The Pricing Model of Pension Benefit Guaranty Corporation Insurance with Regime-Switching Processes

Abstract

This paper aims to evaluate Pension Benefit Guaranty Corporation (PBGC) insurance values through regime-switching models. We separate periods of the economy with faster growth from those with slower growth to observe long-term trends in the economy. We derive a fair PBGC insurance pricing formula under distress termination and intervention termination using regime-switching processes. We set parameters by estimating the S&P 500 index and one-year treasury bills via expectation maximization particle swarm optimization (EM-PSO)-Gradient, which is an extension of the EM-Gradient method. Then, we conduct sensitivity analysis to investigate the impact of model parameters on insurance values. According to the maximum likelihood estimation results, the Akaike information criterion (AIC) and Bayesian information criterion (BIC) estimators show that the regime-switching process has better goodness of fit than the geometric Brownian motion. Scenario analysis also supports the adequacy of our pricing formula.

Essays on Defined Benefit Pension Plans in the USA

“…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 .…”