Skewed Student Distribution Research Articles

Comparison of the accuracy of models in forecasting VAR and ES Through time

Purpose- Identify the best model/method to accurately forecast the Value-at-Risk (VaR) and the Expected Shortfall (ES) of position. Methodology- The dynamic of each retained return series was estimated with one of retained GARCH-type model combined with one of retained probability distributions (normal, fat-tailed, and skewed) in each retained sub-periods (window). In each window (sub-period), the 1-day ahead VaR and ES were forecasted by using the best selected GARCH-type model. More than 4000 1-day ahead VaR and ES were forecasted with each retained model/method. Based on 252-day rolling-window, forecasted VaR and ES with each retained model/method were backtested around 3750 times. Findings- Our results revealed that the best fitting GARCH-specifications combined with skewed Student or GED distribution enable to accurately forecast VaR more often. However, the best methods based on the best fitting GARCH-specifications combined with the best fitting probability distribution do not improve the frequency of acceptance of the null hypothesis stating the accuracy of the method. The accuracy of models tends to deteriorate during crises periods. Conclusion- Modeling and forecasting the dynamic of retained series with skewed probability distributions (skwed student or wked GED) improve the forecasting accuracy of a parametric or semi parametric model. A performan model in sample may not perform well out sample. Forecasted VaR should be complemented with Stressed VaR or ES. Keywords: VaR, ES, parametric, semi-parametric, backtesting, probability distribution, rolling-window. JEL Codes: G11, C10, C51

Long Memory in the Volatility of Selected Cryptocurrencies: Bitcoin, Ethereum and Ripple

This paper examines the volatility of cryptocurrencies, with particular attention to their potential long memory properties. Using daily data for the three major cryptocurrencies, namely Ripple, Ethereum, and Bitcoin, we test for the long memory property using, Rescaled Range Statistics (R/S), Gaussian Semi Parametric (GSP) and the Geweke and Porter-Hudak (GPH) Model Method. Our findings show that squared returns of three cryptocurrencies have a significant long memory, supporting the use of fractional Generalized Auto Regressive Conditional Heteroscedasticity (GARCH) extensions as suitable modelling technique. Our findings indicate that the Hyperbolic GARCH (HYGARCH) model appears to be the best fitted model for Bitcoin. On the other hand, the Fractional Integrated GARCH (FIGARCH) model with skewed student distribution produces better estimations for Ethereum. Finally, FIGARCH model with student distribution appears to give a good fit for Ripple return. Based on Kupieck’s tests for Value at Risk (VaR) back-testing and expected shortfalls we can conclude that our models perform correctly in most of the cases for both the negative and positive returns.

Selection of Value-at-Risk models for MENA Islamic indices

PurposeThe purpose of this study is to investigate the performance of Value-at-Risk (VaR) models for nine Middle East and North Africa Islamic indices using RiskMetrics and VaR parametric models.Design/methodology/approachThe authors test the performance of several VaR models using Kupiec and Engle and Manganelli tests at 95 and 99 per cent levels for long and short trading positions, respectively, for the period from August 10, 2006 to December 14, 2014.FindingsThe authors’ findings show that the VaR under Student and skewed Student distribution are preferred at a 99 per cent level VaR. However, at 95 per cent level, the VaR forecasts obtained under normal distribution are more accurate than those generated using models with fat-tailed distributions. These results suggest that VaR is a good tool for measuring market risk. The authors support the use of RiskMetrics during calm periods and the asymmetric models (Generalized Autoregressive Conditional Heteroskedastic and the Asymmetric Power ARCH model) during stressed periods.Practical implicationsThese results will be useful to investors and risk managers operating in Islamic markets, because their success depends on the ability to forecast stock price movements. Therefore, because a few Islamic financial institutions use internal models for their capital calculations, the regulatory committee should enhance market risk disclosure.Originality/valueThis study contributes to the knowledge in this area by improving our understanding of market risk management for Islamic assets during the stress periods. Then, it highlights important implications regarding financial risk management. Finally, this study fills a gap in the literature, as most empirical studies dealing with evaluating VaR prediction models have focused on quantifying the model risk in the conventional market.

Long memory mean and volatility models of platinum and palladium price return series under heavy tailed distributions

South Africa is a cornucopia of the platinum group metals particularly platinum and palladium. These metals have many unique physical and chemical characteristics which render them indispensable to technology and industry, the markets and the medical field. In this paper we carry out a holistic investigation on long memory (LM), structural breaks and stylized facts in platinum and palladium return and volatility series. To investigate LM we employed a wide range of methods based on time domain, Fourier and wavelet based techniques while we attend to the dual LM phenomenon using ARFIMA–FIGARCH type models, namely FIGARCH, ARFIMA–FIEGARCH, ARFIMA–FIAPARCH and ARFIMA–HYGARCH models. Our results suggests that platinum and palladium returns are mean reverting while volatility exhibited strong LM. Using the Akaike information criterion (AIC) the ARFIMA–FIAPARCH model under the Student distribution was adjudged to be the best model in the case of platinum returns although the ARCH-effect was slightly significant while using the Schwarz information criterion (SIC) the ARFIMA–FIAPARCH under the Normal Distribution outperforms all the other models. Further, the ARFIMA–FIEGARCH under the Skewed Student distribution model and ARFIMA–HYGARCH under the Normal distribution models were able to capture the ARCH-effect. In the case of palladium based on both the AIC and SIC, the ARFIMA–FIAPARCH under the GED distribution model is selected although the ARCH-effect was slightly significant. Also, ARFIMA–FIEGARCH under the GED and ARFIMA–HYGARCH under the normal distribution models were able to capture the ARCH-effect. The best models with respect to prediction excluded the ARFIMA–FIGARCH model and were dominated by the ARFIMA–FIAPARCH model under Non-normal error distributions indicating the importance of asymmetry and heavy tailed error distributions.

