Pricing equity-linked guaranteed minimum death benefits with surrender risk by complex Fourier series expansion method

Abstract

This paper considers the pricing problem of an equity-linked guaranteed minimum death benefit product with an expiration time of T, under the assumption of allowing surrender. To model the dynamics of the underlying asset process, we employ several jump diffusion models with regime switching. As many exotic financial products exhibit path dependency, Monte Carlo simulation methods have commonly been used for their valuation. In this paper, we propose a novel and efficient Fourier-based numerical method that utilizes complex Fourier series expansion to value such products. Through both error analysis and numerical experiments, we demonstrate that our proposed method is more effective than the Monte Carlo method. Finally, we conduct a sensitivity analysis on the contract parameters. Our findings have significant implications for the pricing of complex financial products since our proposed method can be readily applied to a variety of derivative products with path dependency.