Estimation of Expected Shortfall Based on Conditional Extreme Value Theory Using Multifractal Model and Intraday Data in Tehran Stock Exchange

Document Type : Research Paper


1 Associate Prof., Department of Financial Management and Insurance, Faculty of Management, University of Tehran, Tehran, Iran.

2 Ph.D. Candidate, Department of Financial Management, Faculty of Management, University of Tehran, Tehran, Iran.


Objective: After the financial crisis in 2008, market practitioners and financial researchers began to attach more importance to risk measurement and modeling. Expected shortfall is recognized risk measures in financial literature.
Methods: By the estimation of expected shortfall as a coherent risk measure, and by use of conditional extreme value theory and combining new volatility measures, this research attempts to introduce a new model for risk measurement. Intraday data has been used in this research in order to estimate mentioned risk measures.
Results: The results show that in comparison with alternative models, such as GARCH conditional peak over threshold models, multifractal conditional peak over threshold models, which utilize intraday data, perform better in risk estimation. In addition, the use of extreme value theory brings about more favorable results in risk estimation. In this research, we use a new back-testing models in order to back-test expected shortfall.
Conclusion: The use of the normal distribution function for the disruption components to estimate the expected drop has not been successful, and has led to an estimate of the low risk category. The use of Student's t-distribution in estimating risk measures has been acceptable, although in some cases it has led to an estimate of high risk. Considering extreme value theory of value in the above models has in most cases led to improved model performance. This means that it has moderately adjusted the estimates of the upper hand and the estimates of the.


