Value at risk and expected shortfall are the two most popular measures for calculating financial risk. To calculate these measures (Value at risk and expected shortfall) there are many approaches, which can be divided into two main categories; parametric and non-parametric. In parametric approach it is supposed that the distribution of asset return belongs to a specific class of distributions. For some distributions we can claculate easily the mentioned measures. In this paper the the relation of epected shortfall has been proved for four symetric distribution.

The present study compares the performance of the long memory FIGARCH model, with that of the short memory GARCH specification, in the forecasting of multi-period value-at-risk and expected shortfall across 3 industry indices in Tehran Stock Exchange such as chemical, vehicle and metals. The dataset is composed of daily data covering the period from May, 2011 to May, 2015. According to the result of this research accounting for fractional integration in the conditional variance model does not appear to improve the accuracy of the VaR forecasts for the 1-day-ahead, 10-day-ahead and 20-day-ahead forecasting horizons relative to the short memory GARCH specification. Furthermore, the GARCH model has a lower quadratic loss between actual returns and ES forecasts, for the majority of the indices considered in 1-day, 10-day and 20-day forecasting horizons. Therefore, a long memory volatility model compared to a short memory GARCH model does not appear to improve the VaR and ES forecasting accuracy, even for longer forecasting horizons.

One of the main concerns of investors and financial managers is the way of dealing with investment risk; thus identification, calculation and management of risk are important issues in financial fields. So, in this study, the portfolio value-at-risk and expected shortfall are estimated by considering uncertainty in risk factors. The concept of fuzzy random variable, specifically possibility and necessity theory, is used to face uncertainty in financial data. In the following, the terms of fuzzy value-at-risk and expected shortfall introduced with assuming normal and t-student distribution and considering both state of fixed and stochastic for uncertainty factor. The results indicate that assumptions of t-student distribution and stochastic uncertainty factor make the estimation of both risk measures to be more conservative.

expected shortfall measures the loss of a portfolio in mathematical expectation when the amount of loss exceeds a threshold for a certain level of confidence and in a certain time horizon. Multi-horizon expected shortfall extends the concept of expected shortfall for an investment with a set of maturity horizons. In the present study, two stock portfolio models are designed based on the multi-horizon expected shortfall, the first is based on historical simulation and the second is parametric and based on the distribution of normal-Laplace mixture for proper fitting of tail data. Also, expectile is used to compute the expected shortfall in parametric form. The result of the experimental study of stock portfolio models designed on a stock portfolio with eight indices of the Tehran Stock Exchange by coding in the MATLAB software in the period 1390 to 1399 shows that the parametric approach in the test data in average return and Sharpe ratio criterions has a better performance than the historical scenario. Also, the relative error between the period expected shortfall predicted by the stock portfolio and its estimate in the test data in the parametric approach is less.

Financial market developments make it more important to measure market risks correctly. In this paper we investigatethe forecasting accuracy of different historical simulation models in relation to the risk measure expected shortfall and in comparison to established parametric models.we used historical simulation, mirrored historical simulatin, volatility weighted historical simulation, filtered historical simulation and GARCH (1, 1) models. The data that we used consists of Tehran stock exchange market index from 2010 to 2014.Christofferson backtest used for value at risk and mc neil & frey backtest used for expected shortfall. According to unconditional coverage backtesting, mirrored historical simulation model was rejected and others were accepted and according to independence backtesting all models were accepted thus the christoferson backtest will omit the mirrored historical simulation model and According to mc neil and frey backtest all models were accepted and finally the model confidence set procedure showed that semi parametric models are best models to forecast expected shortfall.

Portfolio Selection is one of the most important decisions that institutional investors have to face. Markowitz was the first to introduce risk into the portfolio selection decision by introducing the Mean-Variance Model. This created one of the most important fields in finance, that is Portfolio Optimization and finding the efficient frontier. In the next researches, adding real world constraints to the model broadened this field. With increasing the number of assets or the constraints, Portfolio Optimization becomes an NP-hard problem which is impossible to solve with derivative-based methods, therefore, numerical and metaheuristic methods should be used for solving it. The aim of this research is optimizing portfolio using Whale optimization algorithm. This metaheuristic algorithm is inspired by the behavior of Whales and was introduced in 2016. This research implements the algorithm in the top 50 index in Tehran Stock Exchange and tries to find the efficient portfolio in this index. We also compare the performance of this method to two other metaheuristic algorithms and explain the advantages of the proposed method in portfolio optimization.

Today, Systemic Risk is being analyzed as one of the major issues in financial institutions. Banks are one of the institutions that can be linked to systemic risk based on global experience. Therefore, in the study, we evaluate the systemic risk in the banking system of the country via the marginal expected shortfall (MES) criterion. For the purpose of the present study, 17 banks listed on the Tehran Stock Exchange that had seasonal information required for this research over a period of 1389 to 1397 were selected and the systemic risk in these banks was calculated by MES criterion. The finding of this study show the difference between MES of banks and indicate that if a crisis occurs in the financial system or market, the banks are affected but the drgree of impact is different from the finance crisis. Furthermore, compared with other banks, the estimation of the highest marginal expected shortfall belonged to bank gardeshgari (15. 84) and the lowest belonged to Bank Sarmayeh (-18. 38). In other words, if there is a crisis in the market, Bank Gardeshgari and Bank Sarmayeh are expected to experience a return of 15. 84 percent and-18. 34 percent, respectively.

In this research, the VaR and ES measures is estimated and compared for Tehran security exchange (TSE) and international stock markets by using the conditional EVT based peaks over threshold (POT). In order to obtain independent data, we use a vector autoregressive (VAR) and GARCH model to filter out any serial correlation and heteroskedasticity. Our data are the logarithmic daily returns for the period 2006-2015. We find that the Dubai financial market (DFMG) has the highest VaR and ES for both the lower tail and upper tail. In contrast, the Tehran security Exchange (TSE) has the lowest VaR and ES for both tails. Also, except to DFMG index, Shape parameter (ξ ) is positive for both tails of all indicies and indicate that tails on both sides of the return distribution are heavy.