Asset–liability Management Of Life Insurers In The Negative Interest Rate Environment

Nowadays,global interest rates are generally declining,so Japan and some European countries have implemented negative interest rate policy to stimulate economic growth.In other countries that have not yet implemented negative interest rate policy,their interest rate levels are also close to zero.Furthermore,they are considering implementing negative interest rate economic policies in the future,such as the United States,New Zealand and other countries.Although this unconventional quantitative easing policy will stimulate the development of an economy,it has brought serious operational risks to insurance companies.Take the operation of insurance companies in a low-interest-rate economic environment as an example: on the liability side,insurance companies will have to increase the provision of reserves because of the lower interest rate environment,which will lead to an increase in total liabilities;on the asset side,the investment yield of insurance companies will decline due to a drop in interest rates.Therefore,the total surplus of insurance companies will decrease in a low interest rate environment.In addition,the guaranteed rate of return in many insurance products of insurance companies is at a relatively high level,so a drop in interest rates will prevent insurance companies from fully repaying this part of the guaranteed income to policyholders,which will easily lead to a surrender crisis and further affect the normal operation of insurance companies.Even worst,insurers even have the probability of bankruptcy.Many scholars have also proved from an empirical point of view that there is a positive correlation between the return on assets(ROA)of insurance companies and interest rates.In this case,will insurers’ operations suffer more severely when interest rates fall further,that is,when interest rates fall to the negative territory? It is very important to answer this question,because the interest rate is a very important factor in the operation of insurance companies.The level of interest rate risk management directly determines the performance of asset and liability management of insurance companies,which determines the total surplus of insurance companies at each time.However,from the perspective of risk management and model construction,researchers in the insurance companies and scholars have not conducted corresponding research on the assetliability management strategies of insurance companies in a negative interest rate environment.Consequently,insurance companies are unable to fully cope with the arrival of the negative interest rates.To help insurance industry and academia better understand the impact of the negative interest rate environment on insurance companies,this dissertation first studies the impact of interest rate changes and positive or/and negative interest rate changes on insurance companies’ ROA from an empirical perspective.Interest rate data in this dissertation come from the annual yield to maturity of Japanese government bonds of different maturities,and other datas come from the financial annual report publicly online of all insurance companies in the Japanese life insurance market.The Ordinary Least Squares(OLS)model estimates lead to the following important conclusions: insurance companies will suffer more severe operating losses due to falling interest rates in the negative interest rate economic environment than in the positive interest rate economic environment,which is roughly six times the adverse impact of lower interest rates on insurers’ yield levels in a positive-rate economy.Then,to better measure interest rate risk in a negative interest rate environment,this study examine the applicability of the widely used Macaulay or modified duration and convexity in the negative interest rate environment through a simple test,our results show that traditional Macaulay or modified duration and convexity will overestimate the relationship between bond prices and interest rates.Specifically,Macaulay or modified duration will obtain an unreasonable duration value in the negative interest rate environment,which exceeds bond’s maturity.Therefore,in order to better measure the interest rate risk in the negative interest rate environment,this dissertation proposes a method of duration and convexity based on Vasicek’s stochastic interest rate model.Compared with other stochastic interest rate models,the Vasicek stochastic interest rate model has the advantage of capturing negative interest rates,so it will be an appropriate model to measure the risk of negative interest rates.Correspondingly,our results also show that the duration based on Vasicek’s stochastic interest rate model will have a reasonable duration value even in an economic environment with negative interest rates.Subsequently,we propose a research framework for asset-liability management of life insurers in the negative interest rate environment based on total assets,total liabilities and total surplus.Then,under this framework,we solve the optimization problem with the duration(modified duration and duration based on Vasicek model)and convexity(modified convexity and convexity based on Vasicek model)constraints.Finally,we obtain the best operating decisions of insurance companies under these two different constraints.Our