Study On The Valuation Of Hybrid Pension Liabilities Under Inflation And Longevity Risk

In the early stages of pension development,almost all pension schemes were defined benefit schemes(DB schemes).With changes in the economic and social development environment,the inadequacies of DB-type schemes themselves became increasingly apparent and were unable to meet the requirements of scheme participants for benefits.Since the 1980 s,pension schemes around the world have begun to shift from the DB model to the defined contribution plan(DC plan)model,with the DC model gradually taking over the mainstream of newly established pension schemes.However,in recent years,DC-type plans have also experienced many problems due to the impact of the capital market.Based on this,countries around the world have reflected on DC-type plans and taken many countermeasures,and some plan sponsors in Europe and the US and other countries have started to adopt hybrid plans.With the rapid development of hybrid pension schemes around the world,scholars in various countries have been conducting more and more in-depth research on hybrid pension schemes,and the research areas have become increasingly rich,such as: research on the optimal investment strategy of hybrid pension schemes,research on inter-generational risk sharing,research on product pricing,research on liability valuation,etc.However,with the long-term investment approach adopted by hybrid pension funds,a complete assessment of the level of liabilities of a hybrid pension system is not an easy task,as hybrid pension funds are subject to shocks such as inflation risk,longevity risk,default risk and tax risk during the long-term investment process,which adds to the difficulties in assessing the level of liabilities of hybrid pensions more accurately.To address the aforementioned challenges in assessing the liabilities of hybrid pension schemes,this paper incorporates inflation risk and longevity risk factors into the hybrid pension liability assessment study separately,as follows.Firstly,we include the inflation risk factor in the valuation of hybrid pension scheme liabilities without considering the longevity risk.Inflation risk is assumed to be measured by the consumer price index(CPI),which follows a geometric Brownian motion,and interest rates,which follow a stochastic rate.The nominal assets of the hybrid pension are discounted net of inflation,and the total outstanding liabilities of the hybrid pension are assessed in terms of the discounted real assets.The valuation expressions for the total outstanding liabilities under inflation risk are introduced using methods such as Ito’s formula and stochastic equations,and the model is simulated numerically to analyse the effects of inflation risk on the mixability parameters,equity allocation ratio,equity volatility,inflation rate,and inflation volatility on the total outstanding liabilities of hybrid pensions.The study shows that the value of the total outstanding liabilities of hybrid pensions increases when inflation risk is taken into account compared to the value of the total outstanding liabilities of hybrid pensions without taking inflation risk into account.In addition,the inflation rate is negatively related to the total outstanding liability of the hybrid pension scheme,while the inflation volatility is positively related to it.Policy implications of the above findings are also given.Based on the different benefit adjustment mechanisms,inflation risk affects the assessment of the total outstanding liabilities of hybrid pensions by affecting the real value of the fund assets of hybrid pensions,while longevity risk affects the assessment of the total outstanding liabilities of hybrid pensions by affecting the increase in the actual life expectancy of hybrid pension scheme participants.We then factor in longevity risk in the assessment of the hybrid pension scheme liabilities without taking inflation risk into account.It is assumed that generations surviving beyond age 80 in a hybrid pension scheme are considered to be long-lived generations,with a maximum life expectancy of 105 years,and that the plan sponsor assumes the benefit payments for the long-lived generations in the form of a unitary opening annuity,with interest rates subject to stochastic interest rates.A valuation expression for the total outstanding liability of the hybrid pension scheme under longevity risk is derived using,among other things,a measure transformation approach and knowledge of stochastic differential equation theory.The model is numerically simulated to analyze the impact of mixed parameters,equity distribution ratio and stock volatility on the valuation of outstanding total liabilities of hybrid pension plans under longevity risk.The research shows that the total outstanding liabilities of the hybrid pension plan considering longevity risk is less than that without longevity risk before the 50 th period of fund operation,and increases after the 50 th period.At the same time,the policy implications of the above research results are given.Finally,we summarize the findings of this paper on the valuation of hybrid pension liabilities incorporating inflation risk and longevity risk factors,and give relevant perspectives on other directions of research on hybrid pension schemes.