Term Structure Modeling for Pension Funds: What to Do in Practice?

Abstract

With the increased emphasis on market valuation in accounting rules and solvency regulation, the proper modeling of interest rate dynamics has become increasingly important for pension funds. A number of pension fund characteristics make these models particularly demanding. First, as the obligations of pension funds stretch far into the future, the model should be reasonable both for short rates and very long term rates. Second, as the value of liabilities increases enormously if interest rates approach zero, especially the probability of very low rates should be modeled correctly. Third, as pension rights are usually indexed, the interaction between interest rates and inflation should be addressed. Fourth, in order to allow for long term analysis, the simulation results should preferably be stationary. Fifth, account has to be taken to possible structural breaks in the inflation and interest rate dynamics, if only to comply with maximum return assumptions of supervisors. In this paper we present a new affine discrete-time, three-factor model of the term structure of interest rates that meets these criteria. The factors are the short term rate, expected inflation and stochastic risk aversion. The model is applied to an unbalanced panel of German/euro area zero coupon yields for maturities of one to sixty years, and estimated using the extended Kalman filter.