Intraday Value at Risk Estimation with EVT-COPULA Approach

Document Type : applied


1 Associate Prof., Finance Department, Khatam University, Tehran, Iran

2 MSc. Financial Engineering, Khatam University, Tehran, Iran


Value at Risk is the most general risk measure in banks and financial institutions that lies in the tail of the P&L distribution. To measure VaR of a portfolio of assets, correlation of the assets must be considered. Thus, to properly measure VaR one needs an approach to calculate joint distribution of returns series and also because VaR lies in the tail of P&L distribution, a framework to model tail of the distribution is necessary. Thus, in this research with combining EVT; to model tail of the P&L distribution, and Copula, to model joint distribution and VaR of three most liquid stock in petrochemical industry of Tehran Stock Exchange is calculated and then compared with other approaches. To model extreme events, we use POT approach and we use elliptical copulas to find joint distribution of series and calculating VaR. Results shows the proposed model performs very well compared to other models in calculating VaR of the investigated time period.
JEL: G23, G32
How to cite this paper: Mousavi, S. H., & Pouyanfar, A. (2016). Intraday Value at Risk Estimation with EVT-Copula Approach. Quarterly Journal of Risk Modeling and Financial Engineering, 1(2), 129–144. (In Persian)


Main Subjects

Adrian, T., & Rosenberg, J. (2008). Stock Returns and Volatility : Pricing the Short-run and Long-run Components of Market Risk. The Journal of Finance, LXIII(6), 2997-3030.
Andersen, T. G., Bollerslev, T., Diebold, F. X., Ebens, H., Backus, D., Brandt, M., & Stambaugh, R. (2001). The Distribution of Realized Stock Return Volatility, Journal of Financial Economics, 61(1), 43-76.
Andersen, T., & Bollerslev, T. (1997). Intraday Periodicity and Volatility Presistence in Financial Markets. Journal of Empirical Finance, 4(1), 115-158.
Ayusuk, A., & Sriboonchitta, S. (2015). Copula Based Volatility Models and Extreme Value Theory for Portfolio Simulation with an Application to Asian Stock Markets. Causal Inference in Econometrics, 622(1), 279–293.
Balkema, A., & Haan, D. (1972). Residual Life Time at Great Age. Stanford: Stanford University Press.
Breymann, W., Dias, A., & Embrechts, P. (2010). Dependence Structures for Multivariate High Frequency Data in Finance. Quantitative Finance, 3(1), 1–36.
Dacorogna, M. (2001). Dacorogna-An Introduction to High-Frequency Finance. San Diego: Academic Press.
Diao, X., & Tong, B. (2015). Forecasting Intraday Volatility and VaR Using Multiplicative Component GARCH Model. Applied Economics Letters, (May 2015), 1–8.
Dionne, G., Duchesne, P., & Pacurar, M. (2009). Intraday Value at Risk (IVaR) Using Tick-by-Tick Data with Application to the Toronto Stock Exchange. Journal of Empirical Finance, 16(5), 777–792.
Dionne, G., Pacurar, M., & Zhou, X. (2015). Liquidity-Adjusted Intraday Value at Risk Modeling and Risk Management: An application to Data from Deutsche Borse. Journal of Banking Finance , 59(1), 202-215.
Embrechts, P., McNeil, A., & Straumann, D. (1999). Correlation: Pitfalls and Alternatives. Risk Magazine, 20(1), 69-71.
Embrechts, P., Samorodnitsky, G., Dacorogna, M. M., & Muller, U. A. (1998). How Heavy are the Tails of a Stationary HARCH(k) Process? A Study of the Moments. In Stochastic Processes and Related Topics 69–102. Boston, MA: Birkhauser Boston.
Engle, R. F., & Russell, J. R. (1998). Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data. Econometrica, 66(5), 1127–1162.
Ergun, A. T., & Jun, J. (2010). Time-Varying Higher-Order Conditional Moments and Forecasting Intraday VaR and Expected Shortfall. Quarterly Review of Economics and Finance, 50(3), 264–272.
Fisher, R. A., & Tippett, L. H. C. (1928). Limiting Forms of The Frequency Distribution of The Largest or Smallest Member of a Sample. Mathematical Proceedings of The Cambridge Philosophical Society, 24(2), 180-190.
Haan, D. (1994). Extreme Value Theory and Applications. Boston, MA: Springer US.
Hautsch, N. (2012). Econometrics of Financial High-Frequency Data. Berlin: Springer.
Huang, C. H. C., & Chiou, W. P. (2011). Effectiveness of Copula-Extreme Value Theory in Estimating Value-at-Risk: Empirical Evidence From Asian Emerging Markets. Review of Quantitative Finance and Accounting, 39(4), 447-468.
Hwan, D. & Patton, A. (2015). Modelling Dependence in High Dimensions with Factor Copulas Modelling Dependence in High Dimensions with Factor Copulas. Journal of Business & Economic Statistics. 35(1), 139-154.
Karmakar, M., & Paul, S. (2015). International Review of Financial Analysis Intraday Risk Management in International Stock Markets : A Conditional EVT Approach. International Review of Financial Analysis. International Review of Financial Analysis, 44(1), 34-55.
Klaassen, F. (2002). Improving GARCH Volatility Forecasts with Regime-Switching GARCH. Empirical Economics, 27(2), 223–254.
Kole, E., Koedijk, K., & Verbeek, M. (2007). Selecting Copulas for Risk Management. Journal of Banking and Finance, 31(8), 2405–2423.
McNeil, A. J. (1997). Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory. ASTIN Bulletin, 27(1), 117–137.
McNeil, A. J., & Frey, R. (2000). Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: An Extreme Value Approach. Journal of Empirical Finance, 7(1), 271–300.
Mousavi, M., Raghfar, H., & Mohseni, M. (2014). Estimation of the Value of Risky Stocks (Using Conditional Copula-Garch Method). Iran Economic Research, 18(54), 119-152.
Pickands, J. (1975). Statistical Inference Using Extreme Order Statistics. Institute of Mathematical Statistics Stable, 3(1), 119–131.
Sajjad, R., Hedayati, S. & Hedayati, S. (2015). Estimation of Value at Risk by using Extreme Value Theory. Investment Knowledge, 3(1), 133-155.
Talebnia, G. O., Zare, I., Ahmadi, F., Abadi, N., & Fathi, M. (2011). Predictive Power of Capital Asset Pricing Model (CAPM), Fama and Frnch Three-Factor Model (F & F) and the Value at Risk (VaR) in Choosing the Optimal Portfolio Shares. International Research Journal of Finance and Economics, 80(2), 94-104.
Wang, Z. R., Chen, X. H., Jin, Y. B., & Zhou, Y. J. (2010). Estimating Risk of Foreign Exchange Portfolio: Using VaR and CVaR Based on GARCHEVT-Copula model. Physica A: Statistical Mechanics and Its Applications, 389(21), 4918–4928.
Zangane, (2007). VaR Estimation of market index. Journal of Economic Research, 79 (3), 121-149.