9th Symposium on Finance, Banking, and Insurance
Universität Karlsruhe (TH), Germany, December 11 - 13, 2002

Abstract

Estimation of General Rating Models for Insurance Tariffs

Wolfgang Fels

Verband der Versicherungsunternehmen Österreichs

In general insurance tariffs consist of two components: First risks are classified according to basic criteria, say X_t, which - for example in automobile insurance - depend on the type or the power of the vehicles. Given the basic premiums, X_ta, further extra charges and discounts are rated depending on usually more individual characteristics of the risk (say Z_t). All relevant tariffs can be represented by a Generalised Rating Model that represents the net expected premium by

E(y_t) = X_ta*exp{Z_tb}.

While previous work focused either the estimation of linear (X_ta) or multiplicative models (exp{Z_tb}), we will estimate the parameters of the two linear kernel functions simultaneous by Maximum-Likelihood methods. This allows a valid selection and testing of rating criteria within the market-relevant tariffstructure without misleading evidence due to divergent modelstructures. The efficiency of the suggested tariff can immediately be judged by ML-statistics and information criteria.

We illustrate the model and the estimation with examples from the Austrian motor liability market. Restricted estimations provide tariffs which are consistent with exogenous fixed components like a Bonus-Malus scale or traditionally applied discounts.