results show that in a negative interest rate economic environment,life insurers adopting Vasicek’s stochastic interest rate model-based duration and convexity approach to implement their asset-liability management will have better performance than adopting traditional methods based on the modified duration and convexity.Specifically,life insurers will suffer less interest rate risk and achieve a larger total surplus level at the end of the decision period by adopting the method based on Vasicek model.In addition,since many countries have suffered severe economic damage cause by the COVID-19 pandemic,these countries have tended to implement looser and more aggressive economic policies(i.e.negative interest rate policy)to reduce the negative impact of COVID-19 on the economy during this tough period.Therefore,taking into account the background of negative interest rates and the outbreak of the pandemic will help insurance companies make better optimal decisions.Therefore,in order to re-study the impact of COVID-19 on insurance companies’ asset-liability management strategies,under the insurance company’s asset-liability management research framework based on the above-mentioned Lee-Carter mortality model,this study also established a mortality model with temporary adverse mortality jump process to highlight the adverse impact of COVID-19 on mortality,then derive the best operating decisions for insurance companies in the context of COVID-19.On the one hand,the model with adverse mortality jump process will increase the level of mortality on the liability side of insurance companies in different periods,and on the other hand,it will also affect the duration level on the liability side of insurance companies.so we did not find a model based on short-term adverse mortality jumps.Using the most recent data available at that time,our results show that the COVID-19 pandemic has little impact on the optimal allocation of insurers’ asset-liability management strategies.Furthermore,in order to compare with the best operating decisions of life insurers in a negative interest rate economic environment based on the duration and convexity methods of the Vasicek interest rate model,this study also develop a new risk measure models(i.e.,MAbsolute and M-Square)for insurance companies asset-liability management framework.Based on the total surplus level of insurance companies at the end of the decision in these two different ALM methods,our results show that the insurance company’s asset-liability management strategy based on the risk measure models are not better than the duration and convexity methods based on the Vasicek interest rate model.In order to further investigate whether the ALM framework based on the risk measure models have the possibility to outperform the duration and convexity methods based on the Vasicek interest rate model,we also introduce reinsurance business under this framework to re-analyze the ALM decisions of life insurers.However,our results are still consistent with the case without considering the reinsurance business.The ALM strategy of life insurers based on the duration and convexity methods of Vasicek’s interest rate model is optimal when interest rates are in the negative interest rate environment.This is because that in an economic environment with negative interest rates,compared with other different ALM methods,it is particularly important whether the model can control the risk of negative interest rates.All the method above can reflect the negative interest rate through cash flows of the total assets and total liabilities at each moment,but only the method based on the duration and convexity of the Vasicek interest rate model can control the negative interest rate risk from the perspective of duration and convexity,so it will perform better when the interest rate turn negative.This dissertation is divided into 9 chapters.Based on the theory of interest rate risk management,this study mainly focuses on the empirical test of the impact of positive and negative interest rates on the insurance company’s ROA,the comparative measurement of duration and convexity in the negative interest rate environment,the ALM framework of life insurers in the negative interest rate environment based on duration and convexity constraints,ALM framework including both excess mortality risk caused by COVID-19 and the negative interest rate environment,ALM framework of life insurers based on risk measure models,and the main conclusions and prospects are gradually analyzed.Specifically,the main summary of the content is as follows:Chapter 1,Introduction.It is mainly expounded from the following three aspects.First,the background,research purpose and significance of the topic.Second,research ideas and research structure of this dissertation are discussed based on the research purpose.Third,the main innovation of this dissertation are expounded.Chapter 2,Literature Review.It mainly expounds the implementation background and actual situation of the negative interest rate policy,and then expounds the impact of the negative interest rate environment or interest rate decline on insurance companies,then expounds the theory related to the term structure of interest rate,and finally expounds the measurement method of interest rate risk.The literature review in this chapter has laid a solid research