VaR Analysis for the Shanghai Stock Market (original) (raw)
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Empirical analysis of asymmetric long memory volatility models in value-at-risk estimation
has emerged as the standard tool for measuring and managing financial market risk. In this paper, we study the effects of asymmetric long memory volatility models on the accuracy of stock index return VaR estimates. We also investigate the relevance of Student's t and skewed Student's t-distribution innovations in analyzing volatility stylized facts, such as volatility clustering, volatility asymmetry and volatility persistence or long memory in volatilities, in some developed and emerging stock markets. In order to do so, we evaluate and compare the performance of asymmetric, FIEGARCH and FIAPARCH, versus symmetric, FIGARCH, long memory VaR models, respectively with normal, Student's t and skewed Student's t-distributions. Based on individual market indexes for selected developed and emerging stock markets, the empirical results show that, using Kupiec's likelihood ratio tests, the FIAPARCH(1, d, 1) model with skewed Student's t innovation is more accurate in in-sample VaR analysis for long and short trading positions than the other models. For out-of sample VaR analysis, the FIAPARCH(1, d, 1) model with Student's t-distribution innovation provided more accurate VaR calculations in capturing stylized facts in the volatility of our sample returns. Thus, in-sample and out-of-sample VaR values computed using asymmetric long memory volatility models have better accuracy than those generated using the symmetric FIGARCH model and the correct assumption of return distribution might improve the estimated performance of VaR models in the stock markets. Asymmetric long memory volatility models in value-at-risk estimation 59 2 Baillie et al (1996) provide information about the presence of fractionally integrated behavior in the conditional variance of nominal US dollar-deutschmark exchange rates. 3 The lags of the fractional differencing operator are truncated at 1,000, which is large enough to examine the long memory process. have proposed other asymmetric Student's t densities. 15 Giot and Laurent (2003) show that an asymmetric power autoregressive conditional heteroskedasticity (AR-APARCH) model with a skewed Student's t density succeeds in correctly forecasting (both in-and out-of-sample) the one-day-ahead VaR for three international stock indexes and three US stocks of the Dow Jones index. Models based on the normal or Student's t-distributions clearly underperform when applied to the same data sets. 16 The asymmetry coefficient ξ > 0 is defined such that the ratio of probability masses above and below the mean is (P (ε ≥ 0/ξ )/P (ε < 0/ξ )) = ξ 2 .
Estimation of Value at Risk (VaR) Based On Lévy-GARCH Models: Evidence from Tehran Stock Exchange
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.
Journal of Economic and Financial Sciences, 2012
Given the volatile nature of global financial markets, managing as well as predicting financial risk plays an increasingly important role in banking and finance. The Value at Risk (VaR) measure has emerged as the most prominent measure of downside market risk. It is measured as the alpha quantile of the profit and loss distribution. Recently a number of distributions have been proposed to model VaR: these include the extreme value theory distributions (EVT), Generalized Error Distribution (GED), Student’s t, and normal distribution. Furthermore, asymmetric as well as symmetric volatility models are combined with these distributions for out-sample VaR forecasts. This paper assesses the role of the distribution assumption and volatility specification in the accuracy of VaR estimates using daily closing prices of the Johannesburg Stock Exchange All Share Index (JSE ALSI). It is found that Student’s t distribution combined with asymmetric volatility models produces VaR estimates in out-...
Parametric Value-at-Risk analysis: Evidence from stock indices
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.
International Review of Financial Analysis, 2011
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 use daily data for three groups of stock market indices, namely Developed, Southeast Asia and Latin America. The data covers the period 1987-2009. We conduct our analysis with the adoption of the methodology suggested by Giot and Laurent (2003). Therefore, we estimate 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 Kupie"s (1995) Likelihood Ratio test on the empirical failure test. Moreover, for the case of the skewed Student APARCH model we compute the expected shortfall and the average multiple of tail event to risk measure. These two measures help 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: The case of the Athens Stock Exchange
2006
This paper provides Value-at-Risk estimates 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 use daily data for three stock indexes of the Athens Stock Exchange (ASE) and three stocks of Greek companies listed in the ASE. We conduct our analysis with the adoption of the methodology suggested by Giot and Laurent (2003). Therefore, we estimate an APARCH model based on the skewed Student distribution to fully take into account the fat left and right tails of the returns distribution. We show that the estimated VaR for traders having both long and short positions in the Athens Stock Exchange is more accurately modeled by a skewed Student APARCH model that by a normal or Student distributions.
A new generalization of skew-T distribution with volatility models
Journal of Statistical Computation and Simulation, 2018
In this paper, we propose a new generalized alpha-skew-T (GAST) distribution for generalized autoregressive conditional heteroskedasticity (GARCH) models in modelling daily Value-at-Risk (VaR). Some mathematical properties of the proposed distribution are derived including density function, moments and stochastic representation. The maximum likelihood estimation method is discussed to estimate parameters via a simulation study. Then, the real data application on S&P-500 index is performed to investigate the performance of GARCH models specified under GAST innovation distribution with respect to normal, Student's-t and Skew-T models in terms of the VaR accuracy. Backtesting methodology is used to compare the out-ofsample performance of the VaR models. The results show that GARCH models with GAST innovation distribution outperforms among others and generates the most conservative VaR forecasts for all confidence levels and for both long and short positions.
Assessing the Performance of Value-at-Risk Models in Chinese Stock Market
2008
In this paper, parametric, nonparametric, and semi-parametric models are applied to a hypothetical portfolio-Shanghai Stock Exchange Composite Index to estimate Value-at-Risk in Chinese market. In order to assess the performance of different approaches, the statistic features such as kurtosis, skewness and autocorrelation of daily return have been studied. In addition, this article analyzes the advantages and disadvantages of each model and implements back-tests to check the validation of them.
A Detailed Comparison of Value at Risk in International Stock Exchanges
2003
This work investigates the performance of different models of Value at Risk (VaR). We include a wider range of methods (Parametric, Historical simulation, Monte Carlo simulation, and Extreme value theory models) and several models to compute the conditional variance (exponential moving averages, GARCH and asymmetric GARCH models) under Normal and Student's t-distribution of returns. We analyse four European indexes (IBEX-35, CAC40, DAX and FTSE100), the American Dow Jones and S&P 500 indexes, the Japanese Nikkei 225 index and the Hong Kong Hang Seng index. We examine two periods: a stable period and a volatile one. To choose the best model, we employ a two-stage selection approach. First, we test the accuracy of different models of VaR. We use the unconditional and conditional coverage test, the Back-Testing criterion and the dynamic quantile test. A model survived if all tests indicated the model is accurate. With regard to the first stage, the best models are Parametric and Extreme value theory methods, when they use asymmetric and nonasymmetric GARCH models under Student's t-distribution of returns. Second, we evaluate the loss function of these models. We use several non-parametric tests to test the superiority of a VaR model in terms of the loss function. The result of the second stage indicates that the best model is a Parametric model with conditional variance estimated by asymmetric GARCH model under Student's t-distribution of returns. Nowadays the Parametric models are not as popular because some authors argue that the most conventional parametric specifications have failed in capturing some rare events. However, this paper shows that these models can obtain successful VaR measures if conditional variance is estimated with a GARCH model to capture the characteristic of the returns. This model is usually an exponential GARCH under Student's t-distribution of returns. JEL: G32, G11, C52.
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.