GEV Distribution and Valuation of Guaranteed Unitized Participating Life Insurance

来源 :清华大学,伦敦城市大学 | 被引量 : 0次 | 上传用户:woxiangtoucai
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  Crisis events have significantly changed the view that extreme events in financial markets have negligible probability.It has been a growing pragmatic and theoretical shift in interest from the modeling of normal asset market conditions to the shape and heavy of the tails of the distributions of asset returns that characterize statistical models for extreme events.The Black-Scholes model cannot explicitly explain the negative skewness and the excess kurtosis of asset returns.Typically,in the period of time when the left skewness of asset prices increases,the Black-Scholes model will overprice out-of-the-money call options and underprice in-the-money call options related to when there is greater symmetry in the function of distribution.Especially in the life insurance market,the price of guaranteed unitized participating life insurance contract will be affected by a change in asset volatility which leads to the fluctuations in embedded option value.Thus,when pricing a participating contract with surrender option,it is significant to identify the distribution of stock returns over expansion–recession cycles and the occurrence of catastrophic events,in case of insufficient solvency problem for insurance companies.The primary reason is that these embedded options such as terminal dividend option and the surrender option will determine the fair value of the life insurance contract.Existing literatures rarely considered the pricing for participating life insurance products in the case of GEV(generalized extreme value)asset returns.Therefore,this article is considering the economic crisis which may change the distribution of asset returns.Based on the assumption that the return rate follows the GEV distribution,a multi-factor fair valuation pricing model of guaranteed unitized participating life insurance contract is split into four components: the basic contract,the annual dividend option,the terminal dividend option,and the surrender option.We study the effect of death rate,minimum guaranteed interest rate,annual dividend ratio,terminal dividend ratio and surrender on the embedded option values and calculate the annual premium of the guaranteed unitized participating life insurance contract under different influence factors.The Least-Squares Monte Carlo(LSM)simulation method is used to simulate the pricing model.In addition,we make a comparison in the sensitivity of the pricing parameters under the GEV distribution and Normal distribution.The results show that the option price was highly sensitive to the changes in the tail shape and the value of surrender option under the hypothesis of GEV asset returns is higher than it under the Normal asset returns in most cases.Meanwhile,the changing trends of parameter sensitivity are basically similar under two different distributions.In addition,with the mean of GEV distribution further deviating from Normal distribution,the price of the embedded options would be changed substantially.Especially in the financial crisis and other risk events,GEV distribution can characterize the volatility of return better on assets theoretically,which can improve the precision of embedded option pricing.
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