Extreme Value Theory

Open Access Article

1 - Portfolio selection with Lower tail dependence and Extreme value theory
Said Falahpur Samine Feyzolah

Portfolio selection is an important problem in area of finance. Researchers have always tried to work with a variety of methods and strategies to achieve this important issue.In this research has been trying to present a new approach for portfolio selection with use of More

Portfolio selection is an important problem in area of finance. Researchers have always tried to work with a variety of methods and strategies to achieve this important issue.In this research has been trying to present a new approach for portfolio selection with use of lower tail dependence and Extreme value theory.We show theoretically that lower tail dependence (χ), a measure of the probability that a portfolio will suffer large losses given that the market does, contains important information for risk-averse investors. We then estimate χ for a sample of stocks and show that it differs systematically from other risk measures including variance, semi-variance, skewness, kurtosis, beta, and coskewness. In out-of-sample tests, portfolios constructed to have low values of χ outperform the market index, and portfolios with high values of χ. Our results indicate that χ is conceptually important for risk-averse investors, differs substantially from other risk measures, and provides useful information for portfolio selection. Manuscript profile

Open Access Article

2 - Presenting of nonlinear hybrid model based on Extreme Value Theory for forecasting the Conditional Value at Risk (CVaR)
Ehsan Mohammadian Amiri Ehan Atefi Seyed Babak Ebrahimi

The political and economic instability in recent years and followed by rapid changes in the realm of financial markets, has increased the risk of most financial institutions. So that risk managers at these institutions are worried about the decline in their asset value More

The political and economic instability in recent years and followed by rapid changes in the realm of financial markets, has increased the risk of most financial institutions. So that risk managers at these institutions are worried about the decline in their asset value over the coming days. In recent studies, generally the Conditional Value at Risk is used to measure and forecast the risks existing in financial markets. Therefore, in this research, it has been attempted to introduce, calculate and implement a nonlinear hybrid model for forecasting the Conditional Value at Risk. For this purpose, the new hybrid model based on the Extreme Value Theory and the Holt-Winters exponential smoothing (HWES-EVT) that, in addition to dynamics, cluster characteristics and broad data sequence, also takes into account the forecast Conditional Value at Risk of the industry and Tehran Stock Exchange Indices. For evaluating the accuracy the performance of proposed hybrid model, this modek is compared with the GARCH-EVT model. The results of backtesting show that the proposed hybrid approach provides a more accurate answer to the forecasting of Conditional Value at Risk for these indicators Indices. Manuscript profile

Open Access Article

3 - Assessing the Efficiency of the Value-at-Risk Index (VAR) using Extreme Value Theory in comparison with traditional risk assessment methods
Mehrdokht Mozaffari Hashem Nikoomaram

Generally, the greatest risk in the capital market or in the portfolio of investors occurs when large sudden changes occur in the unfavorable portfolio. These losses are in the distribution sequence, and for this purpose they are called "limitative values". In this rese More

Generally, the greatest risk in the capital market or in the portfolio of investors occurs when large sudden changes occur in the unfavorable portfolio. These losses are in the distribution sequence, and for this purpose they are called "limitative values". In this research, the logarithmic efficiency of the Tehran Stock Exchange Index based on the information received during the time interval between the day (due to the use of high frequency data) during the years 1392 to 1395, and the use of the maximum block approach in measuring the VaR value index is used. It turned out VaR index was calculated using historical simulation methods and variance-covariance method as the traditional risk assessment criteria and the results were compared. The results of data analysis in R software showed that the use of monthly information in calculating the risk-weighted value index has a higher predictive accuracy and the error rate (test error) in this case is lower than traditional risk assessment methods. Manuscript profile

Open Access Article

4 - portfolio optimization based on modeling of dependence structure and extreme value theory
mohamad safaei alireza saranj Mehdi Zolfaghari

Investigating the probablility of rare events occurring (events that occur with very low probability) is an important issue in portfolio risk management. extreme value theory of value provides the mathematical basis for modeling these events and calculating the risk cri More

