Research On Pricing Of Longevity Swap Based On Modified Lee-Carter Model

With the continuous development of economy and society,our country’s medical level and sanitary conditions have been continuously improved,which makes people’s average life expectancy continue to extend,and people’s actual life expectancy is generally higher than the predicted life expectancy.The extension of life expectancy means additional expenditure.Individuals can transfer the risk of this additional expenditure by participating in pension insurance.As the aggregator of this risk,pension institutions and life insurance companies cannot make this risk directly within the insured group.Diversified,this risk because the actual lifespan is higher than the predicted lifespan is the longevity risk,and the longevity risk is a systemic risk to the entire society.Longevity risk has brought more than expected expenses to the life insurance business of individuals,basic pension insurance and insurance companies.How to solve this problem and effectively manage longevity risk has gradually become a hot issue in social research.In the management of longevity risk,The securitization of longevity risk has become the focus of scholars’ research because of its unique advantages of diversifying systemic risks.In this context,this paper chooses the longevity swap pricing problem as its research object.After combing the previous theories related to longevity risk,it is found that effective management of longevity requires two efforts: on the one hand,we need to choose an appropriate model as far as possible to predict the mortality rate of Chinese population in the future;on the other hand,we need to design a reasonable way of risk diversification to manage longevity risk.Under this train of thought,the work of this paper is as follows:firstly,according to the causes of longevity risk,the topic of longevity risk is drawn,and the impact of longevity risk on society is analyzed.this paper points out the importance of managing longevity risk under the background that our society has entered an aging society,and explains the significance of this topic.Secondly,in the aspect of mortality modeling,the classical Lee-Carter model has a certain subjectivity and great restriction on the constraint condition of the mortality index.The Lee-Carter model is improved to remove the restriction on the mortality index.The parameter estimation value is obtained by using the least square method to correct the deviation estimation,and the unit root test and adjustment of the parameter estimation results are carried out.The effects of the modified model and the modified model are compared by using the residual distribution map and the total root mean square error.It is found that the fitting effect of the improved model is better than that of the original model.Then the modified Lee-Carter model is used to predict the mortality of men and women in the future 30 years in China.Thirdly,in the aspect of longevity risk management,this paper briefly describes the development process of longevity swap.After expounding the operating mechanism of longevity swap,this paper introduces two common pricing methods of longevity swap-Sharp ratio method and Wang conversion pricing method,in which Wang conversion method can be subdivided into single-factor Wang conversion method and two-factor Wang conversion method.Then,in the numerical simulation,the mortality prediction data of 61-year-old men in China are selected to simulate the pricing of longevity swap with single-factor Wang transformation and two-factor Wang transformation,respectively.in the process of numerical simulation,the static survival rate is calculated by the data in empirical life table,and the expected survival rate is calculated by modified Lee-Carter model and Monte Carlo simulation method.Finally,it collates the conclusions of this paper and puts forward some suggestions for our country to promote the development of longevity swap,including paying attention to the collection and collation of mortality-related data,preventing the transaction risk of longevity swap and creating a good development environment for longevity swap.Through the study of this paper,we can draw the following conclusions: the fitting effect of the modified Lee-Carter model on China’s population data is better than that of the original model,and the expected survival rate begins to be higher than the static survival rate after 22 years,and the expected survival rate calculated by two-factor Wang transformation is about 0.2‰ higher than that calculated by single-factor Wang transformation.The final calculated swap price decreases at first and then increases with the extension of the swap period,and is negative in the whole swap period,but may become positive with the further extension of the swap period.The difference between single-factor and two-factor Wang exchange price increases with the increase of years.