Forecasting daily conditional volatility and h-step-ahead short and long Value-at-Risk accuracy: Evidence from financial data

In this article we evaluate the daily conditional volatility and h-step-ahead Value at Risk (VaR) forecasting power of three long memory GARCH-type models (FIGARCH, HYGARCH & FIAPARCH). The forecasting exercise is done for financial assets including seven stock indices (Dow Jones, Nasdaq100, S&P 500, DAX30, CAC40, FTSE100 and Nikkei 225) and three exchange rates vis-a-vis the US dollar (the GBP- USD, YEN-USD and Euro-USD). Because all return series are skewed and fat tailed, each conditional volatility model is estimated under a skewed Student distribution. Consistent with the idea that the accuracy of VaR estimates are sensitive to the adequacy of the volatility model used, h-step-ahead VaR forecasts are based on the skewed Student-t AR(1)-FIAPARCH (1,d,1). This model can jointly accounts for the salient features of financial time series. Our findings reveal that the skewed Student AR (1) FIAPARCH (1.d.1) relatively outperforms the other models in out-of-sample forecasts for one, five and fifteen day forecast horizons. However, there is no difference for the AR (1) FIGARCH (1.d.1) and AR (1) HYGARCH (1.d.1) models since they have the same forecasting ability. Results indicate also that skewed Student-t FIAPARCH (1,d,1) model provides more accurate one-day-ahead VaR forecasts for both long and short trading positions than those generated using alternative horizons (5-day and 15-day-ahead). This result holds for each of the financial time series.

Forecasting Financial Assets Volatility Using Integrated GARCH-Type Models: International Evidence

In this article we compare the forecasting ability of two symmetric integrated GARCH models (FIGARCH & HYGARCH) with an asymmetric model (FIAPARCH) based on a skewed Student distribution. Each model is used for forecasting the daily conditional variance of 10 financial assets, for a sample period of about 18 years. This exercise is done for seven stock indexes (Dow Jones, NASDAQ, S&P500, DAX30, FTSE100, CAC40 and Nikkei 225) and three exchange rates vis-a-vis the US dollar (the GBP- USD, YEN-USD and Euro-USD). Results indicate that the skewed Student AR (1) FIAPARCH (1.d.1) relatively outperforms the other models in out-of-sample forecasts for one, five and fifteen day forecast horizons. Results indicate also, no difference for the AR (1) FIGARCH (1.d.1) and AR (1) HYGARCH (1.d.1) models since they have the same forecasting ability.

Forecasting the Jordanian stock index: modelling asymmetric volatility and distribution effects within a GARCH framework

The modelling of market returns can be especially problematical in emerging and frontier financial markets given the propensity of their returns to exhibit significant non-normality and volatility asymmetries. This paper attempts to identify which representations within the GARCH family of models can most efficiently deal with these issues. A number of different distributions (normal, Student t, GED and skewed Student) and different volatility of returns asymmetry representations (EGARCH and GJR- -GARCH) are examined. Our data set consists of daily Jordanian stock market returns over the period January 2000 – November 2014. Using both the Superior Predicative Ability (SPA) and Model Confidence Set (MCS) testing frameworks it is found that using GJR-GARCH with a skewed Student distribution most accurately and efficiently forecasts Jordanian market movements. Our findings are consistent with similar research undertaken in respect to developed 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.

Value-at-risk for the long and short trading position with the Pearson type-IV distribution

We examine the value-at-risk where the volatility and returns are modelled via a typical GARCH(1,1) model and the innovations process is the Pearson type-IV distribution. As case studies, we examine the NASDAQ and FTSE100 indices from 12-Dec-1984 to 21-Dec-2000. The model is fitted to the data via maximisation of the logarithm of the maximum likelihood estimator. In sample backtesting is performed by the success-failure ratio, the Kupiec p-test, the Christoffersen tests, the expected shortfall, and the DQ test of Engle and Manganelli. The results indicate that the Pearson type-IV distribution gives better results compared with the skewed student distribution.

