Pricing Pension Buy-ins

In recent years,due to the extension of life expectancy,the long-term low interest rate and the change of pension accounting standards in western countries,the pension fund deficit risk in the defined benefit plan is increasing,which will lead to many members of the plan cannot receive the committed pension after retirement.To protect the interests of employees,many companies choose to buy pension buy-ins or buy-outs from insurance companies,so as to partially or completely eliminate the pension fund deficit risk.The paper mainly studies the pricing of pension buy-ins.Based on the prior studies about the pricing model of pension buy-ins,we revise the formula of pension assets to make it more realistic.Besides,we consider the influence of government intervention on the pricing formula of pension buy-in.Finally,we give the numerical solution of the pension buy-in price by using Monte Carlo simulation method.Through the sensitivity analysis,we observe the influence of changing model parameters on the price.We find that the rise of long-term average interest rate and initial mortality will both lead to the decline of the price of pension buy-in.The rise of initial proportion of assets in liabilities of an insurance company will lead to the price of pension buy-in rise first,then decline,and finally stabilize.Because the price of pension buy-in reflects the price of longevity risk,interest risk and investment risk embedded in the pension plan,our research will have some enlightenment for the risk management of Chinese pension funds.