Forecasting stock market volatility and information content of implied volatility index

This study investigates the incremental information content of implied volatility index relative to the GARCH family models in forecasting volatility of the three Asia-Pacific stock markets, namely India, Australia and Hong Kong. To examine the in-sample information content, the conditional variance equations of GARCH family models are augmented by incorporating implied volatility index as an explanatory variable. The return-based realized variance and the range-based realized variance constructed from 5-min data are used as proxy for latent volatility. To assess the out-of-sample forecast performance, we generate one-day-ahead rolling forecasts and employ the Mincer–Zarnowitz regression and encompassing regression. We find that the inclusion of implied volatility index in the conditional variance equation of GARCH family model reduces volatility persistence and improves model fitness. The significant and positive coefficient of implied volatility index in the augmented GARCH family models suggests that it contains relevant information in describing the volatility process. The study finds that volatility index is a biased forecast but possesses relevant information in explaining future realized volatility. The results of encompassing regression suggest that implied volatility index contains additional information relevant for forecasting stock market volatility beyond the information contained in the GARCH family model forecasts.     

Predictive ability of asymmetric volatility models at medium-term horizons

Using realized volatility to estimate conditional variance of financial returns, we compare forecasts of volatility from linear GARCH models with asymmetric ones. We consider horizons extending to 30 days. Forecasts are compared using three different evaluation tests. With data from an equity index and two foreign exchange returns, we show that asymmetric models provide statistically significant forecast improvements upon the GARCH model for two of the datasets and improve forecasts for all datasets by means of forecasts combinations. These results extend to about 10 days in the future, beyond which the forecasts are statistically inseparable from each other.     

Empirical Regularities of Financial Market Volatility and Good Modelling Process: Developing Countries’ Exchange Rate Markets Perspective

A survey of contemporary literature suggests that empirical studies on developing economies are few or almost non-existent. Engle and Patton (2001, What good is a volatility model. Quantitative Finance, 1, 237–245) as well as Poon (2005, A Practical Guide to Forecasting Financial Market Volatility. New Jersey: Wiley.) suggest that a good volatility model is one that utilizes the empirical regularities of financial market volatility (of which most were observed on industrialized economies markets). This paper uses exchange rate series from Ghana, Mozambique and Tanzania to show that;

1. they are not different from other financial markets as they exhibit most of the empirical regularities including volatility sign asymmetry, non-normal distribution and volatility clustering. It is however observed that the three exchange rate series are very volatile, with induced volatile shocks highly persistent and asymmetric, and extreme prices commonplace;

2. the ARCH technique (which has been well documented to capture these empirical regularities and produce good forecasts) generally produced a good fit to the three exchange rate series when compared with volatility forecasts generated using the EWMA technique. In the simple analysis of a day-ahead volatility forecast abilities of estimated models, it was observed that best fit does not necessarily ensure best forecast.

     

Asymmetric volatility of stock returns during the Asian crisis: Evidence from Indonesia

This paper investigates the conditional volatility in stock returns in Indonesia over the period covered by the Asian crisis. Rolling regression parameter estimates from three asymmetric volatility models suggested that all parameters, including those capturing asymmetric response, were time-varying. The precise pattern of adjustment was sensitive to model selection. Nevertheless, increases in asymmetric response patterns appear to coincide with the very large exchange rate devaluations in the rupiah over this period and were followed by more general symmetric short-term volatility in the post crisis period. Estimates from a smooth transition volatility model indicated both sign and size asymmetries during the crisis period.     

Financial illness and political virus: the case of contagious crises in the Eurozone

Abstract

This paper investigates the volatility spillover effects from the southern to northern part of the Eurozone during the sovereign debt crisis. Focusing on different phases of the crises, we propose using the dynamic conditional correlation model and the BEKK model to identify possible linkages during the period of 2005–2015. The findings showed that both models behave satisfactorily and are flexible in presenting spillover effects. However, regarding conditional correlations, the asymmetric dynamic conditional correlation model seems to fit better. Additionally, Spain and Italy can significantly damage all strong northern economies, while Greece’s negative shocks are capable of co-moving the French index. Finally, France is the most correlated country within the southern Eurozone.     

