Cliquet-Style Return Guarantees in a Regime Switching LLvy Model

Abstract

This paper considers the valuation of equity-linked life insurance contracts that offer an annually guaranteed minimum return. The policy premiums are invested in a reference portfolio that is modeled by means of a regime switching Levy process where the model parameters depend on a continuous, finite state Markov chain. Thereby, we can take into account persistent changes in the underlying (macro)economic conditions of financial markets and depart from the unsatisfactory assumption of stationary and independent increments in Levy models. While Levy models turn out to be satisfactory for the valuation of short-term financial contracts, the inclusion of macroeconomic changes is a relevant risk driver for (long-term) insurance contracts. This paper demonstrates that a second advantage of regime switching Levy models is their mathematical tractability: In contrast to a large part of the related literature, the results in this paper do not rely on simulation but are easy-to-implement and closed-form expressions based on (fast) Fourier techniques. A numerical example demonstrates the impact of regime switching on the fair value of cliquet-style return guarantees.