A copula regression approach for dynamic policyholder behavior

The evolution of the regulatory framework and the increasing relevance of an accurate estimate of the cash flows suggest a detailed analysis of dynamic policyholder behavior for insurance companies. In actuarial academic literature and industrial practice, it is usual to model lapse rates with a two-stage approach. In the first stage, base lapse rates are identified to estimate the "static" component, whereas in the second stage a correction factor, usually based on the dependency between lapses and one or more economic factors, is estimated to model the "dynamic" component. In this paper, we focus on the second stage considering as an economic factor the spread between a market benchmark yield and the policy credited rate. Therefore, we investigate the dependency structure between lapse rate and market spread via a copula regression model and a copula quantile regression. Those models provide the estimate of the expected and quantile lapse rates conditioned to market spread; the joint use of such two statistical tools allows a complete study of dynamic policyholder behavior, allowing to model the entire dependency structure more flexibly. Moreover, we compare these approaches with nonlinear double-sigmoid regression and we show that copula regression and copula quantile regression can have proper goodness of fit and define prediction intervals that represent the tail behavior of policyholders.