Cliquet-Style Return Guarantees in a Regime Switching Lévy Model
23 Pages Posted: 8 Jul 2016 Last revised: 15 Dec 2016
Date Written: July 8, 2016
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 Lévy 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 Lévy models. While Lévy 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 Lévy 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.
Keywords: insurance contracts, cliquet-style guarantee, ratchet-type guarantee, annual guarantee, regime switching, Lévy model, Fourier pricing.
JEL Classification: G13, G22.
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