Valuation of variable annuities with guaranteed minimum maturity benefits and periodic fees

Abstract

This paper focuses on the valuation of variable annuities with a guaranteed minimum maturity benefit under a regime-switching Lévy model. The model allows policyholders to surrender their annuities and receive a surrender benefit at predetermined tenor times before maturity. Additionally, we consider a state-dependent periodic fee structure where fees are deducted from the policyholder's account if it exceeds a certain level at discrete time points. Incorporating this fee structure, the Fourier cosine series expansion method based on characteristic functions is employed to determine the values and optimal surrender strategies for variable annuity contracts. Finally, we provide a comprehensive set of numerical examples to demonstrate and assess the effectiveness of our approach thoroughly.

Keywords:

• Variable annuities
• optimal surrender
• COS
• regime-switching Lévy model

Acknowledgements

The authors would like to thanks the anonymous referee for valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of Zhimin Zhang was supported by the National Natural Science Foundation of China [grant numbers 12271066, 12171405 and 11871121].