Valuation of a Bermudan DB underpin hybrid pension benefit

TL;DR

This paper develops an arbitrage-free valuation framework for complex pension benefit options, including Bermudan variants, by analyzing optimal switching strategies and comparing different embedded options in pension plans.

Contribution

It introduces a novel valuation approach for Bermudan and other embedded pension options, extending existing models to account for early exercise features and multiple benefit structures.

Findings

Bermudan DB Underpin options can be valued using the proposed arbitrage-free method.

Optimal switching strategies depend on the exercise frontier analysis.

Numerical illustrations show differences between FSE, DB Underpin, and Bermudan options.

Abstract

In this paper we consider three types of embedded options in pension benefit design. The first is the Florida second election (FSE) option, offered to public employees in the state of Florida in 2002. Employees were given the option to convert from a defined contribution (DC) plan to a defined benefit (DB) plan at a time of their choosing. The cost of the switch was assessed in terms of the ABO (Accrued Benefit Obligation), which is the expected present value of the accrued DB pension at the time of the switch. If the ABO was greater than the DC account, the employee was required to fund the difference. The second is the DB Underpin option, also known as a floor offset, under which the employee participates in a DC plan, but with a guaranteed minimum benefit based on a traditional DB formula. The third option can be considered a variation on each of the first two. We remove the requirement from the FSE option for employees to fund any shortfall at the switching date. The resulting option is very similar to the DB underpin, but with the possibility of early exercise. Since we assume that exercise is only permitted at discrete, annual intervals, this option is a Bermudan variation on the DB Underpin. We adopt an arbitrage-free pricing methodology to value the option. We analyse and value the optimal switching strategy for the employee by constructing an exercise frontier, and illustrate numerically the difference between the FSE, DB Underpin and Bermudan DB Underpin options.