分红保险的定价研究
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摘要
分红保险是一种兼具保障功能和投资理财功能的保险产品。该险种在2000年被首次引入中国寿险市场，经过十余年的迅猛发展，现已成为我国寿险行业中的主流产品。最新统计数据显示，2011年中国分红保险全行业保费收入为6206亿元，占寿险保费总收入的88.9%。1
但是，作为现阶段我国保险行业里的热销产品，分红保险也面临着颇为严峻的退保问题。统计结果表明，我国寿险市场退保率在近几年里一直呈现着快速上升的趋势。2011年，国内四家上市保险公司（中国人寿、中国平安、中国太保和新华保险）退保总金额超过650亿元，其中，分红保险一度成为退保的重灾区，约占退保金额的七成左右，即455亿元，则可得到2011年分红保险的退保率为7.3%。2在这样高退保率的局面下，研究基于可退保因素的分红保险的定价模型，从而得到分红保险的准确定价，是我国保险业发展中亟待解决的重要课题之一。
本论文的研究内容包括：
第一章：导论。本章阐述了论文的选题背景和研究意义，并综述了国内外学者对寿险的定价方法和引入退保期权后寿险的定价方法的研究成果。
第二章：分红保险概述。在本章中，首先阐述了分红保险的产生背景、分红保险的概念以及目前寿险市场上分红保险的种类，其次分析了分红保险与传统保险险种相比的特征及其优点，最后，分析了分红保险的红利来源，其主要的来源包括：利差益、死差益和费差益。
第三章：保险定价原理及分红保险的传统定价模型的改进。本章首先简单介绍了保险的定价原理和传统分红保险的定价模型，其次为更加真实的模拟保险市场的保费缴纳方式，将传统定价模型改为费率恒定模型（即合约有效期内分期缴纳的保费以恒定的变化率变化的模型）和保费恒定模型（即合约有效期内保费始终保持不变的模型），最后对现阶段退保率的研究方法进行阐述，我国传统精算方法是运用退保率的计算公式来模拟退保期权的。
第四章：基于可退保因素的分红保险的期权定价方法及模型建立。本章是论文的核心。为提高计算退保期权价值的准确性，本章引入期权定价方法并阐述了期权定价方法的发展，通过对二项式期权定价方法的研究，分别提出了基础保单、分红保险保单以及含退保期权的分红保险保单的定价模型。传统精算方法通常采用退保的经验数据表模拟退保期权的价值，通过建立基于退保因素的分红保险模型，一定程度解决了在高退保率下传统方法模拟退保期权的局限性。同时，运用二项式期权定价方法可有效提高对基于退保因素的分红保险（美式期权）定价的准确性。
第五章：基于可退保因素的分红保险期权定价模型的模拟研究。在本章中，分析并模拟了被保险人年龄、分红比例、市场无风险利率、最低保证收益率、资产波动系数和退保贴现率对基于退保因素的分红保险保费定价问题的影响。并得到以下结论：保单定价与被保险人年龄、分红比例、资产波动系数正相关，与无风险市场利率、最低保证收益率、退保贴现率负相关。其中，市场无风险利率、最低保证收益率、分红比例、资产波动系数以及退保贴现率的改变对分红权及退保权的价值影响尤为突出。
第六章：结论与建议。本章对本文的研究成果进行了总结，提出了基于退保因素的分红保险的定价模型并对该模型进行了模拟分析。在本章最后笔者提出了一些关于降低退保率的建议：准确估计产品收益率，确定合理分红比例；依照精算模型，合理定价分红保险；平滑不同年份分红，满足投保人的红利预期；建立专门投资部门，最大化投资收益；加强业务人员监管，避免虚假宣传。
The participating insurance is an insurance product with the function ofindemnification and investment financing. During ten years’development after firstintroduced into China in 2000, it has become the most popular product in theinsurance industry. According to the latest data, the income of the participatinginsurance has reached 620.6 billion yuan in 2011, as 88.9 percent of the total lifeinsurance income.
Nowadays, the participating insurance has become one of the hottest products inChina’s insurance industry. But, at the same time, it is also facing the criticalproblem of surrender options. The statistical results show that the surrender ratekeeps a high growth trend in the life insurance market. The total money from thesurrender options has reached 65 billion yuan within the four listed insurancecompany (China Life, Ping An, China Pacific Insurance and Xinhua Insurance) in2011. The situation of Pricing Participating Insurance is even worse with 45.5 billionyuan as almost 70 percent of the total surrender options. According to the data abovewe can get the surrender rate which is 7.3 percent in 2011. To research the pricingparticipating insurance with the condition of surrender options and get the accurateprice is one of the most urgent problems for developing the insurance industry.
