Equity-Linked Life Insurance - a Model with Stochastic Interest Rates

Abstract

Assuming constant interest rate Brennan and Schwartz (1976, 1979) obtained the rational insurance premium on an equity linked insurance contract through the application of the theory of contingent claim spricing. Further considerations with deterministic interest rate have been discussed in Aase and Persson (1992) and in Persson (1993). Analysing the single premium case Bacinello and Ortu allow for the short term interest rate to develop in accordance to an Ornstein Uhlenbeck process. In a paper from (1994) they consider extentions to both the single and the periodic premium model.

This paper presents a model similar to the one by Bacinello and Ortu for the periodic premium case with stochastic interest rate dynamics. It is shown that the insurance contract includes an Asian like option contract. Sufficient conditions on the guaranteed amount for the existence of a solution are derived. As no closed form solution will be obtained we discuss different numerical approaches and apply Monte Carlo simulations with a variance reduction technique.

Keywords: Life insurance, stochastic interest rates

JEL Classification: G13