Artzner, P.., Delbean, F., Eber, J. (1998). Coherent Measures of Risk. Mathematical Finance, 9 (3), 203-228.
Balkema, A. A., De Haan, L. (1974). Residual Life Time at Great Age. The Annals of Probability, 2(5), 114-137.
Bhattacharyya, M., Ritolia, G. (2006). Conditional VaR Using EVT–Towards a Planned Margin Scheme. International Review of Financial Analysis, 17 (2), 382-395.
Brooks, C., Clare, A.D., Dalle, M., Persand, J.W. (2005). A Comparison of Extreme Value Theory Approaches for Determining Value at Risk. Journal of Empirical Finance, 12 (2), 339-352.
Calvet, L.E., Fisher, A.J. (2001). Forecasting Multifractal Volatility. Journal of Econometrics, 105, 27-58.
Cotter, J. (2000). Extreme Risk in Future Contracts. Applied Economics Letter, 12(8), 489-492.
Cotter, J., Longin, F. (2006). Margin Setting with High-Frequency DataMPRA Paper 3528, University Library of Munich, Germany.
Danielsson, J., De Haan, L., Peng L., De Vries, C. (2001). Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation. Journal of Multivariate Analysis, 76 (2), 226–248.
Embrechts, P., Kaufmann, R., Patie, P. (2005). Strategic Long-term Financial Risks: Single Risk Factors. Computational Optimization and Applications, 32 (2), 61–90.
Fallahpour, S., Rezvani, F., Rahimi, M. (2015). Estimating Conditional VaR Using Symmetric and Non-Symmetric Autoregressive Models in Old and Oil Markets. Financial Knowledge of Securities Analysis, 8 (26), 45-63. (in Persian)
Gencay, R., Selcuk, F., Ulgulyagci, A. (2003). High Volatility, Thick Tails and Extreme Value Theory in VAR Estimation. Journal of Insurance: Mathematics and Economics, 33, 337-356.
Ghorbel, A., Trabelsi, A. (2009). Measure of Financial Risk Using Conditional Extreme Value Copulas with EVT Margins. Journal of Risk, 11 (4), 51-85.
Gorgani, M., Hadad, A.A., Shahriar, B. (2012). The Calculation of Optimal Interest Rate of Fire Insurance Catastrophe Bonds in Iran using Extreme Value TheoryFinancial Research Journal, 14 (1), 101-116. (in Persian)
Jalaee, S.E., Abolhosseini, A. (2009). Multifractal Characteristics of Iranian Rial’s Exchange Rate. International Economics Studies, 35 (2), 39-48. (in Persian)
Kao, T., Lin, Ch. (2010). Setting Margin Levels in Futures Markets: An Extreme Value Method. Nonlinear Analysis Real World Applications, 11(3), 1704-1713.
Karimi, S. (2012). Estimating Required Margin of the Gold Future Contracts Using Extreme Value Theory. Bachelor’ Thesis, Faculty of Management and Economics Sharif University. (in Persian)
Kjellson, B. (2013). Forecasting Expected Shortfall an Extreme Value Approach. Bachelor's thesis, Faculty of Science Mathematical Statistics Lund University.
Kourouma, L., Dupre, D., Sanfilippo, G., Taramasco, O. (2011). Extreme Value at Risk and Expected Shortfall during Financial Crisis. Halshs Working paper.
Liu, R., Lux, T. (2013). Multifractality and Long-Range Dependence of Asset Returns: The Scaling Behavior of the Marcov-Switching Multifractal Model with Lognormal Volatility Components. Advances in Complex Systems, 11 (5), 669-684.
Longin, F. M. (1995). From Value at Risk, To Stress Testing, The Extreme Value Approach. Journal of Banking & Finance, 24 (7), 1097-1130.
Lux, T., Morales-Arias, L., Sattarhoff , C. (2008). A Markov-switching Multifractal Approach to Forecasting Realized Volatility. Kiel Institute for the World Economy (IfW) 1737Kiel Working Papers.
McNeil, A.J. & Frey, R. (2000). Estimation of Tail-Related Risk Measures for Heteroskedastic Financial Time Series: An Extreme Value Approach. Journal of Empirical Finance, 7 (4), 271-300.
Mohammadi, Sh., Raei, R., Faizabad, A. (2008). Forecasting Value-at-Risk Using Conditional Volatility Models: Evidence from Tehran Stock ExchangeFinancial Research Journal, 10 (25), 109-124. (in Persian)
Norouzzadeh, P., Rahmani, B. (2005). A Multifractal Detrended Fluctuation Description of Iranian Rial–US Dollar Exchange Rate. Physica A: Statistical Mechanics and its Applications, 367, 328-336.
Pickands, J. (1975). Statistical Inference Using Extreme Order Statistics. The Annals of Statistics, 3 (1), 119-131.
Raadpour, M. (2008). Value at Risk at Tehran Stock Exchange. Master's thesis, Faculty of Management and Accounting Shahid Beheshti University. (in Persian)
Raei, R., Bolgorian, M. (2011). A Multifractal Detrended Fluctuation Analysis of Trading Behavior of Individual and Institutional Traders in Tehran Stock Market. Physica A, 390, 3815–382.
Roodposhti, F., Kalantri, D. M. (2004). Multifractal Models in Finance: Characteristics and Applications, Financial Knowledge of Securities Analysis, 7 (24), 68-91. (in Persian)
Soltane, H.B., Karaa, A., Bellalah, M. (2012). Conditional VaR Using GARCH-EVT Approach: Forecasting Volatility in Tunisian Financial Market. Journal of Computations & Modelling, 2 (2), 95-115.
Tehrani, R., Namaki, A., Hedayatifar, L. (2012). The Cross-correlation Structure of Tehran Stock Exchange Indexes by Multifractal Detrended Fluctuation Analysis. Financial Research Journal, 14 (1), 55-68. (in Persian)
Wei, Y., Wang, P. (2008). Forecasting Volatility of SSEC in Chinese Stock Market Using Multifractal Analysis. Physica A., 387, 1585–1592.
Zamani, Sh., Bidgoli, S., Kazemi, M. (2013). Estimation of Tehran Security Index’s Value at Risk using Extreme Value Theory. Journal of Securities Exchange, 21, 115-136. 
(in Persian)