ANALYSIS OF TAIL DEPENDENCE WITHIN THE FRAMEWORK OF COPULA AND EXTREME VALUE THEORY: BIST INDUSTRIAL INDEX-EXCHANGE RATE APPLICATION

Traditional risk management practices in financial markets have long relied on the assumptions of normal distribution and linear correlation. However, the presence of fat tails, volatility clustering, and increased co-movement during extreme events in financial time series reveals that traditional approaches become significantly inadequate, particularly during periods of crisis. In this study, the dependence structure between the Borsa Istanbul Industrial Index (BIST Industrial) and the exchange rate of US Dollar-Turkish Lira (USD/TRY) is examined using a combined framework of Extreme Value Theory (EVT) and copula models. The analysis is based on 981 daily logarithmic returns covering the period from January 3, 2022, to December 3, 2025. Four different copula models—Gaussian, Student-t, Clayton, and Gumbel—are estimated and compared using the Akaike Information Criterion (AIC). The results indicate that the Gumbel copula provides the best fit, implying the presence of strong and asymmetric upper tail dependence between the BIST Industrial Index and the USD/TRY exchange rate, particularly during periods of positive shocks. Furthermore, Value at Risk (VaR) estimates at the 99% confidence level for an equally weighted portfolio reveal that traditional normal-distribution-based methods underestimate the actual risk by approximately 21%. These findings demonstrate that financial risk arises not only from inter-market dependence but also from fat-tailed marginal distributions, highlighting the necessity of EVT-based copula models for more accurate risk measurement.