Market Value Margin via Mean-Variance Hedging

Abstract

We use mean-variance hedging in discrete time, in order to value a terminal insurance liability. The prediction of the liability is decomposed into claims development results, that is, yearly deteriorations in its conditional expected value. We assume the existence of a tradeable derivative with binary pay-off, written on the claims development result and available in each period. In simple scenarios, the resulting valuation formulas become very similar to regulatory cost-of-capital-based formulas. However, adoption of the mean-variance framework improves upon the regulatory approach, by allowing for potential calibration to observed market prices, inclusion of other tradeable assets, and consistent extension to multiple periods. Furthermore, it is shown that the hedging strategy can also lead to increased capital efficiency and consistency of market valuation with Euler-type capital allocations.

Keywords: Cost-of-capital, market consistent valuation, market value margin, mean-variance hedging, Solvency II