Valuing Variable Annuities With Guaranteed Minimum Benefits Under Regime-switching Models

Variable annuity(VA)is an equity-linked insurance product,which fulfils the social needs for the aging population by providing a variety of guaranteed minimum benefits products.Nowadays,the research on the valuation and risk management of VA contract is one of the main focuses of the actuarial research.As the durations of life insurance contracts amount to years or even decades,these contracts are vulnerable to the changes of economic regimes.In this respect,Markov regime-switching models can flexibly describe the impacts of the structural changes in economic conditions while maintaining a high degree of tractability.Therefore,this thesis employs the Markov regime-switching model to describe the underlying asset price process and studies the pricing of the VA without and with mortality risk,where we assume that the insurance company and the policyholder only pay payments and surrender policy on a set of predetermined discrete tenor dates.The main research contents of this thesis are as follows:Firstly,under the assumption that the policyholder cannot surrender the policy early,this thesis studies the pricing of the guarantee minimum maturity benefit(GMMB),the GMMB with mortality risk,and the guarantee minimum death benefit(GMDB)with finite maturity.For each VA contract,this thesis considers four payment functions,namely,the minimum guarantees with constant,lookback and geometric average features,and the cliquet-style guarantee.In each case,the Fourier cosine series expansion(COS)method is applied to derive the valuation formulae of these VA contracts.Secondly,under the assumption that the policyholder can choose to surrender the policy early,this thesis investigates the pricing and optimal surrender strategy for the VA in two different surrender ways.The first one assumes that the policyholder is only allowed to surrender the embedded guarantee and receive a surrender benefit at any discrete monitoring time before maturity,and the policyholder will still receive his/her account value at maturity.Meanwhile,this thesis considers that the minimum guarantee in VA contract has lookback and geometric average features under this assumption.The second one assumes that the policyholder can surrender the whole policy and receive a surrender benefit at any discrete monitoring time before maturity,and this thesis considers the VA contracts with constant and cliquet-style gyarantees under the path-dependent fee structure.For each guantantee,the dynamic programming backward recursion and the COS method are utilized to derive some semi-analytical valuation formulae of VA contracts without mortality risk,and the optimal surrender strategies are explored.Furthermore,the dynamic programming backward recursion,the COS method and the integral discretization scheme are used to caculate the value of VA contract with mortality risk.Finally,this thesis compares the COS method with the Monte Carlo method and analyzes the convergence of COS method.The results show that the COS method is computationally efficient in speed and accuracy.This thesis also demonstrates the use of COS method in a range of sensitivity analysis exercises,which shed light on the pricing and risk management of complex variable annuity products.