foundation for the subsequent empirical research and the establishment of theoretical models.Chapter 3,Empirical Analysis of Interest rates on Life Insurance Companies’ ROA.This chapter mainly analyzes the impact of interest rate changes on the life insurance company’s ROA from an empirical point of view by using the company data of Japan’s life insurance industry and the yield to maturity(YTM)data of Japanese government bonds with different maturities.Firstly,this chapter analyzes the impact of changes in normal interest rates on life insurers’ ROA.Secondly,this chapter also uses the indicator variable of interest rates and the method of splitting interest rates into both positive and negative interest rates to study the effect of positive and negative interest rate environments on life insurers’ ROA respectively.Our results in this chapter highlight the serious impact of negative interest rates on life insurers,and lay the foundation for the interest rate risk hedging methods used by life insurers in the negative interest rate environment below.Chapter 4,Duration and Convexity Based on Vasicek’s Stochastic Interest Rate Model.Under the background of negative interest rate environment,this dissertation derives the duration and convexity formulas of government bonds,corporate bonds,stocks and life annuities based on the Vasicek interest rate model,and compares them with the formulas based on modified duration and convexity respectively.This dissertation also criticizes the setting of stock duration in the past,and analyzes the unreasonable part in the derivation of stock duration proposed by previous scholars.Then,this dissertation also derives the duration formula of life annuity combined with the Lee-Carter mortality model and the Vasicek stochastic interest rate model by viewing the life annuity as a special coupon bond.In this chapter,we derive the the duration and convexity formulas based on modified measures and Vasicek interest rate model,respectively,providing a solid research basis for the asset-liability management framework of life insurers in the negative interest rate environment below.Chapter 5,Asset-Liability Management Framework of Life Insurers.The whole assetliability management framework of life insurance companies is introduced from the perspective of assets and liabilities.For simplicity,the asset side only considers that life insurers will invest their funds in government bonds,corporate bond index and stock index,and the liability side only considers that life insurance companies have immediate life annuity business.Meanwhile,to better characterize the asset-side cash flow at each moment,we also consider the correlation between the Brownian motion of different financial assets.Finally,we can derive the corresponding total surplus of the life insurance company at each time through the total assets and total liabilities at each time.Chapter 6,Optimal ALM Strategies Based on Duration and Convexity.This chapter is one of the core parts of the thesis.First,based on the modified measure and Vasicek interest rate model,the optimal decision-making model of life insurers subject to duration and convexity constraints is derived.Then,we use a numerical example to illustrate how to solve the proposed ALM optimization problem.Then,under the objective function of maximizing the total surplus of this life insurer at the end of the decision period,we obtain the optimal investment ratio of government bond,corporate bond index and stock index and the optimal life annuity units based on the modified measures and the Vasicek interest rate model,respectively.Chapter 7,Optimal Asset Liability Management Strategies of Life Insurers During the COVID-19 Pandemic.This chapter captures the additional impact of COVID-19 on people’s mortality by introducing a mortality model with temporary adverse mortality jump process,comparing it with the standard Lee-Carter mortality model.Then,we derive the optimal solution for life insurers based on the impact of COVID-19 on the liability side and show the effect of COVID-19 on optimal asset-liability management decisions.Chapter 8,Additional Analysis: Asset Liability Management Strategies Based on Risk Measure Models.In order to compare with the optimal solution of life insurance companies with the duration and convexity constraints based on the Vasicek interest rate model,this chapter deduces the optimal ALM strategies of life insurance companies based on the MAbsolute and M-Square risk measures,respectively.In addition,this dissertation also introduces the reinsurance business into the ALM framework based on M-Absolute and MSquare risk measure models and discusses the optimal asset-liability management strategy of life insurers again.Chapter 9,Conclusion and Outlook.This chapter summarizes the main conclusions drawn in this dissertation,shows the shortcomings of this dissertation,and makes a prospect for the follow-up academic research.After studying the impact of negative interest rate environment on life insurers’ ROA,different duration and convexity methods in the negative interest rate environment,life insurers’ ALM framework in the negative interest rate environment,the impact of the COVID-19 pandemic on life insurers’ ALM strategies,and life insurers’ ALM framework based on two risk measure models,the conclusions drawn in this dissertation mainly