Vine Copula-Based Multivariate Value-at-Risk for Extreme Rainfall Risk Assessment

Abstract

Extreme rainfall occurring simultaneously across multiple locations can generate spatially dependent risks that are not adequately captured by independent univariate models. This study develops an R-vine copula-based framework to model spatial dependence and quantify joint extreme rainfall risk across seven rainfall stations in DKI Jakarta and West Java, Indonesia. Station-specific marginal distributions were fitted using a mixed discrete-continuous framework to account for zero and positive rainfall observations. The probability integral transform was then applied to construct the dependence structure using an R-vine copula, followed by Monte Carlo simulation to generate multivariate rainfall scenarios and estimate Value-at-Risk (VaR) at the 95% and 99% confidence levels. The fitted R-vine consists of six tree levels and 21 pair-copulas, representing heterogeneous unconditional and conditional dependence among the stations. Model adequacy was evaluated by comparing Kendall’s tau, empirical cumulative distribution functions (ECDF), and quantile-quantile (QQ) plots between observed and simulated data. Bootstrap resampling was used to assess the uncertainty of the multivariate VaR estimates. The results yield a Kendall’s tau RMSE of 0.0935, indicating a relatively small discrepancy between observed and simulated dependence structures. Based on 100,000 simulations, the multivariate VaR estimates are 46.0744 mm at the 95% confidence level and 92.3355 mm at the 99% confidence level, with bootstrap confidence intervals of 45.4340–46.7030 mm and 90.4392–94.6717 mm, respectively. The ECDF and QQ plots indicate satisfactory agreement between observed and simulated rainfall distributions. Kupiec backtesting further confirms the adequacy of the univariate VaR estimates at both confidence levels. Overall, the proposed R-vine copula framework provides a flexible approach for quantifying spatially dependent joint extreme rainfall risk.