Pricing Model Study On Guaranteed Minimum Withdrawal Benefit In Variable Annuities Under Stochastic Interest Rate

In2011, China Insurance Regulatory Commission (CIRC) issued “Notice oncarrying out variable annuity insurance” and “Variable annuity management interimmeasures insurance”, announced that the pilot program on variable annuities isbeginning. Although the time of variable annuity launched to the market is very short,it has caused increasing research attentions of many academics and the industries.However, its theoretical research is lagging behind against as it’s importance, there arefew results concerning it’s theoretical research, so the study of its pricing is necessaryand important.Motivated by the above statement, the problem of Guaranteed MinimumWithdrawn Benefit (GMWB) is studied in this paper. It allows the policyholder tocomplete periodic withdrawals until extracting the guaranteed amount in the validityperiod of the contract. In the process of its pricing, interest rate risk is an importantfactor and can not be ignored. Therefore, the pricing of GMWB is studied in the paper,by considering the stochastic interest rates.Firstly, some explanation of the meaning of GMWB and methods of withdrawalare presented, and some numerical analysis to illustrate its operation are also given, theanalysis is made for interest rate risk of GMWB. Then, the pricing model under fixedinterest rates is established, the analysis is presented for principles and elements ofthe model, assuming that the interest rate obediences Vasicek model, the pricing modelis given under stochastic interest rates, and then the guaranteed value is decomposedinto the value of regular pension and the value of arithmetic Asian put option. Bothmodels mentioned above assume that the policy holder is still valid survive during thepolicy period. Therefore, in this paper, it is revised by considering the risk of death,the pricing formulas are presented concerning fixed interest rates and stochasticinterest rates, respectively. Finally, Monte Carlo method is applied to simulate thepricing of GMWB, a comparative analysis is given for a fair guarantee fee under fixedinterest rates and stochastic interest rates, and the effects of changes in parameters ofthe fair guarantee fee are discussed. Moreover, the simulation results are presented toshow that the fair guarantee fee under stochastic interest rates is greater than that itunder fixed interest rates, and the related coefficient, asset price volatility, withdrawalrate, the policy period etc parameters will affect the fair guarantee fee also varydepending on the interest rate volatility and different.