| In recent decades,with the continuous improvement of people's living standards and the continuous development of economy,science and technology and medical conditions,the overall mortality rate of China's population has shown a downward trend,and the average life expectancy of the nation has been continuously extended.Coupled with other reasons such as the decline in fertility,China's population is aging.The trend of population aging is that insurance companies have nurtured a huge annuity market,but at the same time it has brought problems to insurance companies:the arrival of a new round of payment and the difficulty of pricing products.Long-term continuous improvement of the insured population mortality rate will lead to systemic longevity risk.On the one hand,the systemic longevity risk will increase the insurance company's annuity liabilities,exerting tremendous pressure on the insurance company's finances,and the insurance company's liquidity and solvency.Both will be very severely tested.On the other hand,the expected future payment of traditional life insurance products in the face of longevity risks has declined,which provides a new way of thinking for optimizing the insurance company's business structure,that is,natural hedging.In addition,China's financial market has developed rapidly,financial legislation has become more sophisticated,and interest rates have gradually become market-oriented.Financial business innovation has accelerated,and product forms have emerged one after another.The insurance industry faces new challenges on the asset side and the liability side.On the liability side,the business structure is uneven,high-saving,low-security,fast-return products are favored by the market,and Shantou products are also frequently appearing,although the tone of insurance return protection has improved,but the business and structure of insurance companies still deserve our attention.On the asset side,insurance capital is making waves in the capital market,and fast-forward and fast-moving,resulting in new changes in the risk characteristics of assets and liabilities.The complex and volatile interest rate environment and the fierce competition in the insurance market have led to the disconnection of assets and liabilities,and the contradiction between the fluctuation of asset returns and the rigidity of liability costs.Insurers face greater mismatch risks,making it harder for insurers to match assets and liabilities.The longevity risk can be divided into individual longevity risk and systemic longevity risk according to the subject and scope of the subject.The systemic longevity risk refers to the risk that the actual experience of the improvement of the mortality is higher than expected,causing the insurance company to suffer unintended losses,and the individual longevity risk.It refers to the risk of living expenses incurred when an individual's actual life expectancy is higher than expected after retirement.Individual longevity risks can often be dispersed by the law of large numbers.Individuals transfer their longevity risk to insurance companies by purchasing an annuity.Insurance companies aggregate and disperse through a large number of homogeneous individual longevity risks to ensure the stability of experience.When the actual average life of the insured group is higher than the expected average life,the systemic longevity risk is generated,and the insurance company cannot disperse through the law of large numbers.The larger the underwriting business,the more losses will be lost in the future.Based on all of the above.In the idealized state,the comprehensive immunization strategy is to make the insurance company's surplus not change with the changes of mortality and interest rates,and generally achieve the effect of immunizing longevity risk and interest rate risk.The comprehensive immunization strategy can be carried out in two steps.The first step is to achieve immunity first at the liability side,and the liabilities bear the risk of longevity and interest rate at the same time.The liabilities of the annuity products and life insurance products in the liability side are opposite to the direction of the mortality change.Just use this property to combine the two products to achieve the overall immunity to longevity risks;the second step is to achieve the immunization of interest rate risk by linkage between the asset side and the liability side.The main research contents and structure of this paper are as follows:The first chapter is an introduction,which explains that in the context of continuous improvement in population mortality,continuous life expectancy and complex interest rate environment,insurance companies face huge longevity risks and interest rate risks.There are many solutions to longevity risks,including capital market methods,insurance companies' self-insurance or hedging,and improvements in mortality prediction models.This paper takes the mortality immunization method in the natural hedging strategy as the entry point,and combines the longevity risk and interest rate risk of the insurance company into the research,and points out the possible innovations and deficiencies in this paper at the end of this chapter.The second chapter mainly analyzes the impact of longevity risk and interest rate risk on life insurance companies in China;the pricing and reserve evaluation of commercial annuities and traditional life insurance products is based on the 'China Life Insurance Mortality Table',but the life table of experience is static.There is a lag in the prediction of future population mortality,which is reflected in both old products and new products.First,for older products,pricing is based on the previous set of mortality tables.The assessment of reserves is based on the latest mortality table,and the real mortality rate is dynamically changing.For new products,pricing and reserve assessments are currently based on the latest mortality table,but the mortality rate is changing year by year until the next set of mortality tables is developed.Life insurance companies have a large proportion of medium and long-term policies.This lag will become more and more obvious as the aging phenomenon deepens and the long-term span of insurance coverage becomes more and more obvious.A large number of medium and long-term policies may generate huge dead-end losses or benefice.First of all,this chapter uses three sets of experience mortality tables in China's life insurance industry to explain the improvement of mortality,which proves that the longevity risk does exist and is serious.Secondly,by simply comparing the three sets of mortality assumptions,life insurance company annuity products and traditions Life insurance product pricing and reserve gaps to study the importance of longevity risk to life insurance companies' operations,and point out the shortcomings of