Research Article Risk Estimation in Exchange Rate Markets Based on Stochastic Copula Approach Erol Terzi , 1 Emre Yildirim , 1 B¨ unyamin Saribacak , 2 and Mehmet Ali Cengiz 1 1 Department of Statistics, University of Ondokuz Mayıs, Samsun, Turkey 2 Department of Computer and Instructional Technologies, University of Ondokuz Mayıs, Samsun, Turkey Correspondence should be addressed to Erol Terzi; eroltrz@omu.edu.tr Received 25 May 2022; Revised 20 July 2022; Accepted 21 July 2022; Published 29 September 2022 Academic Editor: Sundarapandian Vaidyanathan Copyright © 2022 Erol Terzi et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Risk estimation is of great importance in financial risk management. In this study, the risk estimation of the exchange rate portfolio is performed via the stochastic copula approach. is model-based latent process has a parameter that changes over time and thus can model the dependency structure between variables in a comprehensive and dynamic way. First, the marginals of the returns are handled with ARMA-GARCH-type models. en, the dependency between variables is modeled via the stochastic copula approach. Finally, risk estimates are carried out at 95% and 99% confidence level for the foreign exchange portfolios. It is found that the proposed risk estimation model based on the stochastic copula approach outperforms both classical methods and static copula models. 1. Introduction Risk estimation is one of crucial issues in risk management. Investors and firms need accurate estimation risk estima- tions in order to make an investment planning. Value at risk is the most commonly used risk measure in literature. is measure can be defined as the potential loss of a financial position at a given significance level and over a certain period. Modeling of the dependency structure between the financial assets that create the portfolio is vital for accurate risk estimation. In classical risk estimation methods, de- pendency structure between financial returns is modeled with Pearson correlation coefficient. However, experimental studies in the literature suggest that financial returns cannot satisfy necessary assumption for normal distribution. erefore, more flexible approaches are needed in order to model the dependency between returns. One of the alter- native methods used for this propose is copula. Copulas are multivariate distribution functions that can flexibly model the dependency structure between variables. It has growing popularity especially in econometrics and financial literature since it does not require strict assumptions on marginal distributions and can model the dependence between var- iables regardless of marginal distributions. It has found that marginal distributions of returns exhibit skewed and excess kurtosis [1]. On the other hand, there are various rela- tionships between financial assets. Longin and Solnik [2] and Ang and Chen [3] found that returns of financial assets are highly correlated during market downturns than during market upturns. Methods that can model symmetric de- pendency failed to overcome various dependence structures such as tail dependency, and therefore, more flexible ap- proaches are needed in modeling the dependency. ere is a great deal of literature that models the dependencies be- tween variables in financial markets and makes risk esti- mations (Al Rahahleh et al. [4]; Wang and Xu [5]; Peng et al. [6]; and Yang et al. [7]). In this paper, the copula theory is utilized for portfolio risk estimation. Copulas have many applications in econometric and financial fields. Breymann et al. [8] and Cherubini et al. [9] are some of the first studies to use copula in financial risk management. ey estimated the VaR of the portfolio using static copulas. Patton [10] Hindawi Discrete Dynamics in Nature and Society Volume 2022, Article ID 8467691, 8 pages https://doi.org/10.1155/2022/8467691