A Reduced-Form Model for A Life Insurance’s Net Asset Value

Abstract

In this paper we develop a closed-form model for the net asset value of a life insurance portfolio aimed at simplifying the assessment and quantification of the impact of financial stress scenarios on the insurer’s solvency. In fact, using the current practice based on an internal model is timeconsuming and thus it is not relevant when it comes to carry out sensitivity studies that should require rapid action from the management. Due to the nature of the stress scenarios that are mostly related to the financial market determinants, their impact is quite straightforward on the market value of financial assets. Therefore, in this paper, we focus on the distortion caused on the liability side and investigate a reduced-form model for the best estimate liabilities that is not only easily interpretable but also capable of anticipating market variation impact in the liabilities. The model is built based on a dataset drawn from a French life insurer’s projection model using single, double and triple shocks on the interest rates yield curve, equity market value and profit sharing provision. In order to capture as much information as possible from the dataset, several feasible regression specifications are used. The general form of the empirical model is specified as a linear combination of the risk factors and its predictive ability is investigated based using an out-of sample analysis.