonparametric first-order GARCH modelling is proposed. This method offers an alternative to fitting one of the many different parametric GARCH specifications that have been proposed in the literature. A theoretical justification for the algorithm is provided and examples of its application to simulated data from various stationary processes showing stochastic volatility, as well as empirical financial return data, are given. The nonparametric procedure is found to often give better estimates of the unobserved latent volatility process than parametric modelling with the standard GARCH(1,1) model, particularly in the presence of asymmetry and other departures from the standard GARCH specification. Extensions of the basic iterative idea to more complex time series models combining ARMA or GARCH features of possibly higher order are suggested.     

A detailed comparison of value at risk estimates

This work investigates the performance of different models of value at risk. We include several methods (parametric, historical simulation, Monte Carlo, and extreme value theory) and some models to compute the conditional variance. We analyze several international stock indexes and examine two types of periods: stable and volatile periods. To choose the best model, we employ a two-stage selection approach. The result indicates that the best model is a parametric model with conditional variance estimated by an asymmetric GARCH model under Student's t-distribution of returns. This paper shows that parametric models can obtain successful VaR measures if conditional variance is estimated properly.     

Global Banking on the Financial Network Modelling: Sectorial Analysis

This article is particularly concentrated on measuring systemic risk based on network topology of bilateral exposures and obligations specifically for the sectoral level of global banking systems in 2010. Financial network models based on financial exposures are models that aim to depict causal chains of exposures and obligations of counterparties rather than rely solely on statistical correlations on market price-based data for financial institutions. Our starting point is the bilateral claims of the ultimate risk of the main institutional sectors that include banks, non-bank private sectors and non-allocated sectors of the 10 reporting countries that consist of Belgium, France, Germany, Italy, Japan, Spain, Switzerland, Turkey, the United Kingdom and the United States of America. The other non-reporting countries will be merged into one group. The results show that banking systems in countries such as the United States and the United Kingdom in particular are making vast amounts of foreign investments, implying that they constitute a central hub in the core. The results in the contagion effect show that all of the other countries are collapsed after a shock from a core country such as the United Kingdom in both rates of loss given defaults of 100 and 60 %.     

Intra-daily information of range-based volatility for MEM-GARCH

Conventional GARCH modeling formulates an additive-error mean equation for daily return and an autoregressive moving-average specification for its conditional variance, without much consideration on the effects of intra-daily data. Using Engle’s multiplicative-error model (MEM) formulation, range-based volatility is proposed as an intraday proxy for several GARCH frameworks. The performances of these different approaches for two 8-year market data sets: the S&P 500 and the NASDAQ composite index, are studied and compared. The impact of significant changes in intraday data has been found to reflect in the MEM-GARCH volatility. For some frameworks it is also possible to use lagged values of range-based volatility to delay the intraday effects in the conditional variance estimation.     

Monte Carlo option pricing with asymmetric realized volatility dynamics

What are the advances introduced by realized volatility models in pricing options? In this short paper we analyze a simple option pricing framework based on the dually asymmetric realized volatility model, which emphasizes extended leverage effects and empirical regularity of high volatility risk during high volatility periods. We conduct a brief empirical analysis of the pricing performance of this approach against some benchmark models using data from the S&P 500 options in the 2001-2004 period. The results indicate that as expected the superior forecasting accuracy of realized volatility translates into significantly smaller pricing errors when compared to models of the GARCH family. Most importantly, our results indicate that the presence of leverage effects and a high volatility risk are essential for understanding common option pricing anomalies.