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.

     

Tail risk in emerging markets of Southeastern Europe

This article examines the left-tail behaviour of returns on stocks in Southeastern Europe (SEE). We apply conditional extreme value theory (EVT) approach on daily returns of six stock market indices from SEE between 2004 and 2013. Predictive performance of value-at-risk (VaR) and expected shortfall (ES) based on EVT is compared against several alternatives, such as historical simulation and analytical approach based on GARCH with a single conditional distribution. Model backtesting with daily returns shows that EVT-based models provide more reliable VaR and ES forecasts than the alternative models in all six markets. Unlike the alternatives, the EVT-based models cannot be rejected as VaR confidence level is increased. This emphasizes the importance of extreme events in SEE markets and indicates that the ability of a model to capture volatility clustering accurately is not sufficient for a correct assessment of risk in these markets.     

Realized volatility models and alternative Value-at-Risk prediction strategies

We assess the Value-at-Risk (VaR) forecasting performance of recently proposed realized volatility (RV) models combined with alternative parametric and semi-parametric quantile estimation methods. A benchmark inter-daily GJR-GARCH model is also employed. Based on four asset classes, i.e. equity, FOREX, fixed income and commodity, and a turbulent six year out-of-sample period (2007–2013), we find that statistical accuracy and regulatory compliance is essentially improved when we use quantile methods which account for the fat tails and the asymmetry of the innovations distribution. In particular, empirical analysis gives evidence in favor of the skewed student distribution and the Extreme Value Theory (EVT) method. Nonetheless, efficiency of VaR estimates, as defined by the minimization of Basel II capital requirements and its opportunity costs, is reassured only with the use of realized volatility models. Overall, empirical evidence support the use of an asymmetric HAR realized volatility model coupled with the EVT method since it produces statistically accurate VaR forecasts which comply with Basel II accuracy mandates and allows for more efficient capital allocations.     

Modelling VaR for foreign-asset portfolios in continuous time

VaR is widely viewed as a measure of market risk of a portfolio. The purpose of this article is to provide a VaR model for foreign-asset portfolios in continuous time. In the VaR model, the VaRs are not only a function of volatilities of asset returns and exchange rate but also a function of correlation coefficient between foreign assets and exchange rate. Moreover, by backtesting, the empirical results show that the new VaR model can efficiently evaluate the market risk of foreign-asset portfolios.     

Full versus quasi MLE for ARMA-GARCH models with infinitely divisible innovations

We compare the backtesting performance of ARMA-GARCH models with the most common types of infinitely divisible innovations, fit with both full maximum likelihood estimation (MLE) and quasi maximum likelihood estimation (QMLE). The innovation types considered are the Gaussian, Student’s t, α-stable, classical tempered stable (CTS), normal tempered stable (NTS) and generalized hyperbolic (GH) distributions. In calm periods of decreasing volatility, MLE and QMLE produce near identical performance in forecasting value-at-risk (VaR) and conditional value-at-risk (CVaR). In more volatile periods, QMLE can actually produce superior performance for CTS, NTS and α-stable innovations. While the t-ARMA-GARCH model has the fewest number of VaR violations, rejections by the Kupeic and Berkowitz tests suggest excessively large forecasted losses. The α-stable, CTS and NTS innovations compare favourably, with the latter two also allowing for option pricing under a single market model.     

Value at risk forecasting for volatility index

Forecasts of values at risk (VaRs) are made for volatility indices such as the VIX for the US S&P 500 index, the VKOSPI for the KOSPI (Korea Stock Price Index) and the OVX (oil volatility index) for crude oil funds, which is the first in the literature. In the forecasts, dominant features of the volatility indices are addressed: long memory, conditional heteroscedasticity, asymmetry and fat-tails. An out-of-sample comparison of the VaR forecasts is made in terms of violation probabilities, showing better performance of the proposed method than several competing methods which consider the features differently from ours. The proposed method is composed of heterogeneous autoregressive model for the mean, GARCH model for the volatility and skew-t distribution for the error.     

Volatility and VaR forecasting in the Madrid Stock Exchange

This paper provides an empirical study to assess the forecasting performance of a wide range of models for predicting volatility and VaR in the Madrid Stock Exchange. The models performance was measured by using different loss functions and criteria. The results show that FIAPARCH processes capture and forecast more accurately the dynamics of IBEX-35 returns volatility. It is also observed that assuming a heavy-tailed distribution does not improve models ability for predicting volatility. However, when the aim is forecasting VaR, we find evidence of that the Student’s t FIAPARCH outperforms the models it nests the lower the target quantile.      

