Pricing pension buy-outs under stochastic interest and mortality rates

Pricing pension buy-outs under stochastic interest and mortality rates

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Speakers: Ayse Arik, Andrew Cairns

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 dependencebetween 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

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