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A cash balance plan is a defined benefit plan that provides a participant with a periodic pay credit (commonly linked to salary and wages and usually tied to age and/or experience) and prescribes an interest crediting rate (usually tied to a constant maturity bond or a Consumer Price Index) that defines how the accumulation of pay credits will evolve over time. The benefit under the cash balance plan is expressed as a lump sum, known as the cash balance “account” or “current account balance” From [1].
Trends in actuarial standards (see for example the Actuarial Standard of Practice (ASOP 4), “Measuring Pension Plans Obligations and Determining Pension Plan Costs of Contribution Costs” and the FAS 157 – Fair Value Measurements) lean towards the reporting of fair values for cash balance and pension liabilities. Pensions funds practitioners must hence include the value of embedded options to the overall cash balance plan liability in order to meet the overall liability for the plan.
The SOA paper “Embedded Options in Pension Plans”, covers many practical aspects of the valuation of the guarantees, trying to improve the traditional actuarial techniques by adapting the market-consistent techniques which are commonly used in the financial engineering literature. Typical cash-balance are discussed:
-The Capital Preservation /Money back guarantee in which the plan participant must receive at least the sum of the pay credits.
-The Enhanced money back guarantee, in which is applied a cumulative floor (i.e. 2%) to and equity based or to a treasury bond yield based plan.
Fairmat’s valuation models for the described guarantees can be found here. With respect to the models used in the article (the Geometric Brownian Motion and Hull-and-White), in Fairmat, several other models can be used: for example, it possible to use the Pelsser’s Squared Gaussian model which avoid Hull and White negative interest rate generation or alternative more sophisticated equity models such as the Heston (Stochastic Volatility), the Variance Gamma (Jumps) or the Dupire (Local Volatility Model).
References
[1] “Embedded Options in Pension Plans”, January 2014. Available at www.soa.org/files/research/projects/research-emb-opt-val-cash-report.pdf
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