Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion

Wenguang Yu, Yaodi Yong, Guofeng Guan, Yujuan Huang, Wen Su and Chaoran Cui
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Wenguang Yu: School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China
Yaodi Yong: College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
Guofeng Guan: School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China
Yujuan Huang: School of Science, Shandong Jiaotong University, Jinan 250357, China
Wen Su: College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
Chaoran Cui: School of Computer Science & Technology, Shandong University of Finance and Economics, Jinan 250014, China

Mathematics, 2019, vol. 7, issue 9, 1-15

Abstract: Recently, the valuation of variable annuity products has become a hot topic in actuarial science. In this paper, we use the Fourier cosine series expansion (COS) method to value the guaranteed minimum death benefit (GMDB) products. We first express the value of GMDB by the discounted density function approach, then we use the COS method to approximate the valuation Equations. When the distribution of the time-until-death random variable is approximated by a combination of exponential distributions and the price of the fund is modeled by an exponential Lévy process, explicit equations for the cosine coefficients are given. Some numerical experiments are also made to illustrate the efficiency of our method.

Keywords: equity-linked death benefits; Fourier cosine series expansion; guaranteed minimum death benefit; option; valuation; Lévy process (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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