VaR-x: fat tails in financial risk management

Journal of International Financial Markets, Institutions and Money, 2006

This paper studies seven GARCH models, including RiskMetrics and two long memory GARCH models, in Value at Risk (VaR) estimation. Both long and short positions of investment were considered. The seven models were applied to 12 market indices and four foreign exchange rates to assess each model in estimating VaR at various confidence levels. The results indicate that both stationary and fractionally integrated GARCH models outperform RiskMetrics in estimating 1% VaR. Although most return series show fat-tailed distribution and satisfy the long memory property, it is more important to consider a model with fat-tailed error in estimating VaR. Asymmetric behavior is also discovered in the stock market data that t-error models give better 1% VaR estimates than normal-error models in long position, but not in short position. No such asymmetry is observed in the exchange rate data.

Journal of Money and Economy, 2021

Risk (VaR) using GARCH type models with improved return distribution. Value at Risk (VaR) is an essential benchmark for measuring the risk of financial markets quantitatively. The parametric method, historical simulation, and Monte Carlo simulation have been proposed in several financial mathematics and engineering studies to calculate VaR, that each of them has some limitations. Therefore, these methods are not recommended in the case of complications in financial modeling since they require considering a series of assumptions, such as symmetric distributions in return on assets. Because the stock exchange data in the present study are skewed, asymmetric distributions along with symmetric distributions have been used for estimating VaR in this study. In this paper, the performance of fifteen VaR models with a compound of three conditional volatility characteristics including GARCH, APARCH and GJR and five distributional assumptions (normal, Student's t, skewed Student's t and two different Lévy distributions, include normal-inverse Gaussian (NIG) and generalized hyperbolic (GHyp)) for return innovations are investigated in the chemical, base metals, automobile, and cement industries. To do so, daily data from of Tehran Stock Exchange are used from 2013 to 2020. The results show that the GJR model with NIG distribution is more accurate than other models. According to the industry index loss function, the highest and lowest risks are related to the automotive and cement industries.

Review of Quantitative Finance and Accounting, 2011

A number of applications presume that asset returns are normally distributed, even though they are widely known to be skewed leptokurtic and fat-tailed and excess kurtosis. This leads to the underestimation or overestimation of the true value-at-risk (VaR). This study utilizes a composite trapezoid rule, a numerical integral method, for estimating quantiles on the skewed generalized t distribution (SGT) which permits returns innovation to flexibly treat skewness, leptokurtosis and fat tails. Daily spot prices of the thirteen stock indices in North America, Europe and Asia provide data for examining the one-day-ahead VaR forecasting performance of the GARCH model with normal, student's t and SGT distributions. Empirical results indicate that the SGT provides a good fit to the empirical distribution of the log-returns followed by student's t and normal distributions. Moreover, for all confidence levels, all models tend to underestimate real market risk. Furthermore, the GARCH-based model, with SGT distributional setting, generates the most conservative VaR forecasts followed by student's t and normal distributions for a long position. Consequently, it appears reasonable to conclude that, from the viewpoint of accuracy, the influence of both skewness and fat-tails effects (SGT) is more important than only the effect of fat-tails (student's t) on VaR estimates in stock markets for a long position.

2011

The first part of this thesis is devoted to the semiparametric estimation of high quantiles. The classic estimators do not enjoy a desirable property in the presence of linear transformation of the data. To solve this problem, the Peaks Over a Random Threshold (PORT) methodology and PORT estimators are proposed. The consistency and asymptotic normality of the estimators are demonstrated. The finite sample behaviour of the proposed PORT estimators is studied and compared with some competitors. Under the context of financial time series and forecasting Value-at-Risk (VaR), the tendency to clustering of violations problem arises. To deal with this, a new class of independence tests for interval forecasts evaluation is proposed and the choice of one test is addressed. The exact and the asymptotic distributions of the corresponding test statistic are derived. In simulation studies, the proposed test revealed to be more powerful than the other tests under study, with few exceptions. The tendency to clustering of violations problem is related with the discrete Weibull distribution, through the shape parameter. A new estimator for this parameter is proposed. The conditional distribution function and the moments are derived. In order to solve the tendency to clustering of violations problem, a new risk model based on durations between excesses over a high threshold (DPOT) is proposed and compared with state-of-the art models under the probability 0.01, established in the Basel Accords. Under the context of extremal quantiles and using one of the oldest financial time series, the DPOT model and a risk model that uses an PORT estimator are compared with other risk models. In the empirical studies presented, to predict the VaR at a level 0.01 or lower, these models revealed more accuracy than the conditional parametric models widely used by the econometricians.

