隐含期权定价及其对寿险保单价值、风险影响研究
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摘要
在当前精算实务中,保单定价一直采用传统精算方法。而对于保单中的各种选择权,包括保底利率、分红权、解约权、投资账户转换权、不定期保费等权利,则不进行评估,更不进入费率厘定过程。保单价值和作为保单重要构成部分的隐含期权(正是因为各种隐含期权,形成了各种不同的保单)的价值对保单持有人和保险公司始终是一只黑箱。当前,国际会计准则和我国保险会计准则都要求保险公司按照公允价值评估方法对保单及其所隐含的期权进行定价。保险公司若能将保单价值及组成部分进行合理拆分,并进行公允定价,既对保险人和保单持有人更公平,又可以像搭积木一样构成不同保单,实现产品创新,是当前金融产品定价的大势所趋。
用期权定价方法对保单及其隐含价值进行定价,是目前公认的既符合公允价值定价原则又有可操作性的定价方法。相关文献已经对其进行了大量研究,亦有大量有价值的结论出现,其中最受推崇的莫过于Bacinallo(2003b)将分红保单拆分为三个组成部分,利用各部分相减得到三个隐含期权价值的方法,这也是本文模型的构思基础所在,但是Bacinallo(2003b)以及后来的相关文献均未对其选择保单的拆分方式进行解释和论证。本文认为保单用不同方式进行拆分,所得隐含期权的价值应该是不同的,即保单隐含期权价值的计算存在顺序问题；另外,还应考察当利率发生变动时,各隐含期权的价值之间的相互影响规律,才可能在保单产品设计时做出相应规避或搭配；第三,投资决策权由保险公司还是保单持有人拥有,在利益驱动下可能会出现完全相反的投资决策,以往的研究通常将保险人决定投资决策作为暗含前提,本文则提出两种投资决策方式下定价模型,并加以对比。
为解决以上问题,本文设计了一个涵盖多种保单类型的模型,根据隐含期权的类型将保单分成了10种,从而可以在统一模型框架下计算各隐含期权价值,其它问题也都能在该统一模型框架下得到解决。为方便对比,本模型同时运用期权定价方法和传统精算方法进行计算,其中,传统精算方法采用利率敏感解约率模型和静态解约率模型,既对保单持有人的微观行为进行建模,又建立经验解约率宏观模型。
研究结果发现：第一,不同的计算顺序对隐含期权价值和其在保单价值中的占比的影响显著,同一隐含期权在不同保单中的价值不同,显示不同隐含期权组合对其它隐含期权价值的影响确实存在；第二,不同投保年龄下,解约权和分红权在保单中的重要性不同,解约权与分红权之间存在抵换关系；第三,在有保证利率保单中,投保人投资选择权有很高的价值,不可忽视,在无保证利率保单中,投保人投资选择权价值则为负值,显示保证利率对投保人投资价值选择权的影响显著,在提供给保单持有人投资决策权或投资账户可转换权利时,应高度关注保证利率对高风险偏好的鼓励作用;第四,当完全分红时,各隐含期权价值与其在保单价值中的占比明显提高,显示投资连结保险等完全分红的保单应格外关注各隐含期权的影响；第五,在传统精算方法下,可解约保单的价值明显高于期权定价方法下的计算值,显示目前使用的传统精算方法计算的保单价值可能对保单持有人不公平；第六,传统精算方法下的两种解约率模型相比,动态解约率模型考虑了解约率的最重要影响因素—利差,因此保单价值和解约权价值比静态解约率模型的高。
In the present actuarial practice, traditional actuarial method has being used in policy pricing. However, the various policy options, including the guaranteed interest rate, dividend rights, right of rescission, investment account switch rights, irregular premium rights, are not evaluated, and not even being considered in the ratemaking process. The value of the policy and the embedded options (a variety of different policies because of various embedded options) being the important component of the policy, are always a black box to policyholders and insurance companies. At present, the international accounting standards and China's insurance accounting standards require insurance companies to price policy and its embedded options based on fair value. If the insurance company reasonably split the policy value and its components with fair pricing, it is not only more fair to the insurer and the policy holders, but also formed different policies, just like blocks building, by which realize product innovation, which also represents the general trend of current financial products pricing.
