A binomial model for valuing equity-linked policies embedding surrender options

Abstract

The computation of the fair periodical premiums for equity-linked policies in a Cox–Ross–Rubinstein (CRR) [Cox, J.C., et al., 1979. Option pricing: A simplified approach. J. Financial Economics 7, 229–263] evaluation framework is computationally complex. In fact, despite we assume that the equity value evolves according to a CRR lattice, the dynamics of the reference fund made up of equities of the same kind is described by a non-recombining tree since, at each contribution date, a constant contribution is added to the fund value. We propose to overcome this problem by selecting representative values among all the effective reference fund values. Then, the fair periodical premiums for equity-linked policies embedding a surrender option and a minimum guarantee are computed following the usual backward-induction scheme coupled with linear interpolation.