Forecasting stock market volatility: Further international evidence

Abstract

This paper evaluates the out-of-sample forecasting accuracy of eleven models for monthly volatility in fifteen stock markets. Volatility is defined as within-month standard deviation of continuously compounded daily returns on the stock market index of each country for the ten-year period 1988 to 1997. The first half of the sample is retained for the estimation of parameters while the second half is for the forecast period. The following models are employed: a random walk model, a historical mean model, moving average models, weighted moving average models, exponentially weighted moving average models, an exponential smoothing model, a regression model, an ARCH model, a GARCH model, a GJR-GARCH model, and an EGARCH model. First, standard (symmetric) loss functions are used to evaluate the performance of the competing models: mean absolute error, root mean squared error, and mean absolute percentage error. According to all of these standard loss functions, the exponential smoothing model provides superior forecasts of volatility. On the other hand, ARCH-based models generally prove to be the worst forecasting models. Asymmetric loss functions are employed to penalize under-/over-prediction. When under-predictions are penalized more heavily, ARCH-type models provide the best forecasts while the random walk is worst. However, when over-predictions of volatility are penalized more heavily, the exponential smoothing model performs best while the ARCH-type models are now universally found to be inferior forecasters.     

Implied volatility skews and stock return skewness and kurtosis implied by stock option prices

The Black-Scholes* option pricing model is commonly applied to value a wide range of option contracts. However, the model often inconsistently prices deep in-the-money and deep out-of-the-money options. Options professionals refer to this well-known phenomenon as a volatility ‘skew’ or ‘smile’. In this paper, we examine an extension of the Black-Scholes model developed by Corrado and Su that suggests skewness and kurtosis in the option-implied distributions of stock returns as the source of volatility skews. Adapting their methodology, we estimate option-implied coefficients of skewness and kurtosis for four actively traded stock options. We find significantly nonnormal skewness and kurtosis in the option-implied distributions of stock returns.     

Trading volume and stock market volatility: The Polish case

Relying on the mixture of distributions hypothesis (MDH), this paper investigates the relationship between daily returns and trading volume for 20 Polish stocks. Our empirical results show that in the majority of cases volatility persistence tends to disappear when trading volume is included in the conditional variance equation, which is in agreement with the findings of studies on developed stock markets. However, we cannot confirm the testable implications of the MDH in all cases, which indicates that future research on the causes and modeling of Polish stock market volatility is necessary.     

Stock volatility predictability in bull and bear markets

The recent literature on stock return predictability suggests that it varies substantially across economic states, being strongest during bad economic times. In line with this evidence, we document that stock volatility predictability is also state dependent. In particular, in this paper, we use a large data set of high-frequency data on individual stocks and a few popular time-series volatility models to comprehensively examine how volatility forecastability varies across bull and bear states of the stock market. We find that the volatility forecast horizon is substantially longer when the market is in a bear state than when it is in a bull state. In addition, over all but the shortest horizons, the volatility forecast accuracy is higher when the market is in a bear state. This difference increases as the forecast horizon lengthens. Our study concludes that stock volatility predictability is strongest during bad economic times, proxied by bear market states.     

我国股指期货与现货市场信息传递与波动溢出关系研究

股指期货与现货市场关系是监管者关注的重点问题。本文采用我国股指期货上市以来1分钟级高频数据,应用向量误差修正模型、方差分解、多元T-GARCH等,考察期现两市信息传递、波动溢出效应的影响。实证结果表明,尽管股指期货和股票市场之间短期内存在相互引导关系,但股票市场价格变动更多来自于自身影响,起主导作用,而且两市长期均衡收敛也是以股票市场占主导地位;两市存在显著的双向波动溢出,期货市场的波动溢出效应强于股票市场的波动溢出效应;两市场存在明显的非对称效应,期货市场对坏消息更为敏感,而现货市场对好消息更为敏感。     

Forecasting stock market volatility and the informational efficiency of the DAX-index options market

Alternative strategies for predicting stock market volatility are examined. In out-of-sample forecasting experiments implied-volatility information, derived from contemporaneously observed option prices or history-based volatility predictors, such as GARCH models, are investigated to determine if they are more appropriate for predicting future return volatility. Employing German DAX-index return data it is found that past returns do not contain useful information beyond the volatility expectations already reflected in option prices. This supports the efficient market hypothesis for the DAX-index options market.     

Dynamic analysis of stock return volatility in an integrated international capital market

This paper examines the dynamic behavior of the stock return volatility for Canada, Japan, Germany, and the United Kingdom. The evidence indicates that international stock return volatility is mainly influenced by the U.S. stock return volatility and the exchange rate volatility, supporting the international capital market integration hypothesis. There seems to be some correlation between stock return volatility and macroeconomic volatility, but the effect is relatively weaker. In addition to the economic fundamentals, the noise component is found to be time varying, confirming the AR(MA)CH specifications in the stock return models.     

