Endogenous model of surrender conditions in equity-linked life insurance

We propose a model for pricing a unit-linked life insurance policy embedding a surrender option. We consider both single and annual premium contracts. First we analyse a quite general contract, for which we obtain a backward recursive valuation formula based on the Cox et al. [Cox, J.C., Ross, S.A., Rubinstein, M., 1979. Option pricing: a simplified approach. J. Finan. Econ. 7, 229–263] binomial model. Then we concentrate upon a particular case, that is the famous model with exogenous minimum guarantees. In this case we extend our previous analysis in order to take into account the possibility that the guarantees at death or maturity and the surrender values are endogenously determined, and provide necessary and sufficient conditions for the premiums to be well defined.