Estimating stochastic volatility models using daily returns and realized volatility simultaneously

Realized volatility, which is the sum of squared intraday returns over a certain interval such as a day, has recently attracted the attention of financial economists and econometricians as an accurate measure of the true volatility. In the real market, however, the presence of non-trading hours and market microstructure noise in transaction prices may cause bias in the realized volatility. On the other hand, daily returns are less subject to noise and therefore may provide additional information on the true volatility. From this point of view, modeling realized volatility and daily returns simultaneously based on the well-known stochastic volatility model is proposed. Empirical studies using intraday data of Tokyo stock price index show that this model can estimate realized volatility biases and parameters simultaneously. The Bayesian approach is taken and an efficient sampling algorithm is proposed to implement the Markov chain Monte Carlo method for our simultaneous model. The result of the model comparison between the simultaneous models using both naive and scaled realized volatilities indicates that the effect of non-trading hours is more essential than that of microstructure noise and that asymmetry is crucial in stochastic volatility models. The proposed Bayesian approach provides an estimate of the entire conditional predictive distribution of returns under consideration of the uncertainty in the estimation of both biases and parameters. Hence common risk measures, such as value-at-risk and expected shortfall, can be easily estimated.     

Improving forecasts of GARCH family models with the artificial neural networks: An application to the daily returns in Istanbul Stock Exchange

In the study, we discussed the ARCH/GARCH family models and enhanced them with artificial neural networks to evaluate the volatility of daily returns for 23.10.1987–22.02.2008 period in Istanbul Stock Exchange. We proposed ANN-APGARCH model to increase the forecasting performance of APGARCH model. The ANN-extended versions of the obtained GARCH models improved forecast results. It is noteworthy that daily returns in the ISE show strong volatility clustering, asymmetry and nonlinearity characteristics.     

A note on the properties of power-transformed returns in long-memory stochastic volatility models with leverage effect

The autocorrelation function (acf) of powered absolute returns and their cross-correlations with original returns are derived, for any value of the power parameter, in the context of long-memory stochastic volatility models with leverage effect and Gaussian noises. These autocorrelations and cross-correlations generalize and correct recent results on the acf of squared and absolute returns.     

Multivariate mixed normal conditional heteroskedasticity

A new multivariate volatility model where the conditional distribution of a vector time series is given by a mixture of multivariate normal distributions is proposed. Each of these distributions is allowed to have a time-varying covariance matrix. The process can be globally covariance stationary even though some components are not covariance stationary. Some theoretical properties of the model such as the unconditional covariance matrix and autocorrelations of squared returns are derived. The complexity of the model requires a powerful estimation algorithm. A simulation study compares estimation by maximum likelihood with the EM algorithm. Finally, the model is applied to daily US stock returns.     

On asymmetric generalised t stochastic volatility models

In stochastic volatility (SV) models, asset returns conditional on the latent volatility are usually assumed to have a normal, Student-t or exponential power (EP) distribution. An earlier study uses a generalised t (GT) distribution for the conditional returns and the results indicate that the GT distribution provides a better model fit to the Australian Dollar/Japanese Yen daily exchange rate than the Student-t distribution. In fact, the GT family nests a number of well-known distributions including the commonly used normal, Student-t and EP distributions. This paper extends the SV model with a GT distribution by incorporating general volatility asymmetry. We compare the empirical performance of nested distributions of the GT distribution as well as different volatility asymmetry specifications. The new asymmetric GT SV models are estimated using the Bayesian Markov chain Monte Carlo (MCMC) method to obtain parameter and log-volatility estimates. By using daily returns from the Standard and Poors (S&P) 500 index, we investigate the effects of the specification of error distributions as well as volatility asymmetry on parameter and volatility estimates. Results show that the choice of error distributions has a major influence on volatility estimation only when volatility asymmetry is not accounted for.     

Estimating stochastic volatility models of stock returns in Chinese markets

Volatility plays a key role in microstructure issues in the study of financial markets. Stochastic volatility (SV) models have been applied to the study of the behavior of financial variables. Two stock markets exist in China: Shanghai Stock Exchange and Shenzhen Stock Exchange. As emerging stock markets, investors are increasingly concerned about the volatilities of these two stock markets. We briefly introduce how to estimate SV models using the Markov chain Monte Carlo (MCMC) method. In order to do full and comprehensive analyses of the volatilities of stock returns, we estimated SV models using most of the historical data and the different data frequencies of the two Chinese markets. We found that estimated values of volatility parameters are very high for all data frequencies. This suggests that stock returns are extremely volatile even at long-term intervals in Chinese markets.     

