Fair value and demographic aspects of the insured loan

The paper deals with the liability valuation of the insured loan in compliance of the fair value requirements for the financial assets and liabilities, as mapped out by the international boards engaged in this tool. Initially we propose a closed form for the fair valuation of the mathematical provision in a framework in which the randomness in the mortality is considered along with the financial risk component. Furthermore, the aim of the paper is to analyze the relevance of the risk arising from the demographic movements on the insured loan reserve. The approach we follow implies the mathematical provision calculated as current values, this meaning at current interest rates and at current mortality rates. In these two variables the basic risk drivers of a life insurance business dwell and the many-sided risk system consists, in its systematic aspects, in the choice of the adequate models for forecasting the future scenarios. The relevance of the impact of the risk connected to the choice of the mortality table (table risk) on the fair value of the mathematical provision is pointed out and quantified using a measurement tool obtained by conditional expectation calculus. The risk mapping is performed analyzing the accidental risk impact on the insured loan portfolio liabilities. In all likelihood, insured loan portfolios are not large enough to be considered well diversified to the aim of the pooling risk reduction; this consideration makes interesting the measuring of the liability variability caused by the random events connected to mortality (mortality risk). Practical implications of assuming different mortality scenarios on the reserve fair value are presented, a graphic description of the model risk deriving from the choice of the demographic model is provided and numerical evidences of the accidental mortality risk are shown.