Risk Margins in Fair Value Reserves

There is a general consensus that, in the absence of a trading market for loss reserves, a reasonable estimate of the “fair value” of unpaid losses is the risk-free present value of an unbiased estimate of those losses plus a market-based risk margin. If the risk margin is defined as the risk-free present value of the market-clearing cost of the capital required to support the unpaid losses during the run-off period, the size of the risk margin depends on the amount of required capital. Existing literature shows how to calculate the risk margin in cases where the amount of required capital is specified exogenously. However, the European Solvency II directive defines the capital requirement as of any given date as an endogenous variable equal to the amount needed to ensure solvency over a one-year time horizon with 99.5% confidence. This paper derives and illustrates an integrated framework for quantifying the required capital, the implied cost-of-capital-based risk margin and the fair value reserve from the expected volatility, payment and other characteristics of an unpaid loss portfolio consistent with the Solvency II standard. The conceptual framework presented has application to both fair value reserving and economic capital modeling.

Keywords. Economic capital, fair value loss reserve, hindsight loss reserve estimate, risk margin, Solvency II, stochastic loss reserve modeling.