High Capital Mobility and Precautionary Demand for International Reserves

The volatility of reserve increment and the opportunity cost of holding reserves play prime role in models of optimal demand for foreign reserves. Most empirical studies find significant rise in the response of reserve demand to volatility during the era of high capital mobility. In contrast, we find that volatility measured as rolling standard deviation of reserve increment provides upwardly biased estimates whereas conditional volatility derived from GARCH models eliminates such bias and provides elasticity estimate closer to the prediction of buffer stock model (0.5). Though the time varying elasticity estimates derived from Kaiman filter exhibit a sharp rise during crises period, it does not exceed theoretical prediction. The RBI’s intervention policy seems to be asymmetric; leaning with wind when rupee depreciates and leaning against wind when rupee appreciates. This evidence seems to indicate that the policy of exchange rate stability had an in-built objective of providing a competitive edge to exporters.

     

Markov regime-switching Beta-t-EGARCH

We suggest a Markov regime-switching (MS) Beta-t-EGARCH (exponential generalized autoregressive conditional heteroscedasticity) model for U.S. stock returns. We compare the in-sample statistical performance of the MS Beta-t-EGARCH model with that of the single-regime Beta-t-EGARCH model. For both models we consider leverage effects for conditional volatility. We use data from the Standard Poor’s 500 (S&P 500) index and also a random sample that includes 50 components of the S&P 500. We study the outlier-discounting property of the single-regime Beta-t-EGARCH and MS Beta-t-EGARCH models. For the S&P 500, we show that for the MS Beta-t-EGARCH model extreme observations are discounted more for the low-volatility regime than for the high-volatility regime. The conditions of consistency and asymptotic normality of the maximum likelihood estimator are satisfied for both the single-regime and MS Beta-t-EGARCH models. All likelihood-based in-sample statistical performance metrics suggest that the MS Beta-t-EGARCH model is superior to the single-regime Beta-t-EGARCH model. We present an application to the out-of-sample density forecast performance of both models. The results show that the density forecast performance of the MS Beta-t-EGARCH model is superior to that of the single-regime Beta-t-EGARCH model.     

Regime-switching in volatility and correlation structure using range-based models with Markov-switching

This study examines latent shifts in the conditional volatility and correlation for the U.S. stock and T-bond data using the two-state Markov-switching range-based volatility and correlation models. This paper comes up with clear evidence of volatility regime-switching in stock indices and T-bond over the crisis period. As regards the process of correlation, we also find evidence of regime changes in correlations between stock indices and T-bond over several financial crises. We conclude that the phenomena of both volatility and correlation regime-switching are triggered by these financial crises. In addition, the range-based volatility and correlation model with regime-switching method could explicitly point out the true date of structure changes in the data generating process for volatility and correlation variables.     

Dynamic conditional score models: a review of their applications

ABSTRACT

In this paper, applications of dynamic conditional score (DCS) models are reviewed and those models are discussed in relation to classical time series models from the literature. DCS models are robust to outliers, which improves their statistical performance compared to classical models. Three applications are presented in order to compare the statistical performances of DCS and classical models in three very different contexts: (i) The QAR (quasi-autoregressive) plus Beta-t-EGARCH (exponential autoregressive conditional heteroscedasticity) model is presented, which is a score-driven expected return plus volatility model. This model is used for daily returns on the DAX (Deutscher Aktienindex) equity index for the period of January 1988 to December 2017. (ii) The score-driven local level and seasonality plus Beta-t-EGARCH model is presented, which is used for daily AFN/USD (Afghan Afghani/United States Dollar) currency exchange rates for the period of March 2007 to July 2017. (iii) The Seasonal-t-QVAR (quasi-vector autoregressive) model is presented, which is a score-driven multivariate dynamic model of location. For this model, monthly US inflation rate and US unemployment rate are used for the period of January 1948 to December 2017. For all applications, the statistical performance of each DCS model is superior to that of a corresponding classical alternative.     

Regime-switching purchasing power parity in Latin America: Monte Carlo unit root tests with dynamic conditional score

We suggest a Monte Carlo simulation-based unit root test of the purchasing power parity theory for Latin American countries. Under the null hypothesis, we use a Markov regime-switching (MS) model with unit root in the conditional location and MS volatility dynamics. Under the alternative hypothesis, the proposed test incorporates Markov regime-switching autoregressive moving average (MS-ARMA) plus MS volatility dynamics. Under both the null and alternative hypotheses, one of the volatility models estimated is Beta-t-EGARCH, which is a recent dynamic conditional score volatility model. We use data on real effective exchange rate time series for 14 Latin American countries. For each country, we estimate by Monte Carlo simulation the critical values of the unit root test. We provide an economic discussion of the unit root test results and also study the robustness of MS-ARMA plus MS volatility with respect to smooth transition autoregressive models with Fourier function.     

