The valuation of unit-linked policies with or without surrender options

This paper is concerned with the fair valuation of a kind of equity-linked policies with interest rate guarantees, and we deal with this issue in two aspects: the policies with or without surrender options before maturity date. The method we adopted in this paper is a Partial Differential Equation Approach (PDE). The PDE models for the fair valuation of the policies are derived, and their analytic solutions are obtained when surrender is not allowed. For the valuation of the policy with surrender options, the problem is reduced to a PDE model with free boundaries. The impact of the parameters appearing in the model on the surrender options is investigated by both theoretical and numerical analysis.