Managing extreme risk in some major stock markets: An extreme value approach Madhusudan Karmakar ⁎, Girja K. Shukla Indian Institute of Management Lucknow, Prabandh Nagar, Off Sitapur Road, Lucknow, 226 013 UP, India article info abstract Article history: Received 10 May 2013 Received in revised form 2 September 2014 Accepted 2 September 2014 Available online 11 September 2014 The study investigates the relative performance of Value-at-Risk (VaR) models using daily share price index data from six different countries across Asia, Europe and the United States for a period of 10 years from January 01, 2000 to December 31, 2009. The main emphasis of the study has been given to Extreme Value Theory (EVT) and to evaluate how well Conditional EVT model performs in modeling tails of distributions and in estimating and forecasting VaR measures. We have followed McNeil and Frey's (2000) two stage approach called Conditional EVT to estimate dynamic VaR. In stage 1, we model the conditional volatility of each series using an appropriate asymmetric GARCH model which serves to filter the return series such that the asymmetric GARCH residuals are closer to iid than the raw return series. In stage 2, we apply EVT to model the fat tails of the asymmetric GARCH residuals. We have compared the accuracy of Conditional EVT approach to VaR estimation with other competing models. The best performing model is found to be the Conditional EVT for the entire sample. To confirm whether the Conditional EVT would still be the best for a sub-period, we have compared the forecasting accuracy for the sub-sample of bull market. Here too the Conditional EVT maintains its superiority even more precisely. Since the Conditional EVT approach clearly dominates other competing models in terms of VaR forecasting, we would advocate the use of the model when managing tail related market risk in such equity markets. © 2014 Elsevier Inc. All rights reserved. JEL classification: G15 G17 Keywords: Extreme Value Theory Peak over threshold method Conditional EVT Value-at-Risk 1. Introduction In the last two decades, Value-at-Risk (VaR) has become a very popular risk management tool in many different types of organizations. A VaR model measures market risk by determining how much the value of a portfolio could decline with α% probability over a certain time horizon τ as a result of changes in market prices or rates. If for example, α = 1% and τ is one day, the VaR measure would be an estimate of the decline in the portfolio value that could occur with 1% probability over the next trading day. In other words, if the VaR measure is accurate, losses greater than the VaR measure should occur less than 1% of the time. The most commonly used VaR models assume that the probability distribution of the daily financial asset return is normal, an assumption that is far from reality. Many of the asset returns exhibit significant amounts of excess kurtosis. This means that the probability distributions of these daily returns have “fat tails” so that extreme outcomes happen much more frequently than that would be predicted by the normal distribution assumption. In this article, we show how the normal distribution assumption can be relaxed. We propose an extreme value approach popularly known as Extreme Value Theory (EVT) to calculate VaR that allows the user to choose more generalized fat tailed distributions for the daily stock market returns. International Review of Economics and Finance 35 (2015) 1–25 ⁎ Corresponding author. Tel.: +91 522 6696540 (R), +91 522 6696624 (O). E-mail addresses: madhu@iiml.ac.in (M. Karmakar), gkshukla78@gmail.com (G.K. Shukla). http://dx.doi.org/10.1016/j.iref.2014.09.001 1059-0560/© 2014 Elsevier Inc. All rights reserved. Contents lists available at ScienceDirect International Review of Economics and Finance journal homepage: www.elsevier.com/locate/iref