摘要：In this paper we use the No Arbitrage pricing theory in order to derive the fair insurance fee for the Guaranteed Lifelong Withdrawal Benefit (GLWB) option embedded in Variable Annuity contracts (VA);moreover,we verify if the current GLWB fees on the USA market are fair.The typical VA is a unit-linked annuity contract,which is normally purchased by a single premium payment up-front;the premium is invested in one of several funds.The VA also typically contains some embedded guarantees.One of these is the GLWB option:it gives the policyholder the possibility to withdraw annually a certain percentage of the single premium;if the fund value drops to zero the insurer has to pay the guaranteed amount to the policyholder.The guarantee is lifelong.Any remaining account value at the time of death is paid to the beneficiary as death benefit.In line with the actuarial literature,we assume that the fund follows a Geometric Brownian Motion and the insurance fee is paid ongoing as fraction of assets.We take a static approach that hypothesizes the withdrawal amount is always equal to the guaranteed amount.In this case we calculate the fair insurance fee with Monte Carlo simulations under different scenarios and verify that the product is underpriced on the USA market.
关键词：In this paper we use the No Arbitrage pricing theory in order to derive the fair insurance fee for the Guaranteed Lifelong Withdrawal Benefit (GLWB) option embedded in Variable Annuity contracts (VA);moreover,we verify if the current GLWB fees on the USA market are fair.The typical VA is a unit-linked annuity contract,which is normally purchased by a single premium payment up-front;the premium is invested in one of several funds.The VA also typically contains some embedded guarantees.One of these is the GLWB option:it gives the policyholder the possibility to withdraw annually a certain percentage of the single premium;if the fund value drops to zero the insurer has to pay the guaranteed amount to the policyholder.The guarantee is lifelong.Any remaining account value at the time of death is paid to the beneficiary as death benefit.In line with the actuarial literature,we assume that the fund follows a Geometric Brownian Motion and the insurance fee is paid ongoing as fraction of assets.We take a static approach that hypothesizes the withdrawal amount is always equal to the guaranteed amount.In this case we calculate the fair insurance fee with Monte Carlo simulations under different scenarios and verify that the product is underpriced on the USA market.