include the following five points:1.Taking Japan’s negative interest rate environment and all life insurance companies in the market as an example,this dissertation estimate the ordinary least squares(OLS)model with firm-fixed effect and cluster the standard errors at year levels.Our results show that the performance of life insurers is positively correlated with interest rates and that life insurance companies will suffer more serious economic losses due to falling interest rates in an economic environment with negative interest rates,which is about 6 times larger than that in the positive interest rate environment.2.Methods applied to deal with interest rate risk in the positive interest rate environment,such as modified duration,will overestimate the sensitivity of bond prices to interest rates in the negative interest rate environment,resulting in an unreasonable duration value which is larger than the maturity of coupon bond.Similarly,it can be seen that the modified convexity cannot apply in an economic environment with negative interest rates.Since the Vasicek stochastic interest rate model has the advantage of describing negative interest rates,the duration and convexity based on the Vasicek stochastic interest rate model will have a reasonable duration value even in the negative interest rate environment,so insurance companies should use the duration and convexity approach based on Vasicek’s stochastic interest rate model to address interest rate risk when interest rates turn negative rather than use the modified duration and convexity that are widely used in the positive interest rate environment.3.Compared with the optimal solutions of life insures based on the modified duration and convexity,the optimal asset-liability management strategy of life insures based on the duration and convexity of the Vasicek stochastic interest rate model can make insurance companies invest more of their funds into risky assets(i.e.insurers prefer riskier investments)and sell more life annuity units,allowing life insurers to achieve higher total surplus at the end of the decision period.At the same time,from the perspective of asset and liability duration mismatching,when insurance companies use the duration and convexity method based on the Vasicek stochastic interest rate model to make risk management decisions,the duration mismatching of them value is smaller than that based on the modified duration and convexity,so the interest rate risk faced by insurance companies at that time will be smaller.Moreover,the convexity value obtained by the modified convexity method cannot satisfy the requirement that it is greater than or equal to zero at every moment,so it will lower the total surplus of the insurance company at the end of the decision period.Therefore,from the perspective of the severity of interest rate risk and the total surplus at the end of the decision period,life insurers should manage assets and liabilities based on the duration and convexity of the Vasicek stochastic interest rate model when they are in the negative interest rate environment.It provides a good guide for insurance companies to make asset-liability management decisions in an economic environment with negative interest rates.4.Under the above ALM framework of life insurers in the negative interest rate environment,if the additional mortality risk caused by the COVID-19 pandemic is considered and optimal decisions are made at the same time,our results show that the outbreak of COVID-19 is included in life insurers’ ALM framework has little impact on life insurer’s optimal solution.This may be because life insurers are exposed to greater interest rate risk than mortality risk post COVID-19.Therefore,the difference in the duration of life insurers’ liabilities(i.e.the interest rate risk faced by life insurers)due to different mortality rates will affect the duration and convexity matching degree of the assets and the liabilities,which directly affects the optimal decision of life insurers.5.Under the above-mentioned insurance company’s ALM framework,if we use the methods based on risk measurement models(i.e.,M-Absolute and M-Square models)rather than duration and convexity methods based on Vasicek model,then our results show that life insurers will invest all of their funds in risky assets(stock and corporate bond indices),and the total surplus at the end of the decision period is still lower than that based on Vasicek duration and convexity.This is because when life insurers use the risk measure models to implement their ALM,compared with low-return government bond,their own funds will continue to transfer to stock and corporate bond indices with higher return.However,higher return investment also induces higher investment risk,so life insurers still cannot achieve higher total surplus at the end of the decision period.Meanwhile,in order to further improve the total surplus of life insurers based on the risk measure models,we also include the reinsurance business into the existing ALM framework based on risk measure models,but even so,life insurers still obtain lower total surplus at the end of the decision period.That is,life insurers should still adopt a method based on Vasicek duration and convexity to implement their ALM instead of adopting a method based on M-Absolute or M-Square model when interest rates turn negative.