Cyber breach risk modeling for insurance: capturing temporal and cross-group dependence

Abstract Cyber breaches pose a significant threat to both enterprises and society. Analyzing cyber breach data is essential for improving cyber risk management and developing effective cyber insurance policies. However, modeling cyber risk is challenging due to its inherent characteristics, including sparsity, heterogeneity, heavy tails, and dependence. This work introduces a cluster-based dependence model that captures both temporal and cross-group dependencies, providing a more accurate representation of multivariate cyber breach risks. The proposed framework employs a cluster-based kernel approach to model breach severity, effectively handling heterogeneity and extreme values, while a copula-based method is used to capture multivariate dependence. Our findings, validated through both empirical and synthetic studies, demonstrate that the proposed model effectively captures the statistical characteristics of multivariate cyber breach risks and outperforms commonly used models in predictive accuracy. Furthermore, we show that our approach can enhance cyber insurance pricing by generating more profitable insurance contracts.