Pricing Pension Buy-outs
Pension buy-out is a special financial asset which is issued to offload the pension liabilities holistically in exchange for an upfront premium. The aim of this study is to enhance a general pricing model for pension buy-out deals. First, we suggest a pricing model under the independence assumption between financial and insurance markets. The model is based on two main components: investment and longevity risks. We provide a contingent claim framework to price investment risk. Investment risk premium is calculated like funding guarantee options. Longevity risk premium is calibrated depending on the longevity-risk security market with the Wang transform. A sensitivity analysis for the investment and longevity risk premiums is also provided. While we examine the impact of different asset strategies and pension valuation rate on the pricing of investment risk, we evaluate the impact of market price of risk on the pricing of longevity risk. The overall price of the pension buy-out deal is obtained as the sum of investment and longevity risk premiums. Second, we concentrate on the pricing of pension buy-outs under the dependence assumption between interest and mortality rates risks with an explicit correlation structure in a continuous time framework. We apply the change of measure technique to simplify the valuation expression. We also present how to obtain the buy-out price using stochastic models to represent the dynamics of the interest and mortality rates. While we employ a non-mean reverting specification of the Ornstein-Uhlenbeck process and a continuous version of Lee-Carter model for modeling mortality rates, we prefer Vasicek and Cox-Ingersoll-Ross models for modeling short rates. We provide numerical results under various scenarios depending on Monte Carlo (MC) simulations. Moreover, we add the corresponding confidence intervals for the calculated buy-out prices under difierent MC iterations.