Modeling long memory volatility using realized measures of volatility: A realized HAR GARCH model

Long memory is an important feature of the volatility of financial returns. We document that the recently developed Realized GARCH model (Hansen et al., 2012) is insufficient for capturing the long memory of underlying volatility. We develop a parsimonious variant of the Realized GARCH model by introducing the HAR specification of Corsi (2009) into the volatility dynamics. A comparison of the theoretical and sample autocorrelation functions shows that the new model specification better captures the long memory dynamics of volatility. We calculate the multi-period out-of-sample volatility forecasts for several return series and find that the new model is a significant improvement over the classic Realized GARCH model.     

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.     

QUANTILE FORECASTS OF FINANCIAL RETURNS USING REALIZED GARCH MODELS*

This article applies the realized generalized autoregressive conditional heteroskedasticity (GARCH) model, which incorporates the GARCH model with realized volatility, to quantile forecasts of financial returns, such as Value‐at‐Risk and expected shortfall. Student's t‐ and skewed Student's t‐distributions as well as normal distribution are used for the return distribution. The main results for the S&P 500 stock index are: (i) the realized GARCH model with the skewed Student's t‐distribution performs better than that with the normal and Student's t‐distributions and the exponential GARCH model using the daily returns only; and (ii) using the realized kernel to take account of microstructure noise does not improve the performance.     

Structural breaks and GARCH models of stock return volatility: The case of South Africa

This paper investigates the empirical relevance of structural breaks in forecasting stock return volatility using both in-sample and out-of-sample tests applied to daily returns of the Johannesburg Stock Exchange (JSE) All Share Index from 07/02/1995 to 08/25/2010. We find evidence of structural breaks in the unconditional variance of the stock returns series over the period, with high levels of persistence and variability in the parameter estimates of the GARCH(1,1) model across the sub-samples defined by the structural breaks. This indicates that structural breaks are empirically relevant to stock return volatility in South Africa. However, based on the out-of-sample forecasting exercise, we find that even though there structural breaks in the volatility, there are no statistical gains from using competing models that explicitly accounts for structural breaks, relative to a GARCH(1,1) model with expanding window. This could be because of the fact that the two identified structural breaks occurred in our out-of-sample, and recursive estimation of the GARCH(1,1) model is perhaps sufficient to account for the effect of the breaks on the parameter estimates. Finally, we highlight that, given the point of the breaks, perhaps what seems more important in South Africa, is accounting for leverage effects, especially in terms of long-horizon forecasting of stock return volatility.     

Warrant pricing under GARCH diffusion model

The GARCH diffusion model has attracted a great deal of attention in recent years, as it is able to describe financial time series better, when comparing to many other models. This paper considers the problem of warrant pricing when the underlying asset follows the GARCH diffusion model. An analytical approximate solution for European option prices is derived by means of Fourier transform. The approximate solution can be quickly computed by the fast Fourier transform (FFT) algorithm. Monte Carlo simulations show that this approximate solution is correct and the FFT is accurate and efficient, and hence it enables us to investigate the volatility smile implied by the GARCH diffusion model. Then a method is developed to provide the maximum likelihood (ML) estimation of the GARCH diffusion model based on the efficient importance sampling (EIS) procedure. Furthermore, the empirical performance of the GARCH diffusion model applied to the valuation of Hang Seng Index (HSI) warrants traded on the Hong Kong Stock Exchange (HKEx) is investigated. Empirical results show that the GARCH diffusion model outperforms the Black–Scholes (B–S) model in terms of the pricing accuracy, indicating that the pricing model incorporated with stochastic volatility can improve the pricing of warrants.     

CROSS-COUNTRY EVIDENCE ON OUTPUT GROWTH VOLATILITY: NONSTATIONARY VARIANCE AND GARCH MODELS

This paper revisits the issue of conditional volatility in real gross domestic product (GDP) growth rates for Canada, Germany, Italy, Japan, the United Kingdom, and the United States. Previous studies find high persistence in the volatility. This paper shows that this finding largely reflects a nonstationary variance. Output growth in the six countries became noticeably less volatile over the past few decades. In this paper, we employ the modified iterated cumulative sum of squares (ICSS) algorithm to detect structural change in the variance of output growth. One structural break exists in each of the six countries after identifying outliers and mean shifts in the growth rates. We then use generalized autoregressive conditional heteroskedasticity (GARCH) specifications, modeling output growth and its volatility with and without the break in volatility. The evidence shows that the time-varying variance falls sharply in Canada and Japan, and disappears entirely in Germany, Italy, the United Kingdom and the United States, once we incorporate the break in the variance equation of output for the six countries. That is, the integrated GARCH (IGARCH) effect proves spurious and the GARCH model demonstrates misspecification, if researchers neglect a nonstationary variance. Moreover, we also consider the possible effects of our more correct measure of output volatility on output growth as well as the reverse effect of output growth on its volatility. The conditional standard deviation possesses no statistical significance in all countries, except a significant negative effect in Japan. The lagged growth rate of output produces significant negative and positive effects on the conditional variances in Germany and Japan, respectively. No significant effects exist in Canada, Italy, the United Kingdom, and the United States.     