The content for the study in the present paper includes:
Chapter 1: Introduction. This chapter expatiates the background and the meaningof the present paper. Also the pricing method for the life insurance which is changedafter the surrender options introduced is presented.
Chapter 2: The summary of the pricing participating insurance. In this chapter,the background, concept and the categories of the pricing participating insurance have been discussed. The advantage of pricing participating insurance compared tothe traditional insurance has been researched. The bonus for the pricing participatinginsurance mainly includes the interest margin, mortality margin and the expensemargin.
Chapter 3: In this thesis, we construct two models of pricing participatinginsurances. These two models are the constant pricing rate model and the constantprice model. We use the methods of Cox, Ross and Rubinstein option pricing theoryto simulate the value of insurances and then get the true value of bonus options andsurrender options.
Chapter 4: Establishing the model of pricing participating insurances with thecondition of surrender options. This chapter is the core of the paper. The optionvaluation has been introduced to improve the accuracy of calculating the price.Through researching the binomial option valuation method, the models of the basiccontract, the price of non-surrenderable participating contract and the price of wholecontract have been established. Traditional actuarial method always uses experienceddatasheet to simulate the option valuation price. With the model above, thedisadvantage of the traditional method under high surrender rate has been avoided tosome extent. Meanwhile, using the binomial option method can improve theaccuracy for pricing the participating insurances (American style option) with thecondition of surrender options.
Chapter 5: In this thesis, we can safely get the model of pricing participatinginsurance with the condition of surrender options. From the analysis of the modeland simulate the real world cases, we can draw the conclusions that the price ofparticipating insurances is positively related with ages, participating rate and assetvolatility rate and the price of participating insurances also has negative relationshipwith non-risky market rates, minimum guaranteed yield rate and the discount rate ofsurrendering. Moreover, the non-risky market rates, minimum guaranteed yield rate,participating rate, asset volatility rate and the discount rate of surrendering havegreat impacts in bonus options and surrender options.
Chapter 6: Conclusion and advice. Through analyzing the model of pricingparticipating insurances with the condition of surrender options, the advice to reducethe surrender rate has been given. Appropriate participating proportion and price,satisfying the expected return on investment, enhancing the invest income andcontrol are all good ways to reduce the surrender rate.
但是，作为现阶段我国保险行业里的热销产品，分红保险也面临着颇为严峻的退保问题。统计结果表明，我国寿险市场退保率在近几年里一直呈现着快速上升的趋势。2011年，国内四家上市保险公司（中国人寿、中国平安、中国太保和新华保险）退保总金额超过650亿元，其中，分红保险一度成为退保的重灾区，约占退保金额的七成左右，即455亿元，则可得到2011年分红保险的退保率为7.3%。2在这样高退保率的局面下，研究基于可退保因素的分红保险的定价模型，从而得到分红保险的准确定价，是我国保险业发展中亟待解决的重要课题之一。
本论文的研究内容包括：
第一章：导论。本章阐述了论文的选题背景和研究意义，并综述了国内外学者对寿险的定价方法和引入退保期权后寿险的定价方法的研究成果。
第二章：分红保险概述。在本章中，首先阐述了分红保险的产生背景、分红保险的概念以及目前寿险市场上分红保险的种类，其次分析了分红保险与传统保险险种相比的特征及其优点，最后，分析了分红保险的红利来源，其主要的来源包括：利差益、死差益和费差益。
第三章：保险定价原理及分红保险的传统定价模型的改进。本章首先简单介绍了保险的定价原理和传统分红保险的定价模型，其次为更加真实的模拟保险市场的保费缴纳方式，将传统定价模型改为费率恒定模型（即合约有效期内分期缴纳的保费以恒定的变化率变化的模型）和保费恒定模型（即合约有效期内保费始终保持不变的模型），最后对现阶段退保率的研究方法进行阐述，我国传统精算方法是运用退保率的计算公式来模拟退保期权的。
第四章：基于可退保因素的分红保险的期权定价方法及模型建立。本章是论文的核心。为提高计算退保期权价值的准确性，本章引入期权定价方法并阐述了期权定价方法的发展，通过对二项式期权定价方法的研究，分别提出了基础保单、分红保险保单以及含退保期权的分红保险保单的定价模型。传统精算方法通常采用退保的经验数据表模拟退保期权的价值，通过建立基于退保因素的分红保险模型，一定程度解决了在高退保率下传统方法模拟退保期权的局限性。同时，运用二项式期权定价方法可有效提高对基于退保因素的分红保险（美式期权）定价的准确性。
第五章：基于可退保因素的分红保险期权定价模型的模拟研究。在本章中，分析并模拟了被保险人年龄、分红比例、市场无风险利率、最低保证收益率、资产波动系数和退保贴现率对基于退保因素的分红保险保费定价问题的影响。并得到以下结论：保单定价与被保险人年龄、分红比例、资产波动系数正相关，与无风险市场利率、最低保证收益率、退保贴现率负相关。其中，市场无风险利率、最低保证收益率、分红比例、资产波动系数以及退保贴现率的改变对分红权及退保权的价值影响尤为突出。
第六章：结论与建议。本章对本文的研究成果进行了总结，提出了基于退保因素的分红保险的定价模型并对该模型进行了模拟分析。在本章最后笔者提出了一些关于降低退保率的建议：准确估计产品收益率，确定合理分红比例；依照精算模型，合理定价分红保险；平滑不同年份分红，满足投保人的红利预期；建立专门投资部门，最大化投资收益；加强业务人员监管，避免虚假宣传。
