Document Type : Research Article
Author
Department of computer science, Golestan University, Gorgan, Iran
Abstract
This paper develops a novel mathematical framework for modeling operational risk in banking networks, with particular emphasis on rare but high-impact events such as cyber attacks, internal fraud, and system failures. The proposed model combines multivariate Hawkes processes with regime-switching mechanisms to capture both the self-exciting nature of operational losses and the structural changes in the risk environment. The intensity of loss events is modeled as a stochastic process that jumps at each event and decays exponentially, while the regime-switching component allows for transitions between normal and crisis states. We derive closed-form expressions for the moment generating function of cumulative losses and provide analytical approximations for Value at Risk (VaR) and Expected Shortfall (ES). Parameter estimation is performed via maximum likelihood using an EM algorithm adapted for partially observed regimes. The model is calibrated using operational loss data from a major European banking consortium covering 2015-2024. Comprehensive backtesting results across eight competing models demonstrate that the proposed framework significantly outperforms traditional methods such as the Loss Distribution Approach (LDA), standard Hawkes models, and other state-of-the-art approaches, with a 7.32% improvement in regulatory capital accuracy compared to the best benchmark model. The model provides financial institutions with a rigorous tool for capital allocation under Basel III/IV requirements.
Keywords
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