The application of copula functions in financial risk management

Molaei, Shaghayegh; Fathi Vajargah, Kianoush; Mottaghi Golshan, HAmid

doi:10.22124/jmm.2026.33097.3015

The application of copula functions in financial risk management

Articles in Press

Document Type : Research Article

Authors

¹ Department of Statistics, NT.C., Islamic Azad University, Tehran, Iran

² Department of Statistics, Islamic Azad University, North Tehran Branch, Tehran, Iran

³ Department of Mathematics, Shahr.C., Islamic Azad University, Shahriar, Iran

10.22124/jmm.2026.33097.3015

Abstract

This study presents a case study of the dependence structure between BTC and USDT over the period May 2024 to May 2025 using a copula-based framework, and the results are specific to the selected asset pair and time period.
We consider several copula families, including the Farlie-–Gumbel-–Morgenstern (FGM) copula as a baseline benchmark model, alongside more flexible alternatives.
Daily log-returns of Bitcoin (BTC) and Tether (USDT) from May 2024 to May 2025 are analyzed.
Empirical results confirm that both upper and lower tail dependence coefficients converge to zero.
Copula parameters are estimated using maximum likelihood and rank-based methods.
Model comparison based on goodness-of-fit criteria indicates that the Frank copula provides the best representation of the dependence structure, while the FGM copula exhibits limitations due to its restricted dependence range.
Portfolio risk is then assessed through Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR).
The results show that risk estimates are sensitive to the choice of copula model.
At the same time, the framework enables generation of synthetic joint distributions for stress testing.
Stress scenarios indicate that portfolio losses can significantly increase under adverse shocks.

Keywords