**Summary:** This paper presents a method for valuing guaranteed minimum death benefits (GMDB) using the Fourier cosine series expansion (COS) method. The authors first express the value of GMDB using a discounted density function approach and then apply the COS method to approximate the valuation equations. The time-until-death random variable is approximated by a combination of exponential distributions, and the fund price is modeled using an exponential Lévy process. Explicit equations for the cosine coefficients are derived, and numerical experiments are conducted to demonstrate the efficiency of the method. The study also considers the case where the death benefit depends on two stocks or stock funds. The results show that the COS method is effective for valuing GMDB products under various conditions. The paper contributes to the field of actuarial science by providing a practical and efficient approach for valuing GMDB products.**Summary:** This paper presents a method for valuing guaranteed minimum death benefits (GMDB) using the Fourier cosine series expansion (COS) method. The authors first express the value of GMDB using a discounted density function approach and then apply the COS method to approximate the valuation equations. The time-until-death random variable is approximated by a combination of exponential distributions, and the fund price is modeled using an exponential Lévy process. Explicit equations for the cosine coefficients are derived, and numerical experiments are conducted to demonstrate the efficiency of the method. The study also considers the case where the death benefit depends on two stocks or stock funds. The results show that the COS method is effective for valuing GMDB products under various conditions. The paper contributes to the field of actuarial science by providing a practical and efficient approach for valuing GMDB products.