The participating insurance is an insurance product with the function ofindemnification and investment financing. During ten years’development after firstintroduced into China in 2000, it has become the most popular product in theinsurance industry. According to the latest data, the income of the participatinginsurance has reached 620.6 billion yuan in 2011, as 88.9 percent of the total lifeinsurance income.
Nowadays, the participating insurance has become one of the hottest products inChina’s insurance industry. But, at the same time, it is also facing the criticalproblem of surrender options. The statistical results show that the surrender ratekeeps a high growth trend in the life insurance market. The total money from thesurrender options has reached 65 billion yuan within the four listed insurancecompany (China Life, Ping An, China Pacific Insurance and Xinhua Insurance) in2011. The situation of Pricing Participating Insurance is even worse with 45.5 billionyuan as almost 70 percent of the total surrender options. According to the data abovewe can get the surrender rate which is 7.3 percent in 2011. To research the pricingparticipating insurance with the condition of surrender options and get the accurateprice is one of the most urgent problems for developing the insurance industry.
The content for the study in the present paper includes:
Chapter 1: Introduction. This chapter expatiates the background and the meaningof the present paper. Also the pricing method for the life insurance which is changedafter the surrender options introduced is presented.
Chapter 2: The summary of the pricing participating insurance. In this chapter,the background, concept and the categories of the pricing participating insurance have been discussed. The advantage of pricing participating insurance compared tothe traditional insurance has been researched. The bonus for the pricing participatinginsurance mainly includes the interest margin, mortality margin and the expensemargin.
Chapter 3: In this thesis, we construct two models of pricing participatinginsurances. These two models are the constant pricing rate model and the constantprice model. We use the methods of Cox, Ross and Rubinstein option pricing theoryto simulate the value of insurances and then get the true value of bonus options andsurrender options.
Chapter 4: Establishing the model of pricing participating insurances with thecondition of surrender options. This chapter is the core of the paper. The optionvaluation has been introduced to improve the accuracy of calculating the price.Through researching the binomial option valuation method, the models of the basiccontract, the price of non-surrenderable participating contract and the price of wholecontract have been established. Traditional actuarial method always uses experienceddatasheet to simulate the option valuation price. With the model above, thedisadvantage of the traditional method under high surrender rate has been avoided tosome extent. Meanwhile, using the binomial option method can improve theaccuracy for pricing the participating insurances (American style option) with thecondition of surrender options.
Chapter 5: In this thesis, we can safely get the model of pricing participatinginsurance with the condition of surrender options. From the analysis of the modeland simulate the real world cases, we can draw the conclusions that the price ofparticipating insurances is positively related with ages, participating rate and assetvolatility rate and the price of participating insurances also has negative relationshipwith non-risky market rates, minimum guaranteed yield rate and the discount rate ofsurrendering. Moreover, the non-risky market rates, minimum guaranteed yield rate,participating rate, asset volatility rate and the discount rate of surrendering havegreat impacts in bonus options and surrender options.
Chapter 6: Conclusion and advice. Through analyzing the model of pricingparticipating insurances with the condition of surrender options, the advice to reducethe surrender rate has been given. Appropriate participating proportion and price,satisfying the expected return on investment, enhancing the invest income andcontrol are all good ways to reduce the surrender rate.
