A risk-based model for the valuation of pension insurance

In the US, defined benefit plans are insured by the Pension Benefit Guaranty Corporation (PBGC). Taking account of the fact that the PBGC covers only the residual deficits of the pension fund the sponsoring company is unable to cover and that the plans can be prematurely terminated, we consider a model that accounts for the joint dynamics of the pension fund's and sponsoring firm's assets in order to effectively determine the risk-based pension premium for the insurance provided by the PBGC. We obtain a closed-form pricing formula for this risk-based premium. Its magnitude depends highly on the investment portfolio of the pension fund and of the sponsoring company as well as the correlation between these two portfolios.

► The paper advocates a new risk-based approach to modelling the pension insurance of the PBGC. ► We assume pension fund's and plan sponsor's assets follow Black-Scholes dynamics and are correlated. ► We obtain an analytical valuation formula for the premium for the pension insurance of the PBGC. ► The risk-based PBGC premium increases in the correlation.