Forecasting the oil futures price volatility: A new approach

This study provides a new perspective of modelling and forecasting realized range-based volatility (RRV) for crude oil futures. We are the first to improve the Heterogeneous Autoregressive model of Realized Range-based Volatility (HAR-RRV) model by considering the significant jump components, signed returns and volatility of realized range-based volatility. The empirical results show that the volatility of volatility significantly exists in the oil futures market. Moreover, our new proposed models with significant jump components, signed returns and volatility of volatility can gain higher forecast accuracy than HAR-RRV-type models. The results are robust to different forecasting windows and forecasting horizons. Our new findings are strategically important for investors making better decisions.     

Dynamic conditional score models of degrees of freedom: filtering with score-driven heavy tails

This article extends the quasi-autoregressive (QAR) plus Beta-t-EGARCH (exponential generalized autoregressive conditional heteroscedasticity) dynamic conditional score (DCS) model. For the new DCS model, the degrees of freedom parameter is time varying and tail thickness of the error term is updated by the conditional score. We compare the performance of QAR plus Beta-t-EGARCH with constant degrees of freedom (benchmark model) and QAR plus Beta-t-EGARCH with time-varying degrees of freedom (extended model). We use data from the Standard and Poor’s 500 (S&P 500) index, and a random sample of its 150 components that are from different industries of the United States (US) economy. For the S&P 500, all likelihood-based model selection criteria support the extended model, which identifies extreme events with significant impact on the US stock market. We find that for 59% of the 150 firms, the extended model has a superior statistical performance. The results suggest that the extended model is superior for those industries, which produce products that people usually are unwilling to cut out of their budgets, regardless of their financial situation. We perform an application to compare the density forecast performance of both DCS models. We perform an application to Monte Carlo value-at-risk for both DCS models.     

Modelling conditional heteroskedasticity: Application to the “IBEX-35” stock-return index

This paper compares alternative time-varying volatility models for daily stock-returns using data from Spanish equity index IBEX-35. Specifically, we estimate a parametric family of models of generalized autoregressive heteroskedasticity (which nests the most popular symmetric and asymmetric GARCH models), a semiparametric GARCH model, the generalized quadratic ARCH model, the stochastic volatility model, the Poisson Jump Diffusion model and, finally, a nonparametric model. Those models which use conditional standard deviation (specifically, TGARCH and AGARCH models) produce better fits than all other GARCH models. We also compare the within sample predictive power of all models using a standard efficiency test. Our results show that the asymmetric behaviour of responses is a statistically significant characteristic of these data. Moreover, we observe that specifications with a distribution which allows for fatter tails than a normal distribution do not necessarily outperform specifications with a normal distribution.     

Pricing and hedging options with GARCH-stable proxy volatilities

This article considers modelling nonnormality in return with stable Paretian (SP) innovations in generalized autoregressive conditional heteroskedasticity (GARCH), exponential generalized autoregressive conditional heteroskedasticity (EGARCH) and Glosten-Jagannathan-Runkle generalized autoregressive conditional heteroskedasticity (GJR-GARCH) volatility dynamics. The forecasted volatilities from these dynamics have been used as a proxy to the volatility parameter of the Black–Scholes (BS) model. The performance of these proxy-BS models has been compared with the performance of the BS model of constant volatility. Using a cross section of S&P500 options data, we find that EGARCH volatility forecast with SP innovations is an excellent proxy to BS constant volatility in terms of pricing. We find improved performance of hedging for an illustrative option portfolio. We also find better performance of spectral risk measure (SRM) than value-at-risk (VaR) and expected shortfall (ES) in estimating option portfolio risk in case of the proxy-BS models under SP innovations.

Abbreviation: generalized autoregressive conditional heteroskedasticity (GARCH), exponential generalized autoregressive conditional heteroskedasticity (EGARCH) and Glosten-Jagannathan-Runkle generalized autoregressive conditional heteroskedasticity (GJR-GARCH)     

Volatility forecasting: combinations of realized volatility measures and forecasting models

This article examines financial time series volatility forecasting performance. Different from other studies which either focus on combining individual realized measures or combining forecasting models, we consider both. Specifically, we construct nine important individual realized measures and consider combinations including the mean, the median and the geometric means as well as an optimal combination. We also apply a simple AR(1) model, an SV model with contemporaneous dependence, an HAR model and three linear combinations of these models. Using the robust forecasting evaluation measures including RMSE and QLIKE, our empirical evidence from both equity market indices and exchange rates suggests that combinations of both volatility measures and forecasting models improve the forecast performance significantly.     

