Study On Pricing Of Long Life Swaps Based On Bayesian MCMC

With the development of science and technology and the progress of medical and health care,the mortality rate of the population continues to decline,leading to the gradual extension of human life expectancy.The actual life expectancy in the future exceeds the existing life expectancy,resulting in longevity risks.As a system risk,longevity risk has a wide and far-reaching impact on human economy and society.For insurance companies,the existence of longevity risk has led to the extension of the payment period of annuity products,which poses a certain challenge to their solvency.Compared with the traditional risk management method,longevity risk securitization transfers risks by constructing derivatives related to mortality and linking securities yield and mortality.It has the advantages of low risk transfer cost,high transaction efficiency and low risk.At present,scholars mainly focus on the research of longevity bond market,and there is relatively little research on longevity swap,and the issuance of longevity bonds has been difficult to carry out widely,The longevity swap transaction is flexible and easy to promote,so this paper selects the longevity swap as the research object to hedge the longevity risk.First of all,this paper explains the necessity of longevity risk management by sorting out the connotation and impact of longevity risk,which leads to the introduction of traditional longevity risk management tools and longevity risk securitization tools,and focuses on the development and operation mechanism of longevity swaps.Secondly,because the accurate prediction of mortality is the core of longevity risk quantification,in the mortality prediction model,considering the problem of error accumulation in the prediction process of the traditional two-stage method,this paper uses Bayesian MCMC method to predict the mortality of Chinese men and women in the next 20 years based on the Chinese population mortality data.Thirdly,the actuarial present value of the annuity is used to measure the longevity risk of the dynamic improvement part of the mortality rate due to the change of years,and the relative longevity risk proportion in the annuity under different interest rates,ages,maturities and deferred maturities is given according to gender.Then,it introduces the pricing model of long-lived swaps.Considering the incompleteness of the mortality market,this paper conducts risk neutral pricing on the survival probability,uses the future mortality data of the predicted starting year generated by the model as the static survival probability,and uses the mortality data of the predicted year generated by the model as the expected real survival probability,thus obtaining the swap price,and conducting sensitivity analysis on the interest rate,swap price,risk price and other parameters,Then take a long-lived swap product with a specific term as an example to model and price.Then,the loss function of longevity risk is constructed,and variance reduction ratio,Va R and CVa R are calculated using 10000 monitoring values generated by Win BUGS to measure the effectiveness of longevity swap for hedging longevity risk.At the end of the paper,relevant conclusions are sorted out and corresponding suggestions are provided for dealing with longevity risk and promoting the development of longevity swap market.Through research,it is found that interest rate can effectively hedge longevity risk.Under the low interest rate environment,the relative longevity risk is higher.The relative longevity risk increases with the increase of deferred term,age and annuity term,and the proportion of relative longevity risk caused by time effect in men is higher than that in women;The higher the interest rate is,the lower the swap price is,the longer the swap term is,the higher the swap price is,the higher the risk price is,and the smaller the swap price is,and the improvement trend of mortality rate caused by time effect for men is more obvious than that for women;After the long-life swap,the long-life risk has a more stable loss,that is,a larger R value,and a smaller Va R and CVa R value.The longer the swap term,the larger the R value,and the smaller the Va R and CVa R values,indicating that the long-life swap can hedge the long-life risk well.