Valuing Equity-Linked Guaranteed Minimum Death Benefits with European-Style Asian Payoffs Under the Regime-Switching Diffusion Process with Jump

In this paper, we consider a novel and efficient method to price equity-linked guaranteed minimumdeath benefits (GMDB) with European-style geometric Asian and arithmetic Asian payoffs. In thesituation of continuous transition of market economy, we assume that the underlying asset price processfollows regime-switching L´evy model and use complex Fourier series (CFS) expansion method to derivethe approximate value of GMDB products. The error analysis shows an exponential convergence rateunder geometric Asian and arithmetic Asian payoffs. Furthermore, the CFS approach is comparedwith other Fourier transform methods and Monte Carlo simulation, the numerical experiment resultsillustrate our method has a distinct advantage over other methods in both efficiency and accuracy