Estimating Conditional Value at Risk in the Tehran Stock Exchange Based on the Extreme Value Theory Using GARCH Models (original) (raw)
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In this paper, we apply extreme value theory (EVT) and time series models to eight developed and emerging stock markets published in the Morgan Stanley Capital International (MSCI) Index. Based on the Human Development Index (HDI) rankings, which are consistent with the MSCI index, we analyse Singapore, Spain, UK and US for developed stock markets and Chile, Russia, Malaysia and Turkey for emerging stock markets. We use the daily prices (in USD) of eight countries for the period from January 2014 to December 2017 and examine the performances of the models based on in-sample testing. Calculating the value-at-risk (VaR) as a risk measure for both right and left tails of the log-returns of the selected models, we compare these countries in terms of their financial risks. The obtained risk measures enable us to discuss the grouping and the ranking of the stock markets and their relative positions.
Quantitative Finance, 2013
Although stock prices fluctuate, the variations are relatively small and are frequently assumed to be normal distributed on a large time scale. But sometimes these fluctuations can become determinant, especially when unforeseen large drops in asset prices are observed that could result in huge losses or even in market crashes. The evidence shows that these events happen far more often than would be expected under the generalized assumption of normal distributed financial returns. Thus it is crucial to properly model the distribution tails so as to be able to predict the frequency and magnitude of extreme stock price returns. In this paper we follow the approach suggested by and combine the GARCH-type models with the Extreme Value Theory (EVT) to estimate the tails of three financial index returns S&P 500, FTSE 100 and NIKKEI 225 representing three important financial areas in the world. Our results indicate that EVT-based conditional quantile estimates are more accurate than those from conventional GARCH models assuming normal or Student's t distribution innovations when doing not only in-sample but also out-of-sample estimation. Moreover, these results are robust to alternative GARCH model specifications. The findings of this paper should be useful to investors in general, since their goal is to be able to forecast unforeseen price movements and take advantage of them by positioning themselves in the market according to these predictions. JEL classification: C52; C53; D46 ; G15
Forecasting Value-at-Risk using GARCH and Extreme-Value-Theory Approaches for Daily Returns
2017
This paper deals with the application of Univariate Generalised Autoregressive Conditional Heteroskedasticity (GARCH) modelling and Extreme Value Theory (EVT) to model extreme market risk for returns on DowJones market index. The study compares the performance of GARCH models and EVT (unconditional & conditional) in predicting daily Value-at-Risk (VaR) at 95% and 99% levels of confidence by using daily returns. In order to demonstrate the effect of using different innovations, GARCH(1,1) under three different distributional assumptions; Normal, Student’s t and skewed Student’s t, is applied to the daily returns. Furthermore, an EVT-based dynamic approach is also investigated, using the popular Peak Over Threshold (POT) method. Finally, an innovation approach is used whereby GARCH is combined with EVT-POT by using the two-step procedure of McNeil (1998). Statistical methods are used to evaluate the forecasting performance of all the models. In this study, it is found that the GARCH m...
Extreme Value Theory as a financial risk measure of the South African stock market
North West University, 2020
The incidence of rare but extreme events appears to be greater in worldwide nancial markets. This implies the need for good risk modelling systems that can envisage the likelihood of risky events in daily market fundamentals, which can help in assessing the likelihood of extreme events such as the 2007-2008 global nancial crisis. A conspicuous candidate theory when dealing with excessive events is extreme value theory (EVT). EVT naturally became the only statistical modelling approach that pledges rm models that quantify extreme risk measures such as value at risk (VaR), expected shortfall (ES) and other related risk measures. In order to overcome issues that are related with reliance prompted by volatility clustering in nancial markets, this study develops a novel approach by applying EVT models to model extreme losses of the ve South African nancial time series exchange/Johannesburg Stock Exchange (FTSE/JSE) closing banking indices, and explores the e ectiveness of risk measures for measuring risk of investment. Fiveday time series for the period of 02 January 2008 to 20 April 2018 is used and this consists of 2575 observations for each bank. The unsteadiness of this stock market invigorated an interest in assessing the underlying three models; asymmetry regime switching generalised autoregressive conditional heteroscedasticity (GARCH). To be speci c, Markov-switching threshold generalised autoregressive conditional heteroscedasticity (MS-TGARCH), Markov-switching exponential generalised autoregressive conditional heteroscedasticity (MS-EGARCH) and Markov-switching GJR generalised autoregressive conditional heteroscedasticity (MS-GJR-GARCH) models, tted using a skewed student-t distribution via maximum likelihood estimation (MLE) method. To capture extreme quantiles and estimate return levels, the generalised extreme value (GEV) with block minima method (BMM) and the generalised Pareto distribution (GPD) with peaks over threshold (POT) are also tted using MLE algorithm. In addition, the hybrid models for the four risk measures are estimated in order to express the tail risk related to extreme quantiles and return levels. The results of regime switching GARCH models suggest that all the three-asymmetry models provide good estimates of volatility clustering, with MS (2)-EGARCH (1,1) outperforming all the models because this model recorded a frequency of one ve times more than MS (2)-TGARCH (1,1) and MS (2)-GJR-GARCH (1,1). Out of the seven statistical loss functions