Ayşe Arık, Yeliz Yolcu-Okur, Şule Şahin, Ömür Uğur, Pricing Pension Buy-outs under Stochastic Interest and Mortality Rates, Scandinavian Actuarial Journal, 2018(3): pp. 173 - 190 (March 2018).
Abstract
Pension buy-out is a special financial asset issued to offload the pension liabilities holistically in exchange for an upfront premium. In this paper, we concentrate on the pricing of pension buy-outs under dependence between interest and mortality rates risks with an explicit correlation structure in a continuous time framework. Change of measure technique is invoked to simplify the valuation. We also present how to obtain the buy-out price for a hypothetical benefit pension scheme using stochastic models to govern the dynamics of interest and mortality rates. Besides employing a non-mean reverting specification of the Ornstein-Uhlenbeck process and a continuous version of Lee-Carter setting for modeling mortality rates, we prefer Vasicek and Cox-Ingersoll-Ross models for short rates. We provide numerical results under various scenarios along with the confidence intervals using Monte Carlo simulations.
Keywords: change of measure, defined benefit pension plan, interest rate risk, mortality risk, pension buy-out, stochastic models