Cyber risk modeling: a discrete multivariate count process approach

Abstract

In the past decade, cyber risk has raised much interest in the economy, and cyber risk has evolved from a type of pure operational risk to both operational and liability risk. However, the modeling of cyber risk is still in its infancy. Compared with other financial risks, cyber risk has some unique features. In particular, discrete variables regularly arise both in the frequency component (e.g. number of events per unit time), and the severity component (e.g. the number of data breaches for each cyber event). In addition, the modeling of these count variables are further complicated by nonstandard properties such as zero inflation, serial and cross-sectional correlations, as well as heavy tails. Previous cyber risk models have largely focused on continuous models that are incompatible with many of these characteristics. This paper introduces a new count-based frequency-severity framework to model cyber risk, with a dynamic multivariate negative binomial autoregressive process for the frequency component, and the generalized Poisson inverse-Gaussian distribution for the severity component. We unify these new modeling tools by proposing a tractable Generalized Method of Moments for their estimation and applying them to the Privacy Rights Clearinghouse (PRC) dataset.