2016

Financial asset returns are known to be conditionally heteroskedastic and generally non-normally distributed, fat-tailed and often skewed. These features must be taken into account to produce accurate forecasts of Value-at-Risk (VaR). We provide a comprehensive look at the problem by considering the impact that different distributional assumptions have on the accuracy of both univariate and multivariate GARCH models in out-of-sample VaR prediction. The set of analyzed distributions comprises the normal, Student, Multivariate Exponential Power and their corresponding skewed counterparts. The accuracy of the VaR forecasts is assessed by implementing standard statistical backtesting procedures used to rank the different specifications. The results show the importance of allowing for heavy-tails and skewness in the distributional assumption with the skew-Student outperforming the others across all tests and confidence levels. Econometrics 2016, 4, 3 2 of 27

2000

This paper describes alternative approaches to estimate the Value at Risk (VaR) of a position. Four methods are compared: the unconditional case, the model with time varying drift (modeled as an AR(l) process), the model with time varying drift and time varying volatility (modeled as a GARCH(I,l) process) with error terms that are normally distributed, and the model with time varying drift and time varying volatility with error terms that are Student-t distributed. Two issues are important. First, different specifications for mean, variance and fat tailness lead to different point estimates for the associated distribution function and hence to other VaR measures. Second, uncertainty in parameter estimates implies that the VaR also is uncertain. The model with error terms that are t-distributed is the preferred model, since: (I) the time varying volatility incorporates that recent volatility is a better predictor for the future, (2) the time varying volatility makes it possible to us...

This paper presents a comparative evaluation of the predictive performance of conventional univariate VaR models including unconditional normal distribution model, exponentially weighted moving average (EWMA/RiskMetrics), Historical Simulation, Filtered Historical Simulation, GARCH-normal and GARCH Students t models in terms of their forecasting accuracy. The paper empirically determines the extent to which the aforementioned methods are reliable in estimating one-day ahead Value at Risk (VaR). The analysis is based on daily closing prices of the USD/KES exchange rates over the period starting January 03, 2003 to December 31, 2016. In order to assess the performance of the models, the rolling window of approximately four years (n=1000 days) is used for backtesting purposes. The backtesting analysis covers the sub-period from November 2008 to December 2016, consequently including the most volatile periods of the Kenyan shilling and the historical all-time high in September 2015. The empirical results demonstrate that GJR-GARCH-t approach and Filtered Historical Simulation method with GARCH volatility specification perform competitively accurate in estimating VaR forecasts for both standard and more extreme quantiles thereby generally out-performing all the other models under consideration.

2008

This paper introduces new methods of estimating Value-at-Risk (VaR) using Range-Based GARCH (General Autoregressive Conditional Heteroskedasticity) models. These models, which could be either based on the Parkinson Range or Garman-Klasss Range, are applied to 10 stock market indices of selected countries in the Asia-Pacific Region. The results are compared using the traditional methods such as the econometric method based on the ARMA-GARCH models and RiskMetricsTM. The performance of the different models is assessed using the out-of-sample VaR forecasts. Series of likelihood ratio (LR) tests namely: LR of unconditional coverage (LRuc), LR of independence (LRind), and LR of conditional coverage (LRcc) are performed for comparison. The result of the assessment shows that the model based on the Parkinson Range GARCH (1,1) with Student’s t distribution is the best performing model on the 10 stock market indices. It has a failure rate, defined as the percentage of actual return that is s...

The Quarterly Review of Economics and Finance, 2012

We evaluate the performance of several volatility models in estimating one-day-ahead Value-at-Risk (VaR) of seven stock market indices using a number of distributional assumptions. Because all returns series exhibit volatility clustering and long range memory, we examine GARCH-type models including fractionary integrated models under normal, Student-t and skewed Student-t distributions. Consistent with the idea that the accuracy of VaR estimates is sensitive to the adequacy of the volatility model used, we find that AR (1)-FIAPARCH (1,d,1) model, under a skewed Student-t distribution, outperforms all the models that we have considered including widely used ones such as GARCH (1,1) or HYGARCH (1,d,1). The superior performance of the skewed Student-t FIAPARCH model holds for all stock market indices, and for both long and short trading positions. Our findings can be explained by the fact that the skewed Student-t FIAPARCH model can jointly accounts for the salient features of financial time series: fat tails, asymmetry, volatility clustering and long memory. In the same vein, because it fails to account for most of these stylized facts, the RiskMetrics model provides the least accurate VaR estimation. Our results corroborate the calls for the use of more realistic assumptions in financial modeling.

The Journal of Risk, 2016

This paper evaluates the performance of several skewed and symmetric distributions in modeling the tail behavior of daily returns and forecasting Value at Risk (VaR). First, we used some goodness of fit tests to analyze which distribution best fits the data. The comparisons in terms of VaR have been carried out examining the accuracy of the VaR estimate and minimizing the loss function from the point of view of the regulator and the firm. The results show that the skewed distributions outperform the normal and Student-t (ST) distribution in fitting portfolio returns. Following a two-stage selection process, whereby we initially ensure that the distributions provide accurate VaR estimates and then, focusing on the firm´s loss function, we can conclude that skewed distributions outperform the normal and ST distribution in forecasting VaR. From the point of view of the regulator, the superiority of the skewed distributions related to ST is not so evident. As the firms are free to choose the VaR model they use to forecast VaR, in practice, skewed distributions will be more frequently used.