Estimating value-at-risk under a Heath–Jarrow–Morton framework with jump

This article proposes a new methodology for measuring Value-at-Risk (hereafter VaR) using a model that incorporates both volatility and jumps. Heath–Jarrow–Morton (HJM) model has been used for the valuation of interest rate derivatives. This study extends the use of HJM model to the estimation VaR. This article specifically uses a two-factor HJM jump-diffusion model for the computation. The study models the Eurodollar futures prices using its derivatives. In addition, this article uses a new volatility specification of Ze-To (2002) to construct the HJM dynamics. The result indicates that the VaR model using HJM jump-diffusion framework performs well in capturing the nonnormality and in providing accurate VaR forecasts in the in-sample and out-sample tests.     

Markets liquidity risk under extremal dependence: Analysis with VaRs methods

Value-at-Risk (VaR) is a widely used tool for assessing financial market risk. In practice, the estimation of liquidity extreme risk by VaR generally uses models assuming independence of bid–ask spreads. However, bid–ask spreads tend to occur in clusters with time dependency, particularly during crisis period. Our paper attempts to fill this gap by studying the impact of negligence of dependency in liquidity extreme risk assessment of Tunisian stock market. The main methods which take into account returns dependency to assess market risk is Time series–Extreme Value Theory combination. Therefore we compare VaRs estimated under independency (Variance–Covariance Approach, Historical Simulation and the VaR adjusted to extreme values) relatively to the VaR when dependence is considered. The efficiency of those methods was tested and compared using the backtesting tests. The results confirm the adequacy of the recent extensions of liquidity risk in the VaR estimation. Therefore, we prove a performance improvement of VaR estimates under the assumption of dependency across a significant reduction of the estimation error, particularly with AR (1)-GARCH (1,1)-GPD model.     

Forecasting the volatility of S&P depositary receipts using GARCH-type models under intraday range-based and return-based proxy measures

We employ four various GARCH-type models, incorporating the skewed generalized t (SGT) errors into those returns innovations exhibiting fat-tails, leptokurtosis and skewness to forecast both volatility and value-at-risk (VaR) for Standard & Poor's Depositary Receipts (SPDRs) from 2002 to 2008. Empirical results indicate that the asymmetric EGARCH model is the most preferable according to purely statistical loss functions. However, the mean mixed error criterion suggests that the EGARCH model facilitates option buyers for improving their trading position performance, while option sellers tend to favor the IGARCH/EGARCH model at shorter/longer trading horizon. For VaR calculations, although these GARCH-type models are likely to over-predict SPDRs' volatility, they are, nevertheless, capable of providing adequate VaR forecasts. Thus, a GARCH genre of model with SGT errors remains a useful technique for measuring and managing potential losses on SPDRs under a turbulent market scenario.     

Volatility and Market Risk of Rubber Price in Malaysia: Pre- and Post-Global Financial Crisis

The volatility in rubber price is a significant risk to producers, traders, consumers and others who are involved in the production and marketing of natural rubber. Such being the case, forecasting the rubber price volatility is desired to assist in decision-making in this uncertain situation. The 2008 Global Financial Crisis caused some disruptions and uncertainties in the future supply or demand for natural rubber and thus leading to higher rubber price volatility. Using ARCH-type models, this paper intends to model the dynamics of the price volatility of Standard Malaysia Rubber Grade 20 (SMR 20) in the Malaysian market before and after the Global Financial Crisis. Additionally, Value-at-Risk (VaR) approach is implemented to evaluate the market risk of SMR 20. Our empirical result denotes the existence of volatility clustering and long memory volatility in the SMR 20 market for both crisis periods. Leverage effect is also detected in the SMR 20 market where negative innovations (bad news) have a larger impact on the volatility than positive innovations (good news) for post-crisis period. When tested with Superior Predictive Ability (SPA) test, FIGARCH model is the best model across five loss functions for short- and long-term forecasts for pre-crisis period. Meanwhile, over post-crisis period, FIGARCH and GJR GARCH indicate the superior out-of-sample-forecast results and better forecasting accuracy over short- and long-term horizons, respectively. In terms of market risk, the short trading position encounters higher risk or greater losses than the long trading position at both 1 and 5 % VaR quantile for pre-crisis period. In contrast, over post-crisis period, long traders of rubber SMR 20 tend to face limited gains but unlimited losses.