Investigating the probablility of rare events occurring (events that occur with very low probability) is an important issue in portfolio risk management. extreme value theory of value provides the mathematical basis for modeling these events and calculating the risk criteria associated with them, such as the value at risk. The purpose of this paper is to model the dependency structure andextreme value theory of 10 foreign exchange companies of Tehran Stock Exchange (Persian Gulf Holding, Bandar Abbas Refinery, Mobarakeh Steel, Topico, Ghadir, Parsian Oil and Gas, Melli Mes, Gol Gohar, Mobile Communications, Chadormelo).The results indicated the fact that among the stock returns of the top 10 companies evaluated, it is possible that using extreme value theory of value using vine Copula functions, the results of the forecast were greatly increased. Results of the copula function in six modes: simple Copula (t), time-varying Copula (tDCC), and Gaussian distribution-based time-varying Copula (GDCC). tvSJC) was investigated. In all six cases, the use of the Copula -wine method increased the accuracy in predicting optimal stock returns. Manuscript profile

Open Access Article

5 - Portfolio VaR Modelling using EVT-Pair-Copulas Approach
Ali Souri Saeed Falahpor Ali Foroush Bastani Ehsan Ahmadi

The purpose of this research is to model Value-at-Risk (VaR) of portfolio with EVT-Pair-Copulas approach. In the financial literature, a significant amount of empirical studies have been done on the characteristics of financial assets returns and researchers have found More

The purpose of this research is to model Value-at-Risk (VaR) of portfolio with EVT-Pair-Copulas approach. In the financial literature, a significant amount of empirical studies have been done on the characteristics of financial assets returns and researchers have found a set of stylized facts about this subject. In this regard leptokurtic, left-skewed, weak autocorrelation, volatility clustering, and heteroscedasticity can be mentioned. Any estimation of risk without considering these characteristics or using unrealistic assumptions about financial assets returns increases the probability of failure in the risk management process. For this purpose, at first, the marginal distributions of returns are obtained using extreme value theory (EVT). Concerning characteristics of financial assets returns and also the primary filter to apply EVT, we use heteroscedasticity models for the marginal distributions of assets. Then the structure of the dependence between different stocks is estimated by using C-Vine, D-Vine, and R-Vine pair copula models. Afterward, the VaR of portfolio is estimated using the Monte Carlo simulation method. The final results show that the model with GARCH marginal distribution and R-Vine pair copula has been able to achieve the best performance among rival models at 95% confidence level. Manuscript profile

Open Access Article

6 - Investment Portfolio Optimization of Insurance Companies with Copulas and Extreme Value Approach
arash goodarzi reza Tehrani Ali souri

This study determines the optimal investment portfolio of insurance companies by considering underwriting activities. investment decisions in insurance companies are affected by underwriting activities. In this paper, the investment optimization problem of insurers is m More

This study determines the optimal investment portfolio of insurance companies by considering underwriting activities. investment decisions in insurance companies are affected by underwriting activities. In this paper, the investment optimization problem of insurers is modeled using the copula-based conditional risk value, taking into account the results of insurance activities. Also, since the emphasis is on tails of distribution, the probability distribution of variables in tails is estimated using Pareto distribution and in other parts of the distribution using the Empirical probability distribution. Data collected on monthly basis covers two periods in-sample, between 2006 to 2015 and out-of-sample, between 2016 to 2019.The findings show that the optimum portfolio includes eighty percent of risky assets (stock and real estate) and only twenty percent of risk-free assets (bank deposits) and it is outside the legal constraints set by Central Insurance Therefore, legal constraints prevent insurance companies from the optimal selection of investment portfolio. Also, the comparison of out-of-sample performance with in-sample performance of portfolios shows that portfolios based on copula functions have better and more robust performance than traditional models. Manuscript profile

Open Access Article

7 - Financial risk assessment based on Extreme Value Theory and instantaneous data of Tehran Stock Exchange Index
Mehrdokht Mozaffari Hashem Nikoomaram

Value at Risk is one of the most important criteria in financial markets for risk assessment. Various methods have been proposed for measuring this index. Extreme Value Theory is one of the new methods for calculating the value at risk that focuses on Distribution seque More

Value at Risk is one of the most important criteria in financial markets for risk assessment. Various methods have been proposed for measuring this index. Extreme Value Theory is one of the new methods for calculating the value at risk that focuses on Distribution sequence of series, and instead of taking all data into account without considering the limiting assumptions such as the assumption of normalization. In this research, the logarithmic return of Tehran Stock Exchange index based on the data received during the time intervals of the day (due to the use of high frequency data) during the years 1392 to 1395 was summed up and the Block Maxima Approach was used in VaR measurement. Given the correlation between the variance and the time series of the data, the problem was first solved using the E-GARCH model. Then VaR index was calculated in three blocking conditions based on hourly, daily and monthly data. The results showed that the use of monthly data in calculating this index has a higher predictive accuracy. Manuscript profile