Applying option pricing method to price the policy and its intrinsic value is recognized as the only consistent pricing method with fair value both theoretically and practical. This paper thinks the embedded option value should be different by different ways of policy split, which means sequences exist during calculation of embedded option value of the policy; in addition, we should review the interrelationship among embedded options when interest rate changes, in order to eliminate or make the selection in product design; thirdly, the opposite investment decisions will be made by interest driven from either insurer or policy holders. Being implicit premise, the insurer is usually regarded as the investment decision-maker in former researches; while this paper puts forward two pricing models formed by two kinds of investment decision-making method, and gives comparison.
To solve the above problem, this paper has designed a model covering variety types of policy. The policies are divided into10kinds, depending on the types of their embedded options, so that the embedded option value can be calculated under a unified framework, other problems can also be solved in this unified model. For the convenience of comparison, this model makes the calculation by using option pricing method and the traditional actuarial method. Both interest rate sensitive surrender rate model and the static termination rate model are used in the traditional actuarial method, not only to model the policy holder's microscopic behavior, but also to establish the macroscopic model of experience surrender rate.
The conclusion of this research shows:first, the calculation sequence has significant effect in the value of different embedded options, with different influence ratio in the policy value. The same embedded option has different value in different policy, showing different embedded option value do exist because of different combination of embedded options; second, under different age of the insured, the importance of rescission right and the right to receive dividends in the policy differentiates, there is a trade-off existed between these two rights; third, the investment option of the insured has a high value in the policy with guaranteed interest rate, which cannot be ignored, while with the absence of guaranteed interest rate, the investment option value is negative, showing the guaranteed interest rate influences the right of investment option. While providing the policy holder with the right of investment decision or account switch option, we should pay a high attention to ensure the encouragement function of interest rate on high risk preference; fourth, in the total dividend circumstance, the embedded option value and its proportion in policy value was increased, the embedded option influence in total dividend policy, such as investment linked insurance, should be highly considered; fifth, the value of compensation policy is higher under the traditional actuarial method comparing with option pricing method, showing it may be unfair for the policy holder in current situation, currently in use of the policy value may not be fair to the policy holder; sixth, comparing two cancellation rate model under the traditional actuarial method, because it considers the most important influence factor about spread rate, the policy value and termination value of the right of denunciation is higher in dynamic surrender rate model comparing static model.
用期权定价方法对保单及其隐含价值进行定价,是目前公认的既符合公允价值定价原则又有可操作性的定价方法。相关文献已经对其进行了大量研究,亦有大量有价值的结论出现,其中最受推崇的莫过于Bacinallo(2003b)将分红保单拆分为三个组成部分,利用各部分相减得到三个隐含期权价值的方法,这也是本文模型的构思基础所在,但是Bacinallo(2003b)以及后来的相关文献均未对其选择保单的拆分方式进行解释和论证。本文认为保单用不同方式进行拆分,所得隐含期权的价值应该是不同的,即保单隐含期权价值的计算存在顺序问题；另外,还应考察当利率发生变动时,各隐含期权的价值之间的相互影响规律,才可能在保单产品设计时做出相应规避或搭配；第三,投资决策权由保险公司还是保单持有人拥有,在利益驱动下可能会出现完全相反的投资决策,以往的研究通常将保险人决定投资决策作为暗含前提,本文则提出两种投资决策方式下定价模型,并加以对比。
为解决以上问题,本文设计了一个涵盖多种保单类型的模型,根据隐含期权的类型将保单分成了10种,从而可以在统一模型框架下计算各隐含期权价值,其它问题也都能在该统一模型框架下得到解决。为方便对比,本模型同时运用期权定价方法和传统精算方法进行计算,其中,传统精算方法采用利率敏感解约率模型和静态解约率模型,既对保单持有人的微观行为进行建模,又建立经验解约率宏观模型。
研究结果发现：第一,不同的计算顺序对隐含期权价值和其在保单价值中的占比的影响显著,同一隐含期权在不同保单中的价值不同,显示不同隐含期权组合对其它隐含期权价值的影响确实存在；第二,不同投保年龄下,解约权和分红权在保单中的重要性不同,解约权与分红权之间存在抵换关系；第三,在有保证利率保单中,投保人投资选择权有很高的价值,不可忽视,在无保证利率保单中,投保人投资选择权价值则为负值,显示保证利率对投保人投资价值选择权的影响显著,在提供给保单持有人投资决策权或投资账户可转换权利时,应高度关注保证利率对高风险偏好的鼓励作用;第四,当完全分红时,各隐含期权价值与其在保单价值中的占比明显提高,显示投资连结保险等完全分红的保单应格外关注各隐含期权的影响；第五,在传统精算方法下,可解约保单的价值明显高于期权定价方法下的计算值,显示目前使用的传统精算方法计算的保单价值可能对保单持有人不公平；第六,传统精算方法下的两种解约率模型相比,动态解约率模型考虑了解约率的最重要影响因素—利差,因此保单价值和解约权价值比静态解约率模型的高。
