A risk-based premium: What does it mean for DB plan sponsors?

Chen, An; Uzelac, Filip

doi:10.1016/j.insmatheco.2013.10.011

Cited by 7 publications

(8 citation statements)

References 17 publications

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“…Kalra and Jain [9] firstly considered the premature termination of pension fund. Chen [10] extended their results under the assumption that the PBGC functions as a second line of defense, that is to say, the PBGC covers only the residual deficits of the pension fund that the sponsoring company fails to cover, and in the other related paper, Chen and Uzelac [11] examined the case that the distress termination is triggered due to sponsor's underfunding.…”

Section: Introductionmentioning

confidence: 94%

“…In this section, we consider the case that sponsor asset can be underfunded and it is called "distress termination" in [11]. erefore, in this case, we use a stopping time τ p to describe the first time that the sponsor asset falls below or across the threshold ϑy 0 e ]t , given that the sponsor company has corporate debt θy 0 e ]t at time t. We assume ϑ ≥ θ, similar to the assumption used in [11]. Under this framework, the definition of τ p is given as…”

Section: Distress Termination Of Sponsor Assetmentioning

confidence: 99%

“…Mathematical Problems in Engineering By adopting the same method, we have In reality, sometimes both sponsor company and the PBGC only provide a capped retirement income when the employee gets retired early or when the pension fund is highly underfunded. In this case, we can model the support from PBGC by a constant C with C < B R ; by using the similar method as [11], the premium can be calculated. e premium that sponsor company collects from plan participants can also be calculated by the similar method used before.…”

Section: Lemma 2 Let G(t; J T ) and H(t; J T ) Denote The Condition Density Functions Of τ And τ P ; G(t; J T ) And H(t; J T ) Are Then Gmentioning

confidence: 99%

“…e differences between others' contributions and our work are evident. First, different from [9][10][11], we include the market regime for the first time into the premium calculations of PBGC's insurance program. We not only assume that the price dynamics of risky assets depend on the states of the economy but also assume that the proportion of pension fund invested in the risky asset also depends on the states of the economy.…”

Section: Introductionmentioning

confidence: 99%

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Premium Valuation of the Pension Benefit Guaranty Corporation with Regime Switching

Wang

Xie

et al. 2021

Mathematical Problems in Engineering

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The Pension Benefit Guaranty Corporation (PBGC) provides insurance coverage for single-employer and multiemployer pension plans in private sector. It has played an important role in protecting the retirement security for over 1.5 million people since it was established about half a decade ago. PBGC collects insurance premiums from employers that sponsor insured pension plans for its coverage and receives funds from pension plans that it takes over. To address the issue of underfunded plans that the PBGC has, this work studies how to evaluate risk-based premiums for the PBGC. Inspired by a couple of existing work in which the premature termination of pension fund and distress termination of sponsor assets are analyzed separately, our work examines the two types of terminations under one framework and considers the occurrence of each termination dynamically. Given that market regime might have a big impact on the dynamics of both pension fund and sponsor’s assets, we thus formulate our model using a continuous-time two-state Markov chain in which bull market and bear market are delineated. We thus formulate our model using a continuous-time two-state Markov Chain in which bull market and bear market are delineated. In other words, the pension fund and sponsor assets are market dependent in our work. Given that this additional uncertainty described by regime switching makes the market incomplete, we therefore utilize the Esscher transform to determine an equivalent martingale measure and apply the risk neutral pricing method to obtain the closed-form expressions for premium of PBGC. In addition, we carry out numerical analysis to demonstrate our results and observe that premium increases according to the retirement benefit irrespective of the type of terminations. In comparison to the case of early distress termination of sponsor assets, the premium goes up more quickly when premature termination of pension funds occurs first due to the fact that pension fund is the first venue of retirement security. Furthermore, we look at how the premium changes with respect to other key parameters as well and make some detailed observations in the section of numerical analysis.

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Section: Introductionmentioning

confidence: 94%

Section: Distress Termination Of Sponsor Assetmentioning

confidence: 99%

Section: Lemma 2 Let G(t; J T ) and H(t; J T ) Denote The Condition Density Functions Of τ And τ P ; G(t; J T ) And H(t; J T ) Are Then Gmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Premium Valuation of the Pension Benefit Guaranty Corporation with Regime Switching

Wang

Xie

et al. 2021

Mathematical Problems in Engineering

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“…These payments are frequently adjusted to match the risk associated with the provided insurance. Therefore, many studies have been conducted around the premium and PBGC insurance valuation approach (Bodie, 2006;Brown, 2008;Chen and Uzelac, 2014;Chen, Lin, Chang, and Wang, 2022;McCarthy, 2022;Qian, Shen, Wang, and Yang, 2019;Wilcox, 2006;Xie, Wang, Yang, and Zhang, 2021). Bodie (2006), Brown (2008), and Wilcox (2006) find that firms had adverse incentives due to the mispricing of PBGC insurance until 2008, as some sponsors only had to pay the flat rate premium, depending on the number of plan participants 13 .…”

Section: Literature Reviewmentioning

confidence: 99%

Essays on Defined Benefit Pension Plans in the USA

Tabassum¹

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This thesis contains three fundamental and empirical essays with the aim of finding the optimum full funding limit policy for the defined benefit (DB) pension plan system in the USA in terms of Government tax earnings and pension claims. To achieve this aim, I study sponsor contributions and plan terminations in the first two essays and building on these I investigate the optimum policy limit in the third essay of the thesis. In the first essay, I investigate the influence of enforcement of full funding limits on sponsor contributions to private DB pension plans in the US. The full funding limit is a limit on the maximum asset amount that restricts the tax advantages of making voluntary contributions to pension funds. This essay fills a research gap by using only voluntary contributions to analyse the impact of the full funding limit. The results show that, sponsors are less likely to make tax-deductible voluntary contributions when the plans’ funding ratio surpasses the full funding limitation. At the other hand, a lower than required pension plan funding ratio (pension assets/ pension liabilities) increases the likelihood of a voluntary contribution. These findings together support the idea that sponsors want to prefund the balance, but only until any tax advantages are maximized. The second essay includes the full funding limit policy along with both firm and plan specific variables in studying termination decisions using a more comprehensive dataset than used in any previous study. The analysis shows that the condition of the firm only affects the termination decision for PBGC trusteed termination. The state of the plan affects both standard and PBGC trusteed terminations, but in differing ways. The tax rate affects the termination decisions, but in a manner that depends on the funding status of the plan and the type of termination. The third essay determines the optimum value of the full funding limit percentage to ensure better funding positions for defined benefit pension plans and higher profit (i.e., tax earnings – PBGC claims) for the Government. Using estimates from the first two essays and actuarial assumptions for projecting the 757 existing firms for the next 50 years, I generate scenarios to calculate the profit of the Government using tax earnings and PBGC claims for different full funding limitation percentages. My results show that, although the range is larger than the current policy, a narrow range for the full funding limit (110% of pension liability over pension assets) yields the maximum profit. This limit generates the highest tax earnings and the lowest PBGC claims out of all the tested possibilities (which ranged from 100% to 200%). The effect of this limit on tax earnings is the major contributing factor behind this finding.

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