The dynamics of the Monday effect in international stock indices

This examination of the temporal dynamics of the international Monday effect is based on 50 countries. Observed between-country differences are characterised by an economic factor based on four indices. The prior day effect captures the tendency for price changes to follow those on the prior day. A bad (good) day occurs when the price change on the prior day is negative (positive). A panel regression with panel corrected standard errors, is used to characterise the way that the Monday effect and the cognate prior day effect systematically vary between countries over the period 1994 to 2006. At the start of the data in 1994, there is a considerable prior day effect which is larger for poor countries. This between-country difference declines over time and has essentially disappeared by 2006. The bad non-Monday effect and the bad-Monday effect also decline over time. Further analysis with six leading economies provides evidence that the prior day influence on Mondays and non-Mondays dates back to at least 1973.     

Computing the market price of volatility risk in the energy commodity markets

In this paper, we demonstrate the need for a negative market price of volatility risk to recover the difference between Black–Scholes [Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654]/Black [Black, F., 1976. Studies of stock price volatility changes. In: Proceedings of the 1976 Meetings of the Business and Economics Statistics Section, American Statistical Association, pp. 177–181] implied volatility and realized-term volatility. Initially, using quasi-Monte Carlo simulation, we demonstrate numerically that a negative market price of volatility risk is the key risk premium in explaining the disparity between risk-neutral and statistical volatility in both equity and commodity-energy markets. This is robust to multiple specifications that also incorporate jumps. Next, using futures and options data from natural gas, heating oil and crude oil contracts over a 10 year period, we estimate the volatility risk premium and demonstrate that the premium is negative and significant for all three commodities. Additionally, there appear distinct seasonality patterns for natural gas and heating oil, where winter/withdrawal months have higher volatility risk premiums. Computing such a negative market price of volatility risk highlights the importance of volatility risk in understanding priced volatility in these financial markets.     

Explaining international stock correlations with CPI fluctuations and market volatility

This paper investigates the dynamic correlations among six international stock market indices and their relationship to inflation fluctuation and market volatility. The current research uses a newly developed time series model, the Double Smooth Transition Conditional Correlation with Conditional Auto Regressive Range (DSTCC-CARR) model. Findings reveal that international stock correlations are significantly time-varying and the evolution among them is related to cyclical fluctuations of inflation rates and stock volatility. The higher/lower correlations emerge between countries when both countries experience a contractionary/expansionary phase or higher/lower volatilities.     

The dynamics of volatility transmission and information flow between ADRs and their underlying stocks

This research examines the dynamics of volatility transmission and information flow between ADRs and the underlying stocks. Using a bivariate GARCH model with BEKK parameterisation, the study investigates how changes in volatility in the ADR market affect the volatility in the underlying equity market and vice versa. The findings suggest a bidirectional volatility transmission and information flow between the ADR and underlying stock markets. ADRs and underlying stocks respond to their own innovations as well as to the innovations in each other's market. The findings are consistent for all countries in the sample as well as for different sub-periods. The evidence suggests that the differences in synchronicity of trading period between the US market and other developed markets included in the sample has had no effect on the volatility transmission and information flow between ADRs and underlying stocks.     

Regime-switching volatility of six East Asian emerging markets

This paper investigates regime-switching behaviour in the return-generating processes of six East Asian emerging stock markets over the period from 1970 to 2004 and examines the specific characteristics of each regime by utilizing Markov-switching variance models. The results show very strong evidence of more than one regime in each of these stock markets. In addition, the conditional probabilities of each regime derived from the model provide mixed evidence regarding the impact of financial liberalization on return volatility.     

News sentiment and stock market volatility

Review of Quantitative Finance and Accounting - This study investigates the effect of news sentiment on stock market volatility using the Generalized Autoregressive Conditional Heteroskedasticity...     

Putty-clay technology and stock market volatility

Firms' first-order conditions imply that stock returns equal investment returns from the production technology. Much applied work uses the adjustment cost technology, which implies that the realized return is high when the investment-capital ratio is high. This paper derives, for an arbitrary stochastic discount factor, the investment return implied by the putty-clay technology. The combination of capital heterogeneity and irreversibility creates a novel channel for return volatility. The investment return is high when the ratio of investment to gross job creation is low. Empirically, the putty-clay feature helps account for U.S. stock market data.     

