Risk measure and fair valuation of an investment guarantee in life insurance

Investment guarantees are amongst the most important topics in the pricing and management of life insurance. Traditionally, two ways of analyzing the risk are possible: on the one hand, the financial approach based on risk-neutral measure and leading to option pricing and continuous hedging strategy and on the other hand, a more actuarial approach based on ruin probability and distribution of surplus. The purpose of this paper is to try to integrate these two approaches in the management of life insurance contracts with profits. First, we analyze in terms of value at risk and conditional value at risk the effect of putting an investment guarantee. This will be done in an ALM framework, based on different investment strategies of the insurer in terms of risk and matching between assets and liabilities. The liability side will be represented by a guaranteed technical rate; the asset side will be a mix of stocks, cash and bonds in a Gaussian environment with different matching strategies. Consequences of an investment choice in terms of ruin probability and level of solvency will be illustrated. In a second step, fair valuation principles are used in order to compute the market value of the contract and fix the participation rate of the contract. (c) 2005 Published by Elsevier B.V.