An Application of Beta Binomial GAMLSS for the Estimate of Surrender Rates

This paper deals with the estimate of surrender rate with explanatory variables by a Generalized Linear Model for Location, Scale, and Shape (GAMLSS) where the response variable is assumed Beta Binomial. In actuarial practice and literature, the Binomial Generalized Linear Model is frequently used to get an estimate of surrender rates per policy count conditional to policy and policyholder features. We suggest a regressive model based on a Beta Binomial assumption of the response variable. Beta Binomial is a discrete random variable that differs from binomial because the probability of success at each of n trials is not fixed, but beta distributed. Beta Binomial random variable is fit to model binomial phenomena where the probability of success is not fixed but is inferred from data. Beta Binomial random variable has greater variance and skewness than a Binomial random variable with the same mean, because in the Beta Binomial approach the uncertainty about what the true probability is, is taken into account. This uncertainty makes values far from mean more plausible. Finally, the Beta Binomial does not belong to the exponential family. For this reason, a GAMLSS model is used to get parameter estimates.