Monte Carlo Simulation Approach to Calculate Value at Risk: Application to WIG20 and MWIG40

Open access


This paper reports our estimates of the Value at Risk using Monte Carlo simulations for which we developed a computer program. Our approach involves obtaining Monte Carlo parameters by fitting real historical data of different periods to probability distributions. We applied the algorithm to the WIG20 and mWIG40 stock indices, and performed simulations for the Value at Risk at 95% and 99% confidence intervals over six estimation periods ranging from 1 trading day to 250 trading days. This approach was evaluated using the percentage failures and the Kupiec Proportion of Failures test. Our results indicate that this method is highly influenced by the choice of past historical and estimation period lengths considered. Overall, we observed that the Monte Carlo computational scheme is a reliable method for quantifying VaR when parametrized well.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • Basel II 2004 Basel II: International Convergence of Capital Measurement and Capital Standards: A Revised Framework (12.01.2018).

  • Detemple J.B. Garcia R. Rindisbacher M. 2003 A Monte Carlo method for optimal portfolios Journal of Finance vol. 58 no. 1 pp. 401-446.

  • Evans J.R. Olson D.L. 1998 Introduction to Simulation and Risk Analysis Prentice-Hall Inc. New Jersey USA.

  • Glasserman P. 2003 Monte Carlo Methods in Financial Engineering Springer Science+Business Media New York USA.

  • Holton G.A. 2014 Value-at-Risk Theory and Practice Second Edition (self-published) (15.01.2018).

  • Kupiec P.H. 1995 Techniques for verifying the accuracy of risk measurement models The Journal of Derivatives vol. 3 no. 2 pp. 73-84.

  • Savvides S.C. 1994 Risk analysis in investment appraisal Project Appraisal Journal vol. 9 no. 1.

  • Shapiro S.S. Wilk M.B. 1965 An analysis of variance test for normality (complete samples) Biometrika vol. 52 no. 3-4 pp. 591-611.

  • Stephens M.A. 2012 EDF statistics for goodness of fit and some comparisons Journal of the American Statistical Association vol. 69 no. 347 pp. 730-737.

  • WIG data (23.12.2017).