A multivariate threshold stochastic volatility model

We introduce in this paper a multivariate threshold stochastic volatility model for multiple financial return time series. This model allows the dynamic structure of return and volatility to change according to a threshold model while accounting for the interdependence of financial returns. Through the threshold volatility modeling, we can understand the impact of market news on volatility asymmetry. Estimation of unknown parameters are carried out using Markov chain Monte Carlo techniques. Simulations show that our estimators are reliable in moderately large sample sizes. We apply the model to three market indice data and estimate time-varying correlations among the indice returns.     

Clarifying the dynamics of the relationship between option and stock markets using the threshold vector error correction model

This work examines how the option and stock markets are related when using the threshold vector error correction model (hereinafter referred to as threshold VECM). Moreover, compared to previous studies in the literature of application of threshold models, this study not only investigates the impacts of price transmission mechanisms on stock return means but also the volatilities of returns. The model is tested using the U.S. S&P 500 stock market. The empirical findings of this investigation are consistent with the following notions. First, the equilibrium re-establishment process depends primarily on the option market and is triggered only when price deviations exceed a critical threshold. Second, arbitrage behaviors between the option and stock markets increase volatility in these two markets and reduce their correlation.     

Realized volatility of index constituent stocks in Hong Kong

High-frequency financial data are useful for studying the statistical properties of asset returns at lower frequencies, and they have been widely used to study various market microstructure related issues. However, most studies to date have been concentrated on markets in developed economies such as the stock markets in US or UK. This article aims to investigate the statistical properties of stock return volatility in Hong Kong. Using the sample of constituent stocks of Hang Seng Index (HSI) and Hang Seng China Enterprises Index (HSCEI or “H-shares Index”), we found that the mean daily realized volatilities of HSCEI stocks to be significantly higher than their HSI counterpart, while the correlations between H-shares stay relatively lower than that of HSI stocks. A long-memory effect is also reported for the logarithmic standard deviations of all shares, with most of them showing slow decay over the series.     

Estimating stochastic volatility via filtering for the micromovement of asset prices

Under the general framework of a previous paper, a unified approach via filtering is developed to estimate stochastic volatility for micromovement models. The key feature of the models is that they can be transformed as filtering problems with counting process observations. In order to obtain trade-by-trade, real-time Bayes estimates of stochastic volatility, the Markov chain approximation method is applied to the filtering equation to construct a consistent recursive algorithm, which computes the joint posterior. To illustrate the approach, a recursive algorithm is constructed in detail for a jumping stochastic volatility micromovement model. Simulation results show that the Bayes estimates for stochastic volatilities capture the movement of volatility. Trade-by-trade stochastic volatility estimates for a Microsoft transaction data set are obtained and they provide strong affirmative evidence that volatility changes even more dramatically at trade-by-trade level.     

Portfolio optimization when risk factors are conditionally varying and heavy tailed

Assumptions about the dynamic and distributional behavior of risk factors are crucial for the construction of optimal portfolios and for risk assessment. Although asset returns are generally characterized by conditionally varying volatilities and fat tails, the normal distribution with constant variance continues to be the standard framework in portfolio management. Here we propose a practical approach to portfolio selection. It takes both the conditionally varying volatility and the fat-tailedness of risk factors explicitly into account, while retaining analytical tractability and ease of implementation. An application to a portfolio of nine German DAX stocks illustrates that the model is strongly favored by the data and that it is practically implementable.     

On generalised asymmetric stochastic volatility models

Stochastic volatility (SV) models have been considered as a real alternative to time-varying volatility of the ARCH family. Existing asymmetric SV (ASV) models treat volatility asymmetry via the leverage effect hypothesis. Generalised ASV models that take account of both volatility asymmetry and normality violation expressed simultaneously by skewness and excess kurtosis are introduced. The new generalised ASV models are estimated using the Bayesian Markov Chain Monte Carlo approach for parametric and log-volatility estimation. By using simulated and real financial data series, the new models are compared to existing SV models for their statistical properties, and for their estimation performance in within and out-of-sample periods. Results show that there is much to gain from the introduction of the generalised ASV models.     