Volatility spillover and multivariate volatility impulse response analysis of GFC news events

This article applies two measures to assess spillovers across markets: the Diebold and Yilmaz’s (2012) spillover index and the Hafner and Herwartz’s (2006) analysis of multivariate GARCH models using volatility impulse response analysis. We use two sets of data, daily realized volatility (RV) estimates taken from the Oxford-Man RV library, for the S&P500 and the FTSE, plus 10 years of daily returns series for the New York Stock Exchange Index and the FTSE 100 index. Both data sets capture both the global Financial Crisis (GFC) and the subsequent European Sovereign Debt Crisis (ESDC). The spillover index captures the transmission of volatility to and from markets, plus net spillovers. The Volatility Impulse Responses (VIRF) have to be calibrated to conditional volatility estimated at a particular point in time. We explore the impact of three different shocks, the onset of the GFC, the height of the GFC, and the impact of the ESDC. Our modelling includes leverage and asymmetric effects applying a multivariate GARCH model, and further analysis using both BEKK and diagonal BEKK (DBEKK) models. We find the impact of negative shocks is larger, but shorter in duration, in this case a difference between 3 and 6 months.     

Volatility and dynamic conditional correlations of worldwide emerging and frontier markets

This study examines the relationship between time-varying correlations and conditional volatility among 32 worldwide emerging and frontier stock markets and the MSCI World stock market index from January 2000 to December 2012. Correlations are estimated in the standard and asymmetric dynamic conditional correlation model frameworks. The results can be summarized by three main findings: (1) asymmetry in volatility is not a common phenomenon in emerging and frontier markets; (2) asymmetry in correlations is found only with respect to the Hungarian stock market; and (3) the relationship between volatility and correlations is positive and significant in most countries. Thus, diversification benefits decrease during periods of higher volatility.     

Nonlinear exchange rate dynamics under stochastic official intervention

Many studies employ non-linear models to explain or forecast the exchange rate and find their superiority. This article builds an exchange rate model of managed float under conditional official intervention. In the model, the government minimizes social loss through a trade-off between targeting the exchange rate and lowering intervention costs. We obtain an endogenous threshold model and derive an analytical solution of the exchange rate stochastic interventions. The implication of a managed float causing a lower volatility of the exchange rate has been found by past empirical studies. Our model provides not only a justification for the central banks' conditional interventions but also a rationale for the use of regime-switching models of two states (intervention vs. non-intervention) in the empirical studies of exchange rates.     

Malaysia-EU trade at the industry level: Is there an asymmetric response to exchange rate volatility?

Aftab et al. (Empirica 43:461–485, 2016) in this journal assessed the impact of exchange rate volatility on Malaysia-EU trade at commodity level using the linear ARDL approach of Pesaran et al. (J Appl Econom 16:289–326, 2001) and did not find significant effects in most of the 81 Malaysian exporting and 66 importing industries. In this paper, we argue for asymmetric effects of exchange rate volatility on the same industries’ trades which implies using Shin et al.’s (Festschrift in Honor of Peter Schmidt, Springer, New York, 2014) nonlinear ARDL approach. While we find short-run asymmetric effects of volatility in almost all industries, we find evidence of adjustment asymmetry in 17 exporting and nine importing industries. We also find significant impact or short-run cumulative asymmetry in 12 exporting and six importing industries. The most important finding is significant long-run asymmetric effects in 36 Malaysian exporting industries and 25 Malaysian importing industries. Clearly, trade flows react to an increased exchange rate volatility differently than to a decreased volatility.     

Asymmetric effect of advertising on the Chinese stock market

In this paper, we investigate whether investor attention to advertising has an asymmetric effect on Chinese stock returns by using a multivariate Markov switching model with time-varying regime transition probabilities. Using the Chinese stock market as a setting, we obtain lagged conditional volatility from generalized autoregressive conditional heteroskedasticity (GARCH) for modelling the time-varying transition probabilities of the regime-switching process to capture changes in the market regime. Our evidence documents that the high advertising portfolio does earn higher abnormal return than the low advertising portfolio in low-volatility periods. In high-volatility periods, however, the abnormal return is insignificant when the firm increases advertising spending. Our results support the behavioural model argument that in high-volatility period, advertising information diffuses slowly due to cognitive dissonance. Thus, the effect of advertising on stock returns is asymmetric, and it shows statistical significance in low-volatility periods.