Value at Risk (VaR)

Value at Risk (VaR) plays a central role in risk management. There are several approaches for the estimation of VaR, such as historical simulation, the variance-covariance and the Monte Carlo approaches. This work presents portfolio VaR using an approach combining Copula functions, Extreme Value Theory (EVT) and GARCH-GJR models. We investigate the interactions between Tehran Stock Exchange Price Index (TEPIX) and Composite NASDAQ Index. We first use an asymmetric GARCH model and an EVT method to model the marginal distributions of each log returns series and then use Copula functions (Gaussian, Student’s t, Clayton, Gumbel and Frank) to link the marginal distributions together into a multivariate distribution. The portfolio VaR is then estimated. To check the goodness of fit of the approach, Backtesting methods are used. The empirical results show that, compared with traditional methods, the copula model captures the value more successfully.

Value at Risk model based on a switching regime approach was used in this study to optimize portfolios consisting of industry index (petroleum products, investment, chemical products, and metal products). For this purpose, the VaR of returns on index should first be extracted through parametric models of the (GARCH) family in each of the above industries by using regime transitions. After the risk of return on index is obtained for each industry, the optimal portfolio is created in the next step based on VaR minimization, and the optimal value of each industry is determined in the portfolio. According to the results, (MRS-FIEGARCH) model had no superiority in VaR estimation over the other parametric models of the GARCH family. In fact (MS-EGARCH-t) was introduced as the optimal model. Among the designated industries, returns on indices followed regime transitions only in chemical products and investment by showing asymmetric reactions to external shocks. Moreover, the optimal weights were on the rise in the industries where VaR decreased over time, whereas the optimal weight of the portfolio decreased in the industries where VaR increased over time. The higher share of an optimal portfolio belonged to the industries where stock returns had lower rates of VaR. The risk-return-ratio was employed to show that the optimal portfolio with a risk rate was measured by considering the switching regime was superior over the optimal portfolio with a risk rate extracted without considering the switching effects. To create an optimal portfolio, it is then recommended to make investments in the industries characterized by higher stability in prices and lower fluctuations in stock returns in the long run. This approach can be employed to obtain the best results from optimal portfolio preparation in the worst-case scenario of the market fluctuations.

This paper aims to estimate the Value-at-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.

One of the main demands of investors (depositors and shareholders) of banks is transparency. However, in addition to the requirements for meeting this demand, measuring how to meet it has become challenging. So far, researchers have proposed different qualitative criteria for transparency. In this study, while introducing the correlation coefficient between book and market value at risk (VaRs) as a criterion of transparency, we seek to examine the stability of this criterion in different economic conditions. For this purpose, first, by using the e-garch model, the value at risk was estimated based on the balance sheet (book) information and also the market information of the banks' shares, then by calculating the correlation coefficients between book and market VaR’s under normal conditions, we predict book and market VaR’s using vector auto-regressive (VAR) models, along with defining three stress scenarios (Mild - Severe - hyper stress). We examined the significance of the difference between the calculated correlation coefficients in the three stress test modes. We thus tested the stability of the correlation coefficient of the defined scenarios. The findings showed that except for the correlation caused by the unemployment rate factor in mild and hyper-stress scenarios, in other cases, no evidence of H0 rejection was found, indicating the stability of the correlation coefficient between book and market VaRs as a measure of transparency.