In the present actuarial practice, traditional actuarial method has being used in policy pricing. However, the various policy options, including the guaranteed interest rate, dividend rights, right of rescission, investment account switch rights, irregular premium rights, are not evaluated, and not even being considered in the ratemaking process. The value of the policy and the embedded options (a variety of different policies because of various embedded options) being the important component of the policy, are always a black box to policyholders and insurance companies. At present, the international accounting standards and China's insurance accounting standards require insurance companies to price policy and its embedded options based on fair value. If the insurance company reasonably split the policy value and its components with fair pricing, it is not only more fair to the insurer and the policy holders, but also formed different policies, just like blocks building, by which realize product innovation, which also represents the general trend of current financial products pricing.
Applying option pricing method to price the policy and its intrinsic value is recognized as the only consistent pricing method with fair value both theoretically and practical. This paper thinks the embedded option value should be different by different ways of policy split, which means sequences exist during calculation of embedded option value of the policy; in addition, we should review the interrelationship among embedded options when interest rate changes, in order to eliminate or make the selection in product design; thirdly, the opposite investment decisions will be made by interest driven from either insurer or policy holders. Being implicit premise, the insurer is usually regarded as the investment decision-maker in former researches; while this paper puts forward two pricing models formed by two kinds of investment decision-making method, and gives comparison.
To solve the above problem, this paper has designed a model covering variety types of policy. The policies are divided into10kinds, depending on the types of their embedded options, so that the embedded option value can be calculated under a unified framework, other problems can also be solved in this unified model. For the convenience of comparison, this model makes the calculation by using option pricing method and the traditional actuarial method. Both interest rate sensitive surrender rate model and the static termination rate model are used in the traditional actuarial method, not only to model the policy holder's microscopic behavior, but also to establish the macroscopic model of experience surrender rate.
The conclusion of this research shows:first, the calculation sequence has significant effect in the value of different embedded options, with different influence ratio in the policy value. The same embedded option has different value in different policy, showing different embedded option value do exist because of different combination of embedded options; second, under different age of the insured, the importance of rescission right and the right to receive dividends in the policy differentiates, there is a trade-off existed between these two rights; third, the investment option of the insured has a high value in the policy with guaranteed interest rate, which cannot be ignored, while with the absence of guaranteed interest rate, the investment option value is negative, showing the guaranteed interest rate influences the right of investment option. While providing the policy holder with the right of investment decision or account switch option, we should pay a high attention to ensure the encouragement function of interest rate on high risk preference; fourth, in the total dividend circumstance, the embedded option value and its proportion in policy value was increased, the embedded option influence in total dividend policy, such as investment linked insurance, should be highly considered; fifth, the value of compensation policy is higher under the traditional actuarial method comparing with option pricing method, showing it may be unfair for the policy holder in current situation, currently in use of the policy value may not be fair to the policy holder; sixth, comparing two cancellation rate model under the traditional actuarial method, because it considers the most important influence factor about spread rate, the policy value and termination value of the right of denunciation is higher in dynamic surrender rate model comparing static model.
引文
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