引文
5房海滨,陈立文.嵌入退保期权的寿险保单定价分析.北京理工大学学报（社会科学版）, 2006,(5):85-87
8中国保监会《分红保险管理暂行办法》
9唐浩.分红保险纯保费定价探讨. 2006, P10
10博尔奇.保险经济学.北京.商务印书馆.1999，P22.
11百度百科http://baike.baidu.com/view/125301.htm
12《保险公司偿付能力额度及监管指标管理规定》保监会令2003年第l号
13罗海通.《我国分红保险退保率研究》.西南财经大学硕士学位论文
14《期货与期权交易》.汪五一.中国科学技术出版社
[1] F. Black and M. Scholes. The pricing of options and corporate liabilities. Jounralof Politocal Economy, 1973, (81): 637-659
[2] R. Merton. Theory of rational option pricing. Bell Journal of Economics andManagement Science, 1973, (4):141-183
[3] Schimko D.C.,Finance in Continuous Time. Florida: Kolb Publishing Company,1992:175-183
[4] Albizzati, M. O., and H. Geman. Interest rate risk management and valuation ofsurrender option in life insurance policies. The Journal of Risk and Insurance,1994, 61(4): 461-487
[5] Bacinello A R. S A Persson. Design and pricing of equity-linked life insuranceunder stochastic interest rates. Journal of Risk Finance, 2002, 3(2):6-21
[6] Bacinello A R. Fair Valuation of a guaranteed life insurance participatingcontract embedding a surrender option. The Jornal of Risk and Insurance, 2003.70(3):461-487
[7] David F. Schrager, Anteen A. J. Pelsser. Pricing rate of return guarantees inregular premium unit linked insurance. Insurance: Mathemstics and Economics,2004,(35):326-342
[8]楚军红.通货膨胀对寿险需求的影响机制分析[J].经济科学, 1997(3):49-54
[9]毛丹.保单价值的金融定价模型：[复旦大学硕士论文].上海:复旦大学,2000
[10]胥会平.一类具有利率保障的投资连结保单的定价问题: [复旦大学硕士论文].上海:复旦大学, 2001
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[33]张宁.分红保险中的红利来源分析.金融发展研究, 2008, (1):63-65
[34]罗海通.我国分红保险退保率研究.西南财经大学硕士学位论文, 2009
[35]唐浩.分红保险纯保费定价探讨.西南财经大学硕士学位论文, 2006
8中国保监会《分红保险管理暂行办法》
9唐浩.分红保险纯保费定价探讨. 2006, P10
10博尔奇.保险经济学.北京.商务印书馆.1999，P22.
11百度百科http://baike.baidu.com/view/125301.htm
12《保险公司偿付能力额度及监管指标管理规定》保监会令2003年第l号
13罗海通.《我国分红保险退保率研究》.西南财经大学硕士学位论文
14《期货与期权交易》.汪五一.中国科学技术出版社
[1] F. Black and M. Scholes. The pricing of options and corporate liabilities. Jounralof Politocal Economy, 1973, (81): 637-659
[2] R. Merton. Theory of rational option pricing. Bell Journal of Economics andManagement Science, 1973, (4):141-183
[3] Schimko D.C.,Finance in Continuous Time. Florida: Kolb Publishing Company,1992:175-183
[4] Albizzati, M. O., and H. Geman. Interest rate risk management and valuation ofsurrender option in life insurance policies. The Journal of Risk and Insurance,1994, 61(4): 461-487
[5] Bacinello A R. S A Persson. Design and pricing of equity-linked life insuranceunder stochastic interest rates. Journal of Risk Finance, 2002, 3(2):6-21
[6] Bacinello A R. Fair Valuation of a guaranteed life insurance participatingcontract embedding a surrender option. The Jornal of Risk and Insurance, 2003.70(3):461-487
[7] David F. Schrager, Anteen A. J. Pelsser. Pricing rate of return guarantees inregular premium unit linked insurance. Insurance: Mathemstics and Economics,2004,(35):326-342
[8]楚军红.通货膨胀对寿险需求的影响机制分析[J].经济科学, 1997(3):49-54
[9]毛丹.保单价值的金融定价模型：[复旦大学硕士论文].上海:复旦大学,2000
[10]胥会平.一类具有利率保障的投资连结保单的定价问题: [复旦大学硕士论文].上海:复旦大学, 2001
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