Mortality Prediction Of Middle-aged And Old Female In China And A Study On The Longevity Bond

With the improvement of China’s economic environment and medical conditions,China’s population mortality rate is decreasing year by year,and the average life expectancy is increasing year by year.By the end of 2019,the average life span of China has reached 77 years,and the elderly dependency ratio is 16.8%.The average payment period of survival annuity is longer and longer,and the insurer’s payment cost in survival annuity is higher and higher.China’s current pension system is consistent with the international general structure system,which is a three pillar structure,namely,public pension,enterprise pension and individual business pension,which are parallel,and mainly public pension.According to relevant research of the Chinese Academy of Social Sciences,from 2018 to 2022,the number of provinces where pension funds fail to make payments will remain at about 14,close to half of the national provincial units,and these provinces are mainly distributed in the northeast and central and western regions.The risk of accumulated balance depletion in some provinces will increase,and the trend of fund balance concentration to some provinces will become more and more obvious.In the case of unbalanced development of public pension fund and increasing gap,the proportion of commercial pension insurance companies in the pension system will inevitably increase.How to deal with such systematic and long-term risks is an urgent issue for insurance companies to consider,and also the focus of the whole society.When their own ability is not enough to deal with the risk of underwriting,insurance companies usually choose reinsurance,mutual insurance,internal product structure adjustment and other traditional ways to transfer risk.However,these methods did not break through the scope of insurance,and could not really transfer and disperse risks.When a large-scale systematic longevity risk occurs,none of the above methods can provide enough protection for insurance enterprises.Therefore,it is the choice of many insurance companies to turn their perspective to the capital market,combine the risk of investors with aggregate longevity risk,and transfer longevity risk by package securitization of annuity assets.Longevity risk derivatives include longevity bond,longevity swap and q-forward,etc.This paper mainly introduces longevity bond and a series of related setting conditions.At present,there are some classic long-lived bonds issued in foreign countries,and the domestic market is basically in the initial stage of development,so this paper mainly uses the experience of foreign long-lived bonds for reference,introduces several risk bond pricing methods,designs bonds and calculates the risk premium of long-lived bonds.In order to disperse the aggregate longevity risk of mortality reduction,it is necessary to accurately predict the future population mortality.In this paper,the original data of mortality rate in China are first smoothed,and then Lee Carter model,which considers the age effect,time factor and the sensitivity of age to time factor,is selected to model the death data of women aged 45-89 from 1997 to 2018.With the help of the fitted parameters,Arima model is used to predict 2019-20 The mortality rate of Chinese women aged 45-89 in 28 years.Based on the prediction results of Lee Carter model and the extrapolation of Coale kisker model,the mortality rate of 90-99 years old women in China from 2019 to 2028 is obtained.The prediction results show that the mortality rate of middle-aged and old women in China will continue to decline in the next 10 years,which shows that the aggregate longevity risk faced by China’s insurance industry is still rising steadily,and the relevant research on longevity risk management is necessary.This paper compares several risk bond pricing methods,such as the traditional Wang conversion,Sharpe ratio pricing and capital asset pricing,and considers that the risk cube pricing method,which imitates the Cobb Douglas production function,has a higher market significance in measuring the risk premium of long-lived bonds based on the consideration of loss degree and loss frequency.At present,the research on longevity risk management tools in China mainly focuses on the continuous mortality linked bonds related to floating interest rate.The principal in risk bonds designed in this paper are easy to understand,and the diachronic empirical parameter valuation from the historical market is used in the calculation of risk premium,which can be calculated without considering inflation and risk-free bond interest rate.At the same time,the empirical parameter valuation comes from foreign countries The market data analysis of catastrophe bond has a strong empirical effect.In general,this paper has the following innovations:first,referring to the data of the census year,the original data of the sampling survey year are smoothed,and the results with moderate smoothing are selected under the condition of considering both the fitting degree and smoothness,so that it can better reflect the natural law of mortality changing with age;second,the Lee Carter model is used for smoothing In mortality fitting,the absolute value of the number of dead people in different years is used as the weight of the weighted double multiplication,which increases the practicability of the results;thirdly,the principal return rate is used as a function of the survival index in the design of longevity bonds,which makes the pricing process of bonds clearer.