     

Forecasting the volatility of S&P depositary receipts using GARCH-type models under intraday range-based and return-based proxy measures

We employ four various GARCH-type models, incorporating the skewed generalized t (SGT) errors into those returns innovations exhibiting fat-tails, leptokurtosis and skewness to forecast both volatility and value-at-risk (VaR) for Standard & Poor's Depositary Receipts (SPDRs) from 2002 to 2008. Empirical results indicate that the asymmetric EGARCH model is the most preferable according to purely statistical loss functions. However, the mean mixed error criterion suggests that the EGARCH model facilitates option buyers for improving their trading position performance, while option sellers tend to favor the IGARCH/EGARCH model at shorter/longer trading horizon. For VaR calculations, although these GARCH-type models are likely to over-predict SPDRs' volatility, they are, nevertheless, capable of providing adequate VaR forecasts. Thus, a GARCH genre of model with SGT errors remains a useful technique for measuring and managing potential losses on SPDRs under a turbulent market scenario.     

基于GARCH模型的证券投资基金VaR计算与实证研究

基于统计技术的度量金融市场风险值(Value at Risk,VaR)已成为测量市场风险的新标准和新方法。鉴此,如何高效、准确地进行VaR的计算将是问题所在。基于GARCH模型,讨论了对数收益率时间序列在正态、学生t和广义误差(GED)三种不同分布下的VaR计算方法,对样本基金的市场风险进行估计,并通过返回检验来检验模型的准确性。研究结果表明,基于GED分布的GARCH模型计算的VaR值最能真实地反映基金风险。     

How did the demise of international commodity agreements affect volatility of primary commodity prices?

This article has used the T-GARCH and E-GARCH models to answer the following two questions regarding the pattern of volatility of commodity prices following the demise of international commodity agreements (hereafter ICAs) in five key commodities: firstly, the question of whether the collapse or suspension of ICAs contributed to asymmetry in price volatility and secondly, the question of whether the collapse or suspension of ICAs led to an increase in persistence in price volatility. The results show that breakdown of ICAs was generally followed by higher degree asymmetry in price volatility but lower persistence in volatility.     

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.     

Risk assessment of oil price from static and dynamic modelling approaches

The price gap between West Texas Intermediate (WTI) and Brent crude oil markets has been completely changed in the past several years. The price of WTI was always a little larger than that of Brent for a long time. However, the price of WTI has been surpassed by that of Brent since 2011. The new market circumstances and volatility of oil price require a comprehensive re-estimation of risk. Therefore, this study aims to explore an integrated approach to assess the price risk in the two crude oil markets through the value at risk (VaR) model. The VaR is estimated by the extreme value theory (EVT) and GARCH model on the basis of generalized error distribution (GED). The results show that EVT is a powerful approach to capture the risk in the oil markets. On the contrary, the traditional variance–covariance (VC) and Monte Carlo (MC) approaches tend to overestimate risk when the confidence level is 95%, but underestimate risk at the confidence level of 99%. The VaR of WTI returns is larger than that of Brent returns at identical confidence levels. Moreover, the GED-GARCH model can estimate the downside dynamic VaR accurately for WTI and Brent oil returns.     

基于GARCH模型的VaR方法对我国开放式基金风险的分析

本文从我国开放式基金收益率序列的分布与波动性两方面建立了一个估计基金风险的VaR-GARCH模型,在正态分布和能够刻画收益率的尖峰厚尾特征的t分布GED分布三种不同的分布假设下,对基金的VaR值进行估计,并应用Kupiec失败频率检验方法对VaR模型的准确性进行了返回检验。结果显示,基于GED分布的GARCH模型计算的VaR值比基于正态分布和t分布GARCH模型计算的VaR值更真实地反映了基金的风险。     

基于GJR—ALaplace方法的开放式基金风险研究

根据我国开放式基金收益率序列的尖峰、厚尾、有偏和波动时变的特征,引入非对gg,Laplace分布对收益率序列进行刻画和拟合。构建度量基金风险的动态GJR—Asymmetric～Laplace模型,在非对称Laplace分布、Laplace分布和正态分布三种分布假设下测算VaR,并做返回检验。选取12只开放式基金在2007．01．04～2009．12．31期间的日累计净值数据做实证研究。实证表明：除了基金大成债券外,其余11只基金显著通过假设,符合非对称Laplace分布,相rELaplace分布和正态分布来说,非对称Laplace分布能更好地拟合基金收益率序列。正态分布假设下风险度量值通过检验的基金数显著少于Laplace分布假设,而Laplace分布下通过检验的基金数亦少于非对称Laplace分布,可知非对称hplace分布假设下得出的基金动态风险值更为有效。     

跳跃随机波动的阈值模型风险值的贝叶斯估计

文章基于一类跳跃随机波动的阈值模型风险值估计贝叶斯分析,在给定先验分布下,以马尔科夫链蒙特卡洛方法估计模型中的未知参数,并给出了MCMC模拟算法,进而讨论了风险值的预测。根据模拟结果,我们得知,如果没有考虑金融时间序列的外生冲击导致的跳跃行为,将会高估风险值,因此考虑跳跃行为后,将增加风险值估计的精度。     

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.