Unraveling heterogeneity in cyber risks using quantile regressions

Abstract

We consider quantile regressions for adequate cyber-insurance pricing across heterogenous policyholders and calculation of claims cost associated with data breach events. We show that the impact of a firm's revenue is stronger (weaker) in the lower (upper) quantile of the cost distribution. This result suggests that mispricing may occur if small and large firms are priced using the average effect estimated by the traditional least squares approach. Using a novel dataset, our study is the first to take firm-specific security information into account. We find that firms with weaker security levels than the industry average are more likely to be exposed to large-cost events. Regarding data breaches, small or mid-size loss events are related to higher cost per breached record. We compare the premiums of a quantile-based insurance pricing scheme with those of a two-part generalized linear model and the Tweedie model to explore the usefulness of the quantile-based model in addressing heterogeneous effects of firm size. Our findings provide useful implications for cyber insurers and policymakers who wish to assess the impacts of firm-specific factors in pricing insurance and to estimate the cost of claims.