On the market-consistent valuation of health insurance liabilities

Abstract

We are concerned with the market-consistent valuation of lifelong health insurance products, which are subject to adjustments derived from the actuarial equivalence principle and driven by (medical) inflation. Such products are well-established in the European national markets, and the dynamics of the adjustment mechanism is well-understood from an actuarial perspective. However, the question of market-consistent valuation (as is necessary for Solvency II reporting) has not previously been addressed. This gap has led to a situation where some practitioners use stochastic models while others rely on deterministic methods to assign market-consistent values (Best Estimates) to the same type of health insurance liabilities. The purpose of this note is to fill this gap by showing that the Best Estimate of a lifelong health insurance policy depends on the choice of model for the interest and inflation rates. That is, the Best Estimate is not uniquely determined by the currently prevailing term structures of nominal and real spot rates, whence a deterministic calculation is theoretically unjustified. Furthermore, we construct a valuation portfolio such that the Best Estimate valuation decouples into calculations of 1.) deterministic coefficients derived from policy data and 2.) the prices of basis financial instruments that are independent of the individual policy data. Using this decomposition, the policies do not have to be tracked individually along each generated stochastic path. This allows for a more efficient evaluation of the Best Estimate for a large stock of policies with a stochastic model.