Evaluation of Insurance Products with Guarantee in Incomplete Markets

Life insurance products are usually equipped with minimum guarantee and bonus provision options. The pricing of such claims is of vitalimportance for the insurance industry. Risk management, strategic asset allocation, and product design depend on the correct evaluation of thewritten options. Also regulators are interested in such issues since they have to be aware of the possible scenarios that the overall industry willface. Pricing techniques based on the Black & Scholes paradigm are often used, however, the hypotheses underneath this model are rarely met.To overcome Black & Scholes limitations, we develop a stochastic programming model to determine the fair price of the minimum guaranteeand bonus provision options. We show that such a model covers the most relevant sources of incompleteness accounted in the financial andinsurance literature. We provide extensive empirical analyses to highlight the effect of incompleteness on the fair value of the option, and showhow the whole framework can be used as a valuable normative tool for insurance companies and regulators.