Open Access Article

8 - Application of Extreme Value Theory in Value at Risk forecasting
Hosein Falahtalab Mohammadreza Azizi

Quantifying the uncertainty is one of the most important subject in financial issues, so nowadays in each financial and investment activity risk assessment and management is required. Value-at-risk (VaR) has become a popular risk measure since it was adopted by the Inte More

Quantifying the uncertainty is one of the most important subject in financial issues, so nowadays in each financial and investment activity risk assessment and management is required. Value-at-risk (VaR) has become a popular risk measure since it was adopted by the International agencies in 1988. Precise prediction of VaR provides proper evaluation criteria in areas such as investment decision-making and risk management. Due to the fat-tailed distribution in most real financial time-series, extreme value theory (EVT) is a powerful tool in determining the VaR by concentrating on the shape of the fat-tailed probability distribution. In This study, Peak Over Threshold (POT) approach used for value at risk forecasting by Tehran Stock Exchange (TSE) data. The results show this approach is better than traditional approaches such as historical simulation and variance-covariance methods. Manuscript profile

Open Access Article

9 - Modeling volatility and conditional VaR measure using GARCH models and theoretical EVT in Tehran Stock Exchange
Saeed Fallahpoor Reza Raee Saeed Mirzamohammadi seyed mohammad hasheminejad

Trying to identify an appropriate model to enhance measurement accuracy by using value at risk measures is of particular importance. Conditional Value at Risk (CVaR) with having some of the shortcomings of VaR, is a more reliable measure. In this study, the characterist More

Trying to identify an appropriate model to enhance measurement accuracy by using value at risk measures is of particular importance. Conditional Value at Risk (CVaR) with having some of the shortcomings of VaR, is a more reliable measure. In this study, the characteristics of the Tehran Stock Exchange index data usage FIGARCH-EVT model to calculate value at risk if states have been more accurate. GARCH-EVT hybrid implementation model and its development, FIGARCH-EVT model, we found that the effect of clustering, dynamic and long-term memory has been included in the modeling. FIGARCH model for log data output index, which will be modeled in terms of the above properties. In addition, the wide trail property index return data using extreme value theory (EVT) is used for residual FIGARCH model. To compare the results, NORMAL-GARCH models and t-Student-GARCH, historical simulation and GARCH-EVT indicator is used for data output. The results of the model using retrospective tests were evaluated. The results of this study indicate that the data distribution is skewed and asymmetrical index returns do not follow a normal distribution. The tests Standardized Exceedance Residuals and The Cumulative Violation Process and  Expected shortfall backtesting and loss function Lopez FIGARCH-EVT model over other models is more accurate. Manuscript profile

Open Access Article

10 - Portfolio Optimization under Varying Market Risk Conditions: Copula Dependence and Marginal Value Approaches
Jila Ahmadi Hasan Ghodrati Ghezaani Mehdi Madanchi Zaj Hossein Jabbari Aliakbar Farzinfar

10.22034/amfa.2023.1967167.1797

This paper aims to investigate the portfolio optimization under various market risk conditions using copula dependence and extreme value approaches. According to the modern portfolio theory, diversifying investments in assets that are less correlated with one another al More

This paper aims to investigate the portfolio optimization under various market risk conditions using copula dependence and extreme value approaches. According to the modern portfolio theory, diversifying investments in assets that are less correlated with one another allows investors to assume less risk. In many models, asset returns are assumed to follow a normal distribution. Consequently, the linear correlation coefficient explains the dependence between financial assets, and the Markowitz mean-variance optimization model is used to calculate efficient asset portfolios. In this regard, monthly data-driven information on the top 30 companies from 2011 to 2021 was the subject to consideration. In addition, extreme value theory was utilized to model the asset return distribution. Using Gumbel’s copula model, the dependence structure of returns has been analyzed. Distribution tails were modeled utilizing extreme value theory. If the weights of the investment portfolio are allocated according to Gumbel’s copula model, a risk of 2.8% should be considered to obtain a return of 3.2%, according to the obtained results. Manuscript profile

Open Access Article

11 - Dependence structure and portfolio risk in Iran exchange market by using GARCH-EVT-Copula method
Farhad Ghaffari sahar fathi

Abstract In this research, the GARCH-EVT-COPULA method is investigated to determine the dependency structure and portfolio risk estimation on the foreign exchange market data in Iran. GARCH-EVT models are used to mariginal distribution of each of four currency returns s More