used, this model gives a predictive accuracy of 71.45%. Moreover, results obtained by GEV and GPD showed positive shape parameters indicating a Frechet type distribution with GPD giving a type II Frechet distribution that are appropriate for the data. While estimating extreme quantiles, the 95% and 99% quantiles for GPD model did not change signi cantly, and the same was observed in the GEV distribution. Therefore, the two distributions performed similarly at both intervals. However, GEV shows a better performance as compared to the GPD, since the bias estimation is less for the GEV contrasted to the GPD, giving 6.48% less bias of the GEV than the GPD. In addition, once in 3 years, a daily loss of approximately 7.022% would be observed across the ve banks while using the GEV model. But with the GPD model only 0.9604% would be observed across all the banks. This made a GPD model a better model than a GEV in estimating extreme loses. Finally, the results of risk measures indicated that the Glue VaR risk measure has less risk estimates as contrasted with the other three measures from GEV model and GPD model. To take into account market liquidity constraints and Basel regulations, 5-day risk horizons in addition to the more typical 1-day horizon were being considered. This implies that the computation of economic capital using Glue VaR risk is more conservative than using other risk measures under the GEV model. Therefore, the conclusion that can be made is that GEV and GPD estimates of Glue VaR risk under di erent con dence e levels exhibit analogous characteristics as observed from VaR, ES and conditional tail expectation (CTE). This study extends to stationary features of EVT models. Extension of these models in the literature is quite complicated since it requires speci cation not only on how the usual threshold and MLE parameters change over time, but also those with the bulk distribution component of the models. The study also shows, in the risk management of nancial capital or portfolios, that evaluating the probability of rare extreme events is an important question. This means that EVT provides the robust basis necessary for the statistical modelling of such events and for the computation of extreme risk measures. Furthermore, a base for future researchers for conducting studies on emerging markets, more speci cally in the South African context has also been contributed
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.
Conditional VaR using GARCH-EVT approach: Forecasting Volatility in Tunisian Financial Market
2012
In this paper Extreme Value Theory (EVT) and GARCH model are combined to estimate conditional quantile (VaR) and conditional expected shortfall (the expected size of a return exceeding VaR) so as to estimate risk of assets more accurately. This hybrid model provides a robust risk measure for the Tunisian Stock Market by combining two well known facts about security return time series: dynamic volatility resulting in the well-recognized phenomenon of volatility clustering, and non-normality giving rise to fat tails of the return distribution. We fit GARCH models to return data using pseudo maximum likelihood to estimate the current volatility and use a GPD-approximation proposed by EVT to model the tail of the innovation distribution of the GARCH model. This methodology was compared to the performances of other well-known modeling techniques. Results indicate that GARCH-EVT-based VaR approach
2008
We propose methods in estimating Value-at-Risk (VaR) and expected shortfall (ES); the conditional loss over VaR. Our methodology incorporates the two popular conditional volatility models namely GARCH and exponential weighted moving average (EWMA) in estimating current volatility and applying extreme value theory (EVT) in estimating tail distribution. This study covers ten Asian equity markets, which are Hong Kong, Japan, Singapore, China, Indonesia, Korea, Malaysia, Philippines, Taiwan and Thailand during the period 1993 to 2007. As expected, our conditional EVT models outperform other models with normality assumption in almost all the cases. On the other hand, the conditional EVT models are not trivially different from the filtered historical simulation model (or conditional HS). Regarding the conditional volatility models, even though GARCH can reflect more flexible adjustment than EWMA, the result shows that the simpler EWMA-based models are still useful in both VaR and ES estim...
2007
This paper conducts a comparative evaluation of the predictive performance of various Value at Risk (VaR) models such as GARCH-normal, GARCH-t, EGARCH, TGARCH models, variance-covariance method, historical simulation and filtred Historical Simulation, EVT and conditional EVT methods. Special emphasis is paid on two methodologies related to the Extreme Value Theory (EVT): The Peaks over Threshold (POT) and the Block Maxima (BM). Both estimation techniques are based on limits results for the excess distribution over high thresholds and block maxima, respectively. We apply both unconditional and conditional EVT models to management of extreme market risks in stock markets. They are applied on daily returns of the Tunisian stock exchange (BVMT) and CAC 40 indexes with the intension to compare the performance of various estimation methods on markets with different capitalization and trading practices. The sample extends over the period July 29, 1994 to December 30, 2005. We use a rolling...
International Journal of Innovative Research in Engineering & Management
In light of the latest global financial crisis and the ongoing sovereign debt crisis, accurate measuring of market losses has become a very current issue. One of the most popular risk measures is Value-at-Risk (VaR). A set of symmetric and asymmetric GARCH type models based on various error distributions were applied on Dhaka Stock Exchange DS30 Index from January 28, 2013 to May 29, 2017 for estimating and forecasting the market Value-at-Risk of the index. The most adequate GARCH family models for estimating volatility in the Dhaka stock exchange was found to be as the asymmetric TGARCH (1,1) model with GED. TGARCH (1,1) model with GED was allowed by Kupiec test with 99% of confidence level. The proposed VaR model would help the investors in their emerging capital markets.