Combining Parametric and Non-Parametric Methods to Compute Value-At-Risk

Abstract

We design a system for calculating the quantile of a random variable that allows us combining parametric and non-parametric estimation methods. This approach is applicable to evaluate the severity of potential losses from existing data records; therefore, it is useful in many areas of economics and risk evaluation. The procedure is based on an initial parametric model assumption and then a nonparametric correction is introduced. In addition, a second correction is proposed so that the value at risk estimator is asymptotically optimal. Our procedure allows smoothing the tail behavior of the empirical distribution. Due to the lack of sample information for extreme values, smoothness in the tail cannot be achieved if classical nonparametric estimators are used. We apply this method to a real problem in the area of motor insurance.