Systemic Risk Dependence Analysis of Indonesian Banking Stocks Using Multivariate Copula Approach and Monte Carlo Simulation

Abstract

This study aims to measure and analyze the dependence structure and systemic risk of the four largest banking stocks in Indonesia by market capitalization, namely BBCA, BBRI, BMRI, and BBNI, using the copula approach. Given the limitations of Pearson correlation in capturing nonlinear relationships and tail dependence phenomena under extreme market conditions, the copula approach serves as a superior alternative method due to its ability to separate the dependence structure from the marginal distributions of individual assets. The data employed are daily closing prices spanning from January 1, 2019, to May 31, 2026, covering the COVID-19 pandemic crisis period and the post-pandemic recovery phase. The analytical procedure begins with volatility modeling using an ARMA(1,0)-eGARCH(1,1) specification with Student-t distributed innovations to accommodate fat-tailed properties and asymmetric leverage effects. The model residuals are transformed into the uniform domain via pseudo-observations based on the empirical Probability Integral Transform (PIT). Five copula families are evaluated, namely Gaussian, Clayton, Gumbel, Frank, and Student-t, with model selection criteria based on the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). Empirical results indicate that the Gaussian Copula emerges as the optimal model, yielding an AIC value of -2378.57 and a log-likelihood of 1190.29. This finding suggests that although a substantially positive correlation exists, the dependence structure among banking stocks tends to be linear and symmetric, with no evidence of significant lower tail dependence. Monte Carlo simulation with 50,000 iterations applied to an equal-weighted portfolio generates a daily Value-at-Risk (VaR) estimate of 0.1984% at the 95% confidence level and an Expected Shortfall (ES) of 0.1127% at the same confidence level. From a practical perspective, these findings confirm that diversification strategies within the Indonesian banking stock portfolio remain reasonably effective for mitigating daily market risk. Nevertheless, rigorous monitoring and the implementation of additional stress testing remain essential to anticipate large-scale systemic macroeconomic shocks.