Econometric modeling and value-at-risk using the Pearson type-IV distribution

The recent financial crisis of 2007–2009 has challenged the requirements of Basel II agreement on capital adequacy as well as, the appropriateness of value-at-risk (VaR) measurement for properly “back-tested” and “stress-tested” models. This paper reconsiders the use of VaR as a measure for potential risk of economic losses in financial markets. We incorporate a GARCH model where the innovation process follows the Pearson-IV distribution, and the results are compared with the skewed Student-t distribution, in the sense of Fernandez and Steel. As case studies we consider the major historical indices of daily returns, DJIA, NASDAQ Composite, FTSE100, CAC40, DAX, and S&P500. VaR and backtesting are performed by the success–failure ratio, the Kupiec LR test, the Christoffersen independence and conditional coverage tests, the expected shortfall with ESF1 and ESF2 measures, and the dynamic quantile test of Engle and Manganelli. The main findings indicate that the Pearson type-IV distribution gives better results, compared with the skewed student distribution, especially at the high confidence levels, providing a very good candidate as an alternative distributional scheme.

The Role of High Frequency Intra-Daily Data, Daily Range and Implied Volatility in Multi-Period Value-at-Risk Forecasting

In this paper, we assess the informational content of daily range, realized variance, realized bipower variation, two time scale realized variance, realized range and implied volatility in daily, weekly, biweekly and monthly out-of-sample Value-at-Risk (VaR) predictions. We use the recently proposed Realized GARCH model combined with the skewed student distribution for the innovations process and a Monte Carlo simulation approach in order to produce the multi-period VaR estimates. The VaR forecasts are evaluated in terms of statistical and regulatory accuracy as well as capital efficiency. Our empirical findings, based on the S&P 500 stock index, indicate that almost all realized and implied volatility measures can produce statistically and regulatory precise VaR forecasts across forecasting horizons, with the implied volatility being especially accurate in monthly VaR forecasts. The daily range produces inferior forecasting results in terms of regulatory accuracy and Basel II compliance. However, robust realized volatility measures such as the adjusted realized range and the realized bipower variation, which are immune against microstructure noise bias and price jumps respectively, generate superior VaR estimates in terms of capital efficiency, as they minimize the opportunity cost of capital and the Basel II regulatory capital. Our results highlight the importance of robust high frequency intra-daily data based volatility estimators in a multi-step VaR forecasting context as they balance between statistical or regulatory accuracy and capital efficiency.

Are Realized Volatility Models Good Candidates for Alternative Value at Risk Prediction Strategies?

In this paper, we assess the Value at Risk (VaR) prediction accuracy and efficiency of six ARCH-type models, six realized volatility models and two GARCH models augmented with realized volatility regressors. The α-th quantile of the innovation’s distribution is estimated with the fully parametric method using either the normal or the skewed student distributions and also with the Filtered Historical Simulation (FHS), or the Extreme Value Theory (EVT) methods. Our analysis is based on two S&P 500 cash index out-of-sample forecasting periods, one of which covers exclusively the recent 2007-2009 financial crisis. Using an extensive array of statistical and regulatory risk management loss functions, we find that the realized volatility and the augmented GARCH models with the FHS or the EVT quantile estimation methods produce superior VaR forecasts and allow for more efficient regulatory capital allocations. The skewed student distribution is also an attractive alternative, especially during periods of high market volatility.

Value-at-risk for long and short trading positions: Evidence from developed and emerging equity markets

The financial crisis of 2007–2009 has questioned the provisions of Basel II agreement on capital adequacy requirements and the appropriateness of VaR measurement. This paper reconsiders the use of Value-at-risk as a measure for potential risk of economic losses in financial markets by estimating VaR for daily stock returns with the application of various parametric univariate models that belong to the class of ARCH models which are based on the skewed Student distribution. We used daily data for three groups of stock market indices, namely Developed, Southeast Asia and Latin America. The data covered the period 1987–2009. We conducted our analysis with the adoption of the methodology suggested by Giot and Laurent (2003). Therefore, we estimated an APARCH model based on the skewed Student distribution to fully take into account the fat left and right tails of the returns distribution. The main finding of our analysis is that the skewed Student APARCH improves considerably the forecasts of one-day-ahead VaR for long and short trading positions. Additionally, we evaluate the performance of each model with the calculation of Kupiec's (1995) Likelihood Ratio test on the empirical failure test. Moreover, for the case of the skewed Student APARCH model we computed the expected shortfall and the average multiple of tail event to risk measure. These two measures helped us to further assess the information we obtained from the estimation of the empirical failure rates.

Value‐at‐risk for long and short trading positions

AbstractIn this paper we model Value‐at‐Risk (VaR) for daily asset returns using a collection of parametric univariate and multivariate models of the ARCH class based on the skewed Student distribution. We show that models that rely on a symmetric density distribution for the error term underperform with respect to skewed density models when the left and right tails of the distribution of returns must be modelled. Thus, VaR for traders having both longand shortpositions is not adequately modelled using usual normal or Student distributions. We suggest using an APARCH model based on the skewed Student distribution (combined with a time‐varying correlation in the multivariate case) to fully take into account the fat left and right tails of the returns distribution. This allows for an adequate modelling of large returns defined on long and short trading positions. The performances of the univariate models are assessed on daily data for three international stock indexes and three US stocks of the Dow Jones index. In a second application, we consider a portfolio of three US stocks and model its long and short VaR using a multivariate skewed Student density. Copyright © 2003 John Wiley & Sons, Ltd.