Fair Valuation of Various Participation Schemes in Life Insurance

Fair valuation is becoming a major concern for actuaries, especially in the perspective of IAS norms. One of the key aspects in this context is the simultaneous analysis of assets and liabilities in any sound actuarial valuation. The aim of this paper is to illustrate these concepts, by comparing three common ways of givig bonus in life insurance with profit: reversionary, cash or terminal. For each participation scheme, we compute the fair value of the contract taking into account liability parameters (guaranteed interest rate and participation level) as well as asset parameters (market conditions and investment strategy). We find some equilibrum conditions between all thos coefficients and compare, fro man analytical and numerical point of view, the systems of bonus. Developments are made first in the classical binomial model and than extended in a Black and Scholes economy.