existing life pricing and reserve assessments using static life tables.Finally,this chapter also examines the impact of interest rate risk on life insurance company product pricing and reserve assessment.We find that when the mortality rate changes,the annuity product and the traditional life insurance product reserve gap are opposite.According to the Markowitz theory,when the risk factors are negatively correlated,the risk can be reduced or dispersed.Therefore,if this negative correlation is properly utilized,the risk inflow exposure can be reduced and efficient risk control can be achieved.The actuarial present value of annuity products and life insurance products is negatively correlated with mortality,which paves the way for the subsequent introduction of immunization models.In the third chapter,we first introduce the theory of interest rate risk immunization model,and transplant the idea of interest rate risk immunity to longevity risk to establish a mortality immunization model.Then,assuming that the insurance company only operates annuity products and life insurance products,it uses Taylor expansion to study the overall liabilities,and derives the concept of mortality duration and convexity,and solves the optimal life insurance liability ratio of the mortality immunization model.The proportion of annuity liabilities.Finally,we consider the longevity risk and interest rate risk at the same time,and establish a comprehensive immunization model that combines longevity risk and interest rate risk,and adopts the method of binary Taylor expansion and duration gap optimization to study.The ratio of optimal annuity liabilities to life insurance liabilities,and the way in which assets and liabilities are associated.Under the strategy of asset-driven liabilities,after the duration of the company's asset end is determined,the product portfolio of the liability side and the company's entire financial leverage must match;under the debt-driven asset strategy,when the business strategy of the liability side is determined,the asset end is long.The period and the company's entire financial leverage must also be determined to match the liability side.The fourth chapter is also the core part of this paper.This chapter builds a comprehensive immunization strategy under stochastic interest rates.First,we introduce the stochastic interest rate model and the dynamic mortality prediction model,and use the CIR model and the Lee-Carter model to predict the interest rate and mortality,and prepare for the comprehensive analysis of the comprehensive immunization strategy.Then,we assume the specific situation of life insurance company annuity products and life insurance products,and solve the optimal proportion of annuity product liabilities and life insurance product liabilities under the dual Taylor expansion and long-term gap optimization comprehensive immunization strategy.When life insurers maintain this portfolio ratio,the company's overall liabilities are immunized,they do not change with changes in mortality.In addition,we also analyzed the corresponding asset-liability linkage strategy,and plotted the relationship between each liability-side product portfolio,asset end-period and asset-liability ratio.Finally,we conducted a sensitivity analysis of the two key values in the comprehensive immunization strategy.The sensitivity analysis of the duration mainly analyzed the three factors of insurance age,insurance period and extension time.The optimal combination ratio sensitivity analysis was mainly It covers three aspects:the age of insurance,the duration of insurance,and whether there is a risk of basis.In the fifth chapter,we examined the effects of the comprehensive immunization strategy,and gave a comparison and evaluation.The pre-immune reserve distribution and the post-integration distribution were compared and analyzed,and the comprehensive immunization model and the single mortality immunization model were performed.In contrast,the main comparative statistics are mean,standard deviation,and Value at Risk at 95%confidence.The sixth chapter draws the conclusions of this paper and gives relevant suggestions.The conclusion of this paper is:First,the comprehensive immunization strategy is indeed a good strategy for managing longevity risk and interest rate risk.It can reduce the volatility of insurance company liabilities,enable assets and liabilities to be linked,and allow surplus to be free from fluctuations in mortality.And the impact of interest rate fluctuations.And the integrated immunization strategy does not require a mature capital market,does not require insurance companies to find counterparties,and does not require transaction costs.Second,the results of the comprehensive immunization strategy are more reliable than the strategy of only immunization with mortality alone.Because the fluctuation of interest rates exacerbates the risk of longevity,the number of life insurance policies to be matched for each annuity sold under the comprehensive immunization strategy is higher than the number of life insurance policies under the single mortality immunization strategy,which indicates that the longevity risk exists when there is interest rate risk.The single mortality immunization model underestimated the risk of longevity.Finally,the author puts forward relevant suggestions for the current life insurance companies,markets and regulatory authorities in China.It is worth noting that,in order to simplify the analysis,the methods and effects of mortality immunization are emphasized,and the details are not treated.we draw on the foreign treatment methods,we assume that there is no significant difference between the life insurance insured population and the annuity insured population(no adverse selection,there is no basis risk).The pricing mortality rate is predicted by the Lee-Carter model,and the optimal hedging strategy is studied considering the dynamic change of mortality.Here,the annuity and life insurance product pricing share a mortality curve.In addition,in the case of financial market volatility,insurance companies face interest rate risk,so we take interest rate risk into account,predict the interest rate through CIR model and use it for pricing,thus making up for the fixed interest rate is not in line with reality.This article does not do too much research on convexity.When the interest rate and mortality rate change greatly,the error may be large.In the unary Taylor expansion,the second derivative can be used to measure the convexity well;but in the binary Taylor expansion,the second-order immunity is difficult to measure,especially the second-order hybrid partial derivative is difficult to deal with.Therefore,we also introduce a duration gap analysis model.In general,the research in this paper still has certain significance. |
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