The Study Of Two Group Mortality Based On Two-factor Dynamic Copula And GAS Model

In recent years,mortality improvements around the world are putting more and more pressure on social security systems,pension funds,life insurance companies,and individuals,and thus call for more efficient management of longevity risk.Advances in science and technology have led to an increasing degree of mortality among different countries.Coping with this trend,longevity risk-related capital market solutions have grown in recent years.The natural hedging of annuity policies and life insurance is not perfect and requires risk hedging.Modeling mortality dependence for multiple populations has significant implications for mortality/longevity risk management.A natural way to assess multivariate dependence is to use Copula models.There are not many models that use the Copula model to investigate the relationship of mortality.In 2017,some scholars used the dynamic factor Copula model to study.The model can indeed describe the correlation between different groups,but his model will be a common factor and The load factor of the country factor is set to the same dynamic process.On this basis,we distinguish the load factor variation of different factors.In this paper,we first use time series analysis to simulate the mortality dynamics of each population,that is,use the ARMA-GARCH model to determine the marginal distribution of different populations,and then establish a dynamic multi-factor Copula based on common factors and group-specific factors.The population mortality model and the generalized autoregressive fractional(GAS)framework are used to describe the variation of the load factor of the two factors,respectively.Taking Swiss Re Kortis longevity trend bond as an example,this paper uses our model to estimate the probability distribution of bond index LDIV and some risk measures,and compares it with the estimation results of single factor Copula model and static Copula model.We found that our estimates are closer to those presented by the Risk Modeling Corporation(MRS).Finally,based on the Kortis bond,a new type of longevity bond was developed,which used the bond to hedge the residual risks faced by insurance companies that sell annuity insurance and life insurance,and gave the optimal hedge ratio.