Robust Artificial Neural Networks for Pricing of European Options

The option pricing ability of Robust Artificial Neural Networks optimized with the Huber function is compared against those optimized with Least Squares. Comparison is in respect to pricing European call options on the S&P 500 using daily data for the period April 1998 to August 2001. The analysis is augmented with the use of several historical and implied volatility measures. Implied volatilities are the overall average, and the average per maturity. Beyond the standard neural networks, hybrid networks that directly incorporate information from the parametric model are included in the analysis. It is shown that the artificial neural network models with the use of the Huber function outperform the ones optimized with least squares. JEL Classification: G13, G14     

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.     

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.     

A variance frontier model of market volatility: an empirical application

Two variance frontier models are proposed and empirically estimated here to test market volatility. By measuring market volatility by temporal variances, the impact of skewness and asymmetry is directly estimated over monthly return data on several market indices over two subperiods: January 1965–December 1974 and Auguast 1982–December 1991. The empirical applications tend to provide strong support to the asymmetrical impact of skewness on variance and also the persistence of market volatility.     

Testing serial correlation in fixed effects regression models based on asymptotically unbiased autocorrelation estimators

Testing the presence of serial correlation in the error terms in fixed effects regression models is important for many reasons. This paper proposes portmanteau tests based on the sum of the squares of autocorrelation estimators. This approach is a direct extension of the Box–Pierce or Ljung–Box test from single time series to panel data settings. In fixed effects regression analysis, we may estimate the autocorrelations using the within-group autocorrelations of the residuals. However, the within-group autocorrelations may be severely biased when the length of the time series is not very large compared with the cross-sectional sample size, as a result of the incidental parameters problem. We overcome this problem by using asymptotically unbiased autocorrelation estimators for long panel data recently proposed by the author. Monte Carlo simulations reveal that the proposed tests have good size properties and are powerful against a wide range of alternatives.     

Estimation of Dynamic Mixed Hitting Time Model Using Characteristic Function Based Moments

We present a characteristic function-based method for the estimation of dynamic mixed hitting time model for duration between events and price changes. The model specifies duration between events as the first time a latent component of multivariate Brownian motion crosses a random boundary. Meanwhile, another (correlated) Brownian component generates the prices. The proposed estimation method facilitates computation and overcomes problems related to the discretization error in the moment conditions and the non-tractability in the joint probability density function. An empirical application using transaction level data on stocks of a large capitalization company traded on the Indonesia Stock Exchange is illustrated. Estimation results suggest that durations and return volatility have strong persistence and, further, there is a negative instantaneous relation between volatility and contemporaneous duration. The impact of considering the causality relation between volatilities and durations on instantaneous volatility estimate are also investigated.     

Bitcoin as an alternative investment vehicle

This paper documents time series momentum in Bitcoin returns. The paper finds persistence in returns for one to 8 weeks that partially reverses over longer horizons, consistent with sentiment theories of initial under-reaction and delayed over-reaction. The time series momentum in Bitcoin returns is similar to that of the other asset returns while the time span is much shorter. This may be due to much quicker nature and shorter term memory of Bitcoin investors. A combined portfolio of S&P500 and Bitcoin momentum strategy shows enhanced expected return, skewness, kurtosis and Value at Risk for given levels of portfolio return volatility.     

Fuzzy-wavelet based prediction of Earth rotation parameters

Prediction of Earth rotation parameters (ERPs) is of importance especially for near real-time applications including navigation, remote sensing, and hazard monitoring. Therefore, prediction of ERPs at least over a few days in the future is necessary.Fuzzy-inference systems (FIS) are increasingly popular and have advantage over classical FFT that lacks stochastic stability due to non-stationarity, multiscaling, and persistent autocorrelations. Wavelet filtering can be used to handle such phenomenon. A FIS rule-base created from ERP time series, where the volatilities (returns) of the preprocessed series are used, and high frequency signals removed, is summarized. The performance of this system, trained using the fuzzy-wavelet method, is compared with that of a conventional FIS, trained on raw time series. The results show that the predictions by the fuzzy-wavelet method are superior to the FIS-only model for short-term predictions (up to 10 days in future). The improvement of prediction accuracy is found to be about 30% in terms of RMS error.