State-Price Deflators and Risk-Neutral valuation of Life Insurance Liabilities

Worldwide life insurance regulations are converging towards stochastic valuation of liabilities. Some regulatory framework requires the actuary to estimate the market consistent value of the liabilities. Often, a risk neutral ESG is used to project and discount future liabilities cash flows. Life insurer’s liabilities cash flows are impacted by policyholders’ dynamics: lapses, dynamic lapses, and surrenders. Such dynamics are related to economic variables for which applying risk-neutrality is challenging, to say the least. An alternative approach is to use a real world ESG with deflators. The purpose of this paper is to contribute to the financial economics literature on state-price deflators. In this paper, we compare the calculations of the market value of a call option under the risk neutral valuation (the Q-measure) and the real world valuation with the deflators (The P-measure). We also look at the Market Value of Liabilities, and the Expected Present Value of Future Profits (PVFP) under the risk neutral valuation and the real world valuation with the deflators for a profit-sharing Single Premium Deferred Annuity (SPDA)s subject to a participation rate, a spread on the index earning, and a minimum guarantee rate. The models built for this paper point to the following conclusions Firstly, State-Price Deflators and risk neutral valuation result in equivalent valuation for publicly traded securities; and secondly, State-Price Deflators and risk neutral valuation result in equivalent valuation for non-traded cash flows such as deferred annuities allowing for participation rate in an equity index, a cap and a spread.