The Research On Annuity Pricing Related Risks And Actuarial Model

With the advent of an aging society, pension insurance and enterprise supplementary pension insurance can't meet the individual increasing needs of enjoying good retired life. Annuity is personal independent realization to ensure retirement life demand. This article focuses on annuity risk factors and related actuarial pricing model. Moreover, this study provides domestic annuity products development directions. This paper aims at offering scientific and effective guidance pricing method for insurance companies.As to the risk factors of annuity pricing, the main risks include mortality risk and interest rate risk. Mortality risk means mortality improvement factor varied with time. This study provides a new method for timely and accurate forecast. Interest rate risk study shows that fluctuation factors have different effects on different pricing interest rates. For annuity pricing actuarial models, this article provides corresponding models from the market demand, customer utility and company solvency etc. It demonstrates market acceptable rates, adverse selection conditions and market demand equilibrium rates. Furthermore, based on the use of empirical data, this study gives the profit-oriented rate considering the factors correlation.This paper first analyses annuity pricing risk factors, as follows:First, mortality risk assessment. This article presents individual mortality rate changes over time. From the domestic historical life tables and the annual nation demographic data, a consistent forecast conclusion and parameter estimation about age and sex were obtained, and the time lag problem of insurance industry life tables was effectively resolved. With the annuity data from a large nationwide life insurance company, we get the mortality experience results. On the other hand, the existence of adverse selection factors was verified. It illustrates that people with high income and low mortality are more willing to buy annuity by using a single period utility maximization model. The phenomenon is particularly evident in the era of low interest rates. By using a generic utility functions instead of specific one as well as taking into account interest factor, it demonstrates that low mortality populations have tendency to reduce the current consumption. Through empirical analysis of the annuity data, we find out the larger amount policy is accompanied with lower mortality. Moreover, comprensive mortality force and its first order derivative are both lower than individual one. It's remarkable that this study uses distribution function of the General risk other than a specific risk for the first time. At the same time, the paper gives the empirical analysis.Secondly, interest rate risks assessment. Considering continuous interest rate model, such as Vasicek, CIR and the generalized CKLS model, this article makes contrasts Vasicek model with CKLS model. We find out the expectations and simulation results are relatively consistent. For a low fixed discount rate, stochastic interest rate discounted results and fixed interest rate discounted results are similar. But, high fixed discount rate results are much lower than the corresponding stochastic interest rate discount results. It shows higher fixed discount rate is more risky than smaller one, especially for long-term annuity. Combined with the actual situation of the insurance company assets, this study gives the expected annual assets return rate creatively through the existing interest rate models. It offers a good basis to use profit-oriented comprehensive pricing model.Thirdly, the assessment of the risk factors correlation. Through empirical analysis, for the mortality rate and surrender rate, the mortality rate and surrender rate have different correlation factors in different years. Factors are positive in some years, but may be negative in other years; for mortality and interest rates, mortality rates and the interest rate are almost irrelevant, pricing assumption can be assumed that mortality rate is independent of economic environment. The assumption has been a debate for many years. For surrender rate and market interest rate, they change in the same direction.Lastly, the longevity risk and its preventive measures. With the annual national demographic data, considering the correlation between the decreasing mortality factors over time, this study gives the upper and lower estimation of survival probability through different orders of Taylor expansions. The difference between the upper and lower one is relatively small. The forecast result is adequate from the credibility theory. It offers a useful way to forecast survival probability timely and objectively in the future. With regard to longevity risk, issuing survival bonds can hedge it. This article gives the additional margin and the price of market risk about survival bonds.Then analyzes the actuarial pricing model, as follows:First, market demand model. Currently, whether from customer demand requirement or company solvency, rates were calculated unilaterally and the expense factors were not included. Given the expense factors, the equivalent conditions are deduced between customer demand pricing and company solvency pricing. The results of the study show that both rates are the same with minimization requirement under equivalent conditions. From the optimization view, its optimized expense factors should be 0, which reflects the market has much stricter requirement on expense loading. Reducing insurance company additional expenses is a direct requirement of market demand. The larger the number of insured people, the smaller the rates will be. At the same time, the study gives the balance process example between the rate and the purchase number adjustment.Secondly, customer utility model. It was reported that the probability to purchase annuity is the same regardless mortality rate level. The hypothesis may be unfit for actual underwriting condition. We successfully separate low mortality rate from the purchase possibility and then give results under scenario analysis. The result shows that both assumptions have greater impact on survival level adjustment factor. The survival level adjustment factor is greater than 1 and the study shows the adverse selection factors exist.Thirdly, bankruptcy probability model. Given the minimum capital requirement for a company, the reported solvency results were obtained from static mortality rate. Considering the mortality factors changed with time as well as the annual dividend factors, the present work studies their effects on the solvency of the company. The improvement in the life table has greater impact on the company's bankruptcy probability.Fourthly, the profit-oriented pricing model. Based on data analysis, the interaction between associated risk factors was introduced to this model. Using the relevant risk factors, combined with the expected asset return rate of profit sharing product, the rate under profit target was deduced for the first time.As the extension of the study, we point out the annuity development directions in the future. First, the variable annuity products. These products don't guarantee return rate and principal safety. Insurance companies will not be liable for interest rate risk, but to mortality risk and expense risk. Secondly, the equity-indexed annuity products. The minimum guarantee was achieved by options purchase and potential ideal return was realized by stocks investment. Thirdly, reverse mortgage products. Empirical research results have much significance to the practice.