Information demand and stock market volatility

We study information demand and supply at the firm and market level using data for 30 of the largest stocks traded on NYSE and NASDAQ. Demand is approximated in a novel manner from weekly internet search volume time series drawn from the recently released Google Trends database. Our paper makes contributions in four main directions. First, although information demand and supply tend to be positively correlated, their dynamic interactions do not allow conclusive inferences about the information discovery process. Second, demand for information at the market level is significantly positively related to historical and implied measures of volatility and to trading volume, even after controlling for market return and information supply. Third, information demand increases significantly during periods of higher returns. Fourth, analysis of the expected variance risk premium confirms for the first time empirically the hypothesis that investors demand more information as their level of risk aversion increases.     

There's more to volatility than volume

It is widely believed that fluctuations in transaction volume, as reflected in the number of transactions and to a lesser extent their size, are the main cause of clustered volatility. Under this view bursts of rapid or slow price diffusion reflect bursts of frequent or less frequent trading, which cause both clustered volatility and heavy tails in price returns. We investigate this hypothesis using tick by tick data from the New York and London Stock Exchanges and show that only a small fraction of volatility fluctuations are explained in this manner. Clustered volatility is still very strong even if price changes are recorded on intervals in which the total transaction volume or number of transactions is held constant. In addition the distribution of price returns conditioned on volume or transaction frequency being held constant is similar to that in real time, making it clear that neither of these are the principal cause of heavy tails in price returns. We analyse recent results of Ane and Geman (2000 Ane, T and Geman, H. 2000. Order flow, transaction clock, and normality of asset returns. J. Finance, 55(5): 2259–2284. [Crossref], [Web of Science ®] , [Google Scholar]: J. Finance, 55, 2259–2284) and Gabaix et al. (2003 Gabaix, X, Gopikrishnan, P, Plerou, V and Stanley, H.E. 2003. A theory of power-law distributions in financial market fluctuations. Nature, 423: 267–270. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]: Nature, 423, 267–270), and discuss the reasons why their conclusions differ from ours. Based on a cross-sectional analysis we show that the long-memory of volatility is dominated by factors other than transaction frequency or total trading volume.     

Financial liberalization and changes in the dynamic behaviour of emerging market volatility: Evidence from four Latin American equity markets

This paper examines whether the dynamic behaviour of stock market volatility for four Latin American stock markets (Argentina, Brazil, Chile and Mexico) and a mature stock market, that of the US, has changed during the last two decades. This period corresponds to years of significant financial and economic development in these emerging economies during which several financial crises have taken place. We use weekly data for the period January 1988 to July 2006 and we conduct our analysis in two parts. First, using the estimation of a Dynamic Conditional Correlation model we find that the short-term interdependencies between the Latin America stock markets and the developed stock market strengthened during the Asian, Latin American and Russian financial crises of 1997–1998. However, after the initial period of disturbance they eventually returned to almost their initial (relatively low) levels. Second, the estimation of a SWARCH-L model reveals the existence of more than one volatility regime and we detect a significant increased volatility during the period of crisis for all the markets under examination, although the capital flows liberalization process has only caused moderate shifts in volatility.     

Intraday volatility and periodicity in the Malaysian stock returns

Many empirical studies using high-frequency intraday data from a variety of markets indicate that PGARCH models give superior return volatility forecasts than those produced from standard GARCH models. This paper investigates into modelling approaches of four versions of PGARCH models of high-frequency data of Bursa Malaysia, in particular where the intraday volatility of double U-shaped pattern. It is examined through half-hourly dummy variables, quarterly-hourly dummy variables, Fourier Functional Form (FFF) based variables and spline-based variables. The non-periodic GARCH models, i.e., GARCH, EGARCH and TARCH are used for comparison of performance of best fit. The analysis show that among the four versions of PGARCH models, the half-dummy and the spline-based versions perform the best. EGARCH produced consistently superior results to other GARCH specifications.     

The importance of the volatility risk premium for volatility forecasting

In this paper, we study the role of the volatility risk premium for the forecasting performance of implied volatility. We introduce a non-parametric and parsimonious approach to adjust the model-free implied volatility for the volatility risk premium and implement this methodology using more than 20 years of options and futures data on three major energy markets. Using regression models and statistical loss functions, we find compelling evidence to suggest that the risk premium adjusted implied volatility significantly outperforms other models, including its unadjusted counterpart. Our main finding holds for different choices of volatility estimators and competing time-series models, underlying the robustness of our results.     

International comovement of stock market returns: A wavelet analysis

The assessment of the comovement among international stock markets is of key interest, for example, for the international portfolio diversification literature. In this paper, we re-examine such comovement by resorting to a novel approach, wavelet analysis. Wavelet analysis allows one to measure the comovement in the time–frequency space. In this way, one can characterize how international stock returns relate in the time and frequency domains simultaneously, which allows one to provide a richer analysis of the comovement. We focus on Germany, Japan, UK and US and the analysis is done at both the aggregate and sectoral levels.