Embedded Value in Life Insurance

Abstract

This technical report illustrates the basic principles for a fair valuation system in life insurance. The report is particularly concerned with the market consistent derivation of the Value of Business In Force (VBIF) for portfolios of profit-sharing policies, properly allowing for the cost of the embedded options and guarantees, according to the European Embedded Value Principles (EEVP) stated by the CFO Forum. Some relevant issues concerning the practical utilization of the system and the consistent interpretation of the results are illustrated by numerical examples. Particular attention has been paid to the harmonization with the results provided by more traditional valuation methods. The report is concluded by a description of some relevant details concerning the application of the valuation system to the life portfolios of the RAS Group.Results - The value of business in force (VBIF), the value of the minimum guaranteed return options (the put component of VBIF), the time value of the puts, the expected returns of the segregated funds and other quantities useful for controlling price and risk of the asset-liability portfolios are derived. Theoretical and practical issues are discussed concerning the theory of valuation, the market consistent pricing, the finance of insurance.The valuation procedure - The outstanding portfolios are analysed in the framework of the asset-liabilty valuation under uncertainty. The valuation of the financial components of future profits, as well as of the embedded options, is performed using a stochastic pricing model based on the no-arbitrage principle. The model is calibrated on market data, in order to capture the current interest rate levels, the interest rate volatilities, the stock price volatilities and correlations.In the valuation procedure closed form pricing expressions as well as Monte Carlo simulations are used. The accounting rules defining the segregated fund returns are allowed for. Financial uncertainty is analysed by modelling interest rate risk for each relevant currency, stock price risk, credit risk. Technical uncertainty is measured taking into account mortality/longevity risk, surrender risk, expenses inflation risk.Harmonization - Using the valuation system a logical connection can be created between the traditional approach - based on a single best estimate scenario - and the stochastic valuation model, specified under both the risk-neutral and the real world probabilities. Financial and technical risks, as well as the cost of the embedded options, are measured in terms of value (risk premiums and/or additional costs) and in terms of risk discount spread (discount rate margins).