High-low range in GARCH models of stock return volatility

We suggest a simple and general way to improve the GARCH volatility models using the intraday range between the highest and the lowest price to proxy volatility. We illustrate the method by modifying a GARCH(1,1) model to a range-GARCH(1,1) model. Our empirical analysis conducted on stocks, stock indices and simulated data shows that the range-GARCH(1,1) model performs significantly better than the standard GARCH(1,1) model both in terms of in-sample fit and out-of-sample forecasting ability.     

Asymmetry, realised volatility and stock return risk estimates

In this paper we estimate minimum capital risk requirements for short and long positions with three investment horizons, using the traditional GARCH model and two other GARCH-type models that incorporate the possibility of asymmetric responses of volatility to price changes. We also address the problem of the extremely high estimated persistence of the GARCH model to generate observed volatility patterns by including realised volatility as an explanatory variable into the model??s variance equation. The results suggest that the inclusion of realised volatility improves the GARCH forecastability as well as its ability to calculate accurate minimum capital risk requirements and makes it quite competitive when compared with asymmetric conditional heteroscedastic models such as the GJR and the EGARCH.     

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.     

Measuring volatility persistence in the presence of sudden changes in the variance of Canadian stock returns

Abstract.  It is well known that volatility persistence is overestimated if regime shifts are not accounted for in the standard GARCH model. This research detects time periods of sudden changes in variance using the iterated cumulated sums of squares (ICSS) algorithm. Using weekly data for the Canadian stock market indicates that after accounting for endogenously determined volatility shifts in the GARCH model, the estimated persistence in volatility is significantly reduced. This casts some doubt on previous findings that volatility in financial markets is highly persistent. The findings have important implications for investors and financial market participants. JEL classification: G1     

Inflation targeting in Latin America: Empirical analysis using GARCH models

This paper studies inflation dynamics in eight Latin American countries, some of which have adopted formal inflation targets (IT) as their monetary policy frameworks. We analyze the possible benefits associated with IT, not only in terms of inflation level and volatility, but also regarding other nonlinear characteristics of these series, such as volatility persistence or the fulfillment of the Friedman hypothesis. To describe inflation dynamics we use an unobserved components model, where each component can follow a GARCH type process. Once we estimate the model, the main findings of the empirical exercise confirm the favorable performance of IT.     

On the predictive power of ARJI volatility forecasts for Bitcoin

Motivated by the recent literature on cryptocurrency volatility dynamics, this paper adopts the ARJI, GARCH, EGARCH, and CGARCH models to explore their capabilities to make out-of-sample volatility forecasts for Bitcoin returns over a daily horizon from 2013 to 2018. The empirical results indicate that the ARJI jump model can cope with the extreme price movements of Bitcoin, showing comparatively superior in-sample goodness-of-fit, as well as out-of-sample predictive performance. However, due to the excessive volatility swings on the cryptocurrency market, the realized volatility of Bitcoin prices is only marginally explained by the GARCH genre of employed models.     

Long-Memory,Asymmetry and Fat-Tailed GARCH Models in Value-at-Risk Estimation: Empirical Evidence from the Global Real Estate Markets

In this paper, we address the question of whether long memory, asymmetry, and fat-tails in global real estate markets volatility matter when forecasting the two most popular measures of risk in financial markets, namely Value-at-risk (VaR) and Expected Shortfall (ESF), for both short and long trading positions. The computations of both VaR and ESF are conducted with three long memory GARCH-class models including the Fractionally Integrated GARCH (FIGARCH), Hyperbolic GARCH (HYGARCH), and Fractionally Integrated Asymmetric Power ARCH (FIAPARCH). These models are estimated under three alternative innovation’s distributions: normal, Student, and skewed Student. To test the efficacy of the forecast, we employ various backtesting methodologies. Our empirical findings show that considering for long memory, fat-tails, and asymmetry performs better in predicting a one-day-ahead VaR and ESF for both short and long trading positions. In particular, the forecasting ability analysis points out that the FIAPARCH model under skewed Student distribution turns out to improve substantially the VaR and ESF forecasts. These results may have several potential implications for the market participants, financial institutions, and the government.

