Time dynamics of cyber risk

This is the first paper to analyze the three main cyber loss datasets (Advisen, SAS OpRisk
and PRC), yielding the most comprehensive cyber loss data yet considered in the literature. We
first study the problem of report delay bias by applying a two-stage model and document a faster
rate of increase for cyber risk frequency compared with the original data. Based on these results,
we then focus on the time dynamics of cyber risk frequency and severity, where we separately study
the properties of full distribution and tail of loss severity. We find the loss distribution of cyber
events shifts leftwards for both monetary loss and non-monetary loss (such as accounts/records
breached) in the recent period, but the trend of tail risk is different for these two types of loss.
Based on our new multiple change point detection method, we show the tail risk of non-monetary
loss is increasing, while the other is not, although they both consistently exhibit heavy-tailedness
over time. Our results are important for cyber risk management and understanding the insurability
of cyber risk.