Valuation of a DB underpin hybrid pension under a regime-switching Lévy model

Abstract

This paper studies the valuation problem of the defined benefit (DB) underpin guarantee. We consider that the salary process follows a geometric Brownian motion, and the stochastic price index process of the funds in the defined contribution (DC) account is modeled by a regime-switching Lévy process. Under this framework, the explicit valuation formula of the DB underpin option is derived by the Fourier cosine series expansion (COS) method, and the corresponding error analysis is provided. Numerous simulation experiments are performed to illustrate the accuracy and efficiency of the proposed method. In addition, the convergence of this method and its sensitivity with respect to various model paraments are analyzed.