     

Trading asymmetric trend and volatility by leverage trend GARCH in Taiwan stock index

This article develops a leverage trend Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model by incorporating asymmetric trend of returns of the exponential autoregressive and asymmetric volatility of GARCH models to study the asymmetric effects. Using in-sample daily data of Taiex over the period 4 January 1980 to 25 August 1997 and postsample daily data over the period 26 August 1997 to 10 September 2007, the evidence reveals that a curvaceous risk–return relationship and both asymmetric volatility and asymmetric trend of returns are significant in Taiex. The episode of asymmetric trend of returns is that the positive information creates a higher return trend than the negative information of the same amount, while similarly to most studies, the evidence of asymmetric volatility appears that the negative information makes a higher volatility than the positive information of the same size. Most remarkably, we evidence that the volatility asymmetry effect is a conservative trading factor and the return trend asymmetry effect is an active trading factor. In comparison of post-sample performance using rolling-window technique, the leverage trend GARCH model indeed outperforms the other three models with single asymmetry adjusted or without asymmetry adjusted, while the asymmetry nonadjusted model performs the worst. It implies that the return trend asymmetry (active trading) and the volatility asymmetry effects (conservative trading) tend to compensate, but not offset each other.     

基于ARIMA与GARCH模型的国际油价预测比较分析

在分析影响油价波动因素的基础上,利用1986年1月至2010年12月的WTI国际原油价格月度数据,分别建立ARIMA和GARCH模型对油价进行预测。并通过对2011年1月至2012年4月WTI原油价格进行外推预测,检验模型的预测效果。比较分析发现,在短期预测中,ARIMA和GARCH模型对油价的预测均比较准确,但当油价由于受到重大事件的影响而有较大波动时,模型的预测精度下降;在长期预测中,GARCH模型的预测效果优于ARIMA模型;整体来看,GARCH模型预测的精度高于ARIMA模型。因此,在国际油价预测中,用GARCH模型是比较合适的。     

TRADING VOLUME,VOLATILITY, AND GARCH EFFECTS IN THE SOUTH KOREAN WON/US DOLLAR EXCHANGE MARKET: EVIDENCE FROM CONDITIONAL QUANTILE ESTIMATION*

Under the MDH, this paper investigates the asymmetry in the positive relationship between unexpected volume and volatility, and whether the unexpected volume series as a proxy for the rate of information arrival absorbs the GARCH effects. This is achieved by applying a quantile regression approach to the won/dollar exchange market with reliable data on trading volumes. Interestingly, the results show that in a freely floating exchange rate system, the positive relationship increases as exchange rate returns are higher. Contrary to previous studies, despite a significantly positive relationship, the inclusion of volumes alone does not reduce volatility persistence at medium or high levels of returns. In addition, the reform of the South Korean exchange rate system had an impact on the relationship, which occurred in response to a financial crisis.     

Stock market uncertainty and interest rate behaviour: a panel GARCH approach

Using a dynamic panel GARCH model for Asian countries, we find that interest rates are significantly lower when stock market uncertainty is high. Evidence of a positive relationship between stock market uncertainty and interest rate volatility is also provided.     

Does VIX or volume improve GARCH volatility forecasts?

This article considers whether the inclusion of two additional variables can improve volatility forecasts over a standard GARCH-based model. We consider three alternative ways of incorporating the volatility index (VIX) and trading volume as exogenous variables within a selection of GARCH models. We are particularly interested in whether these variables have additional incremental forecast power over and above the baseline GARCH specification. Our results suggest that both the VIX and volume do provide some additional forecast power, and this is generally improved when considering both of these series jointly in the model. However, while the results may be statistically significant the gain is marginal and the coefficient values small. Moreover, in a horse race exercise VIX does not outperform the GARCH approach. In answering the question of whether VIX produces better forecasts than the GARCH model, then the answer is no, but the informational content of VIX cannot be ignored and should be incorporated into forecast regressions.     

Is market liquidity less resilient after the financial crisis? Evidence for US Treasuries

Understanding market liquidity resilience, i.e. the capacity of liquidity to absorb shocks, of United States Treasuries is crucial from a financial stability standpoint. The conventional resilience measure has limitations due to the use of the liquidity level. We propose a new complementary approach to analyze resilience based on liquidity volatility. For this purpose, we focus on the link between returns volatility and liquidity volatility, which is a relatively unexplored field. We fit a bivariate conditional correlation (CC-) GARCH model for the 10-year bond returns and five liquidity indicators from January 2003 to June 2016 to analyze persistence and spillovers between these variables in a parsimonious way. We find that after the crisis, spillovers between liquidity volatility and returns volatility are higher, feedback loops are more likely and volatility persistence is lower, which is consistent with a lower resilience. Our results help to explain recent episodes of high volatility in this market.     

GARCH with omitted persistent covariate

This paper analyzes the effect of omitting a persistent covariate in the GARCH-X model. In particular, we show that if the relevant persistent covariate is omitted and the usual GARCH(1,1) model is fitted, the model will be estimated approximately as an IGARCH model. This may well explain the ubiquitous evidence of the IGARCH in empirical volatility analysis.