The Role of Covariates in Cyber Risk Ratemaking Using GAMLSS

Relying on the SAS® OpRisk Global Data which is the world’s largest collection of publicly reported operational losses, we performed a detailed analysis of the frequency and severity of cyber risk claims with the intention of generating information that helps in the ratemaking process for insurance of this type of risk. We developed two types of analysis, the first considering the Loss Distribution Approach (LDA) and the second using Generalized Additive Models for Location, Scale and Shape (GAMLSS). For both approaches, we adjusted two models, one for the frequency and another for the severity of claims. Additionally, through GAMLSS, we could estimate the coefficients that compose the calculation model for a risk premium, analysing intensity, the covariates effect, allowing to generate a priori estimates for the premium to be calculated for each policy based on the individual risk profile of the insured. Our work shows how much the introduction of covariates can increase the financial need to be charged as well as how much the premium value changes depending on the risk class. Insurance premium estimates may become too high leading to disinterest in both parties, for the insurer in accepting such a risk and on the policyholder due to the high cost.