A Study On The Pricing Of Longevity Risk Bonds With Minimum Guaranteed Coupon

As human living standards and medical technology continue to improve,there is a global trend toward a gradual decline in mortality and a gradual increase in life expectancy.Although longevity is a positive development,it also brings a series of risks and challenges.In the case of life insurance,this occurs when the real remaining life of the population exceeds the expected remaining life calculated on the basis of the experience tables of the insurance sector.Such risks are aggregated risks,which are by nature systematic risks that are difficult to diversify through the law of large numbers.Therefore,in the context of increasing longevity risk,it has become a difficult challenge to find appropriate risk management tools for the relevant life insurance companies.Since traditional longevity risk management tools are limited in terms of implementation cost and applicability conditions and have little effect,many scholars in recent years have looked to the capital market to diversify longevity risk and thus help life insurance companies to avoid longevity risk.Therefore,this paper selects a longevity bond as the research object and designs a longevity risk bond with "minimum guaranteed coupon" and full repayment at maturity based on the capital market with Chinese characteristics.A multi-population mortality prediction model is constructed using the GM(1,1)-based optimal performance method,and a CIR stochastic interest rate model and a single-factor Wang transformation pricing method are introduced to provide a pricing model for the bond and conduct numerical simulations and sensitivity analysis.Specifically.In terms of mortality prediction,instead of simply using the traditional Lee-Carter model,we construct a multi-population mortality prediction model based on the GM(1,1)optimal performance method based on the theories of convergence of mortality rates among different groups and optimal performance after finding that the model fits poorly when there is less historical mortality data,and demonstrate through MSE that the method has a better fit for the Chinese mortality prediction with better fitting and prediction effects.In the design of the longevity bond,a longevity risk bond with "minimum guaranteed coupon" and full repayment at maturity is constructed,drawing on the features of the more popular products in the Chinese insurance and investment markets.The minimum return guarantee for investors is achieved to better promote new products such as longevity risk bonds in China.In terms of pricing method,after sorting out several common pricing methods in incomplete markets,this paper chooses the single-factor Wang transformation pricing method,which calculates the price of risk λ through the annuity market and then transforms the mortality index to calculate the bond price more closely to the reality.When choosing the discount rate,because of the long maturity of long-lived risk bonds,the simple use of a fixed discount rate is likely to make the pricing results seriously deviate from the actual,this paper chooses the CIR stochastic interest rate model with mean reversion and constant positive.In summary,this paper designs a long-lived risk bond with a minimum guaranteed coupon after a thorough review of previous research results,and uses the GM(1,1)model to establish a mortality forecasting model more suitable for China under a multi-population perspective,and applies the Wang transformation pricing method and uses the CIR interest rate model to accurately measure the actuarial present value of the bond with a Monte Carlo simulation method.The findings of this study have some practical value,especially for life insurance companies,which can provide them with important risk management tools to help them cope with longevity risk,improve solvency,and promote smooth and healthy development.For investors,it also provides them with a wider variety of investments and promotes the prosperous development of the capital market.