Abstract In this research, the GARCH-EVT-COPULA method is investigated to determine the dependency structure and portfolio risk estimation on the foreign exchange market data in Iran. GARCH-EVT models are used to mariginal distribution of each of four currency returns series. For the joint model, we choose five copuls with different dependence structure such as Frank, Clayton, Gumble, Normal and t-Student copulas. In this research portfolio risk is measured using VaR and CVaR.The statistical sample of this study is the daily exchange rate of USD,EURO, Pound and AED for the free market with 5 working days from September to the end of 1396.Based on the results of the research, using the Akaike information criterion values, the t-student function is the best fitted copula model for investigating the dependency structure.Exchange rates have the same upper and lower tail dependencies. Accordingly, in the markets for boom (severe positive) and stagnation (severe negative), the dependence between the two exchange rates is the same. Manuscript profile

Open Access Article

12 - The assessment of extreme value theory and Copula - Garch models in prediction of value at risk and the expected short fall in portfolio Investment Company in Tehran stock exchange.
ali alizadeh Mirfeiz Fallah

The present study has endeavored to represent a more precise model to calculate the risk of banks in this study by ARIMA-GARCH-COPULA Model has been introduced.In obtaining the iid distributions and variance estimation the mean model and conditional variance have been d More

The present study has endeavored to represent a more precise model to calculate the risk of banks in this study by ARIMA-GARCH-COPULA Model has been introduced.In obtaining the iid distributions and variance estimation the mean model and conditional variance have been determined and estimated simultaneously.In so doing, the ARIMA methodology has been employed to model the average return on assets of the study, and for modeling the research conditional variance of GARCH have been applied. Also mean error criterion has been used to compare the different models of VAR estimation, and for the purpose of testing statistical results backtesting methods have been employed. Based on mean error criterion, the proposed model of the study at hand has demonstrated the most accuracy The GEV model derived from the EVT has been ranked second The output of the Dow ranking method, however, has been very similar to one another According to Dow ranking method, the GEV model has had the lowest loss function at 5% level of significance, and at 1% level of significance, the HS model has demonstrated the least loss function. ES calculations have also been carried out for the four models with ARIMA-GARCH-COPULA model showing the least loss. Manuscript profile

Open Access Article

13 - Statistical ranking of different VaR and ES models by using Model Confidence Set approach for the banking industry: With an emphasis on Conditional Extreme Value Theory
Alireza Saranj marziyeh nourahmadi

In this paper, we deal with the ranking of different VaR and ES approaches using daily banking industry index data over the period 2008 to 2016, with an emphasis on Conditional Extreme Value approach. In the first stage, we use Bernoulli coverage and independence of vio More

In this paper, we deal with the ranking of different VaR and ES approaches using daily banking industry index data over the period 2008 to 2016, with an emphasis on Conditional Extreme Value approach. In the first stage, we use Bernoulli coverage and independence of violation tests for VaR models and McNeil & Frey’s backtest for ES models to examine the validity of these models. In the second stage, we import the loss functions of the valid models remained from the first stage into the MCS function and rank statistically them. The loss function used for VaR models is Dowd loss function and the one used for ES models is Olsen loss function. The results show that the in both VaR and ES models, the conditional EV with normal standardized residuals, the conditional EV with student's t standardized residuals and GARCH with student's t residuals models are respectively ranked first to third. Manuscript profile

Open Access Article

14 - Estimating Extreme downside risk premium using Extreme Value Theory Approach
Maryam Davallou Mahdiyeh Dashti

Recent year’s financial crisis gives rise to pay attention to extreme losses. Investors suffer from extreme losses and since unusaull outcomes probability is not far, investors concern about extreme tail of return distribution. This paper is aimed to examin extrem More

Recent year’s financial crisis gives rise to pay attention to extreme losses. Investors suffer from extreme losses and since unusaull outcomes probability is not far, investors concern about extreme tail of return distribution. This paper is aimed to examin extreme downside risk (EDR) that is calculated by extreme value theory (EVT) which is designed to explain uncommon events. For this purpose, a sample composed of 243 listed firms in Tehran Stock Exchange is examined for 1384 to 1394. Portfolio study approach and Fama- McBeth (1973) regression are used to EDR pricing test. The results confirm EDR pricing and statistical significancy of extreme downside risk in TSE. This research shows that potential loss from extreme downside returns, EDR, is captured by asset pricing as a risk factor. Also, the effects of other risk measures including volatility, valu at risk and right tail mesure are stronger than EDR and if their effectes is controlled, EDR risk premium is no longer statistically significant.  Manuscript profile

