变额年金保险中最低提取利益保证的定价模型研究

Pricing Model Study on the Guaranteed Minimum Withdrawal Benefit in Variable Annuities

本文对提供最低提取利益保证的变额年金保险进行了深入分析,总结了最低提取利益保证的主要特征(重置条款、奖励条款、惩罚条款),并将这些特征进行了定量的分析。本文在Daniel Bauer等(2006)提出的定价模型的基础上进行了创新和改进,在定价过程中加入了国外年金市场上通行的最低提取利益保证的三大主要特征,研究出一套可操作性较强的定价方法,旨在为将来国内保险公司设计开发此类产品时,提供一些建议和理论指导参考。

China has launched a pilot project on Variable Annuities since May 2010, trying to enrich the product mix and establish a multi-level product structure to cater to the need of different levels of consumers. A variable annuities policy is a financial contract between a policyholder and an insurance company which promises a stream of annuities cash flows. At the initiation of the contract, the policyholder pays a single lump sum premium to the issu er. The trusted fund is then invested in a well diversified reference portfolio of a specific class of assets. Under the policy, the insurer promises to make variable periodic payments to the policyholder on preset future dates. The variable payments would depend on the performance of the reference portfolio, thus the policyholders are provided with the equity participation. Variable Annuity products are the mainstream pension products abroad, among all the guarantees the most popular one is guaranteed minimum withdrawal benefit （GMWB） ,which is also at the greatest risk. A GMWB provides the policyholder with the right to withdraw the initial investment over a certain period of time, irrespective of investment performance, as long as annual withdrawals do not exceed a pre-specified amount. To finance these guarantees, most commonly insurers continuously deduct an option fee at a constant rate from the policyholder＇s ac- count value. China Insurance Regulatory Commission hasn＇t allowed the domestic insurance companies issue this type of Variable Annuities. As isthe most popular guarantee on foreign markets, GMWB does well in meeting the needs of retirement income. It is necessary for our market. country to make up how to apply this type of guarantee in our Besides these, GMWB has three important features, which are step-up features, roll-up features and the bonus features. Step-up ： If the portfolio does well and the contract value exceeds the guaranteed withdrawal balance, then it is reset higher, equal to the contract value. These resets are allowed at certain intervals. Roll-up ： If the insured doesn＇t withdrawal after the commencement of the extraction crease. Penalty： If the withdrawal amount is greater than the will be deducted the amount of the penalty payment. Now China＇ Variable Annuities market has just started, period, the guaranteed withdrawal balance will inpercentage agreed in the contract, the excess amount and the insurance companies who got the authorizations are positively preparing for this new product. But there are very few literatures about Variable Annuities, especially the price models of different guarantees, so this paper＇ studies have a strong practical significance. The article＇s target is to provide references for the domestic insurance companies on theory and practice. During the first part of this paper, the definition of Variable Annuities and different guarantees are given. The second part reviews literatures on GMWB recent years home and abroad. The third part firstly introduces three common additional terms of GMWB, and then provides a numerical example of the payoff from a GMWB rider on two different sceneries （on good or bad market）. Then in the context of good market, we add the step-up features, rollup features and the bonus features into a GMWB rider respectively, and give numerical examples of these. The fourth part gives a pricing model on GMWB, which is based on Daniel Bauer et al （2006） with several improvements. Daniel Bauer et al （2006） introduce a model, which permits a consistent and extensive analysis of all types of guarantees currently offered within Variable Annuity contracts. Besides a valuation assuming that the policyholder follows a given strategy with respect to surrender and withdrawals, they price the contract under optimal policyholder behavior. They try to price all the guarantees, but when it come to GMWB, they simply it too much. Almost all the pricing models haven＇t added the three additional features; this paper fills this gap by doing this. The basic idea is to find the total income at the end of the policy and then discounted it using the risk-free interest rate. in order to get the total income, we use the state variablesto describe the policy each time and consider the policy change in three steps. Lastly as Daniel Bauer et al （2006）, we price the contract under a given strategy andoptimal policyholder behavior.