Journal of Data Science and Modeling

Multi-Stage Risk Modeling Based on GARCH EVT Copula with Bootstrap Uncertainty Analysis

Articles in Press

Document Type : Research Manuscript

Author

Azar Ghyasi

Department of mathematics, Faculty of Statistics, Mathematics and Computer Science, Allameh Tabataba'i University, Tehran, Iran

https://doi.org/10.22054/jdsm.2026.91882.1085
Abstract
This paper develops a comprehensive framework for portfolio risk measurement integrating GARCH models for conditional volatility, Extreme Value Theory (EVT) for tail risk, and copula functions for dependence. The framework is validated using 1,000 simulated daily observations for two assets, with GARCH(1,1) models for volatility and a $t$-copula for dependence. EVT thresholds are selected using mean excess plots and stability analysis \citep{Coles:et:al:2001}.
Results indicate heavy tails, with kurtosis up to 8.74, volatility persistence exceeding 0.98, GPD shape parameters of 0.23 and 0.29, and a $t$-copula tail dependence coefficient of 0.374. Monte Carlo simulation yields one-day-ahead VaR and CVaR estimates of $-0.74\%$ and $-1.14\%$, respectively. Compared with historical simulation and alternative models, the proposed framework produces VaR estimates 46.67\% lower, while bootstrap confidence intervals demonstrate substantial uncertainty in extreme risk estimates. Kupiec backtesting does not reject the VaR forecasts ($p$-value = 0.5632), although the Christoffersen independence test indicates potential for improvement through more flexible volatility specifications.

Keywords

GARCH
Extreme Value Theory
Copula
Value-at-Risk
Expected Shortfall
Block Bootstrap
Subjects
Journal of Data Science and Modeling

Articles in Press, Accepted Manuscript
Available Online from 15 September 2026

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