Open Access Article

15 - Futures Contracts Margin Setting by CVaR Approach Based on Extreme Value Theory
mirFeyz Fallahshams ali Saghafi alireza naserpoor

this study, using gold coins spot price returns, in the period from 2008 to 2016, estimates IME gold coin futures contracts Initial margin, by Value at Risk and ConditionalValue at Risk (CVAR) approaches. It use variance- covariance modeles, based on normal and T-studen More

this study, using gold coins spot price returns, in the period from 2008 to 2016, estimates IME gold coin futures contracts Initial margin, by Value at Risk and ConditionalValue at Risk (CVAR) approaches. It use variance- covariance modeles, based on normal and T-student distributions,  general pareto distribution and adaptive GPD models fore estimating initial margin requerment for futures contracts open positions. Fore VaR moles backtesting, it applies Christoffersen conditonal coverage liklihood ratio(LRcc) test and lopez and Blanco-Ihle loss functions. MAE and RMSE loss functions have been used for Conditional Value at Risk (CVAR) models Evalution. The paper finds that all models have been underperforming in low confidence level and Variance - covariance models based on T-student Distribution and adaptive GPD has outperformed the other models that support the fat tailed nature of gold coin spot price data historical distribution. Manuscript profile

Open Access Article

16 - VAR and ES calculation based on the Extreme Value Theory (block maxima and GPD): Evidence from Tehran Stock Exchange (TSE)
Mansour Kashi S. Hassan Hoseini mohammad Mousa Ghaliliou saeed Golkarian Arani

   Current study, has explores the VAR and ES in the Tehran Stock Exchange (TSE) by using the Extreme Value Theory (block maxima and GPD). Earlier estimates of the preliminary findings of the analysis that uses statistics, Empirical Distribution Function, Mean More

   Current study, has explores the VAR and ES in the Tehran Stock Exchange (TSE) by using the Extreme Value Theory (block maxima and GPD). Earlier estimates of the preliminary findings of the analysis that uses statistics, Empirical Distribution Function, Mean Excess Function and QQ plot, Pareto and heavy-tailed behavior were found data. To estimate the optimal threshold value, we have Mean Excess Function and hill plot applied. To estimate the optimal threshold value, Mean Excess Function and Hill plot use the statistics mentioned for the positive and negative returns, the threshold value for GPD models are about ./75  And ./60  have provided. Comparing the estimated residual value model classic extreme (monthly, quarterly, six month and one year) and the GPD, concluded the optimal performance GPD calculated on the value of extreme block which is highly sensitive to the choice of the period. Finally, to estimate VAR and ES, we GPD model demonstrated that a better performance was applied. The results showed that VAR and ES should not be the dominant financial risk management. In other words, dependence on individual risk scale for ignoring the problem will create portfolio risk information. So to contain the missing information by VAR and ES, it is essential that the various aspects of the distribution of losses / profits look like heavy-tailed. Manuscript profile

Open Access Article

17 - Estimation of Value at Risk with Extreme Value Theory approach and using Stochastic Differential Equation
Amir Shafiee reza raei Hossein Abdoh Tabrizi saeed falahpor

The occurrence of financial crises in recent decades has caused a lot of damage to the economy as well as economic enterprises in many countries. The Extreme Value Approach is a new approach to the phenomenon of financial crisis, which has been able to analyze the event More

The occurrence of financial crises in recent decades has caused a lot of damage to the economy as well as economic enterprises in many countries. The Extreme Value Approach is a new approach to the phenomenon of financial crisis, which has been able to analyze the events that are less likely to occur but the damage caused by them is significant. In this study, we use the Extreme Value theory and Stochastic differential equations to find a new method for estimating the more precisely the value at risk. For this purpose, after estimating the parameters of the Stochastic differential equations, which includes the geometric Brownian motion, the geometric Brownian motion with the jump, the nonlinear GARCH model, and the Heston model, simulate the Monte Carlo simulations of future paths and then use peak over threshold approach, to estimate the value We at risk. The results of the simultaneous use of Stochastic differential equations and Extreme value theory are compared with historical simulations and variance-covariance approaches for value at risk. The results of Back-test techniques on value at risk indicate the superiority of the Heston model in estimation of value at risk. Manuscript profile

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