An Analysis of the Solvency II Regulatory Framework's Smith-Wilson Model for the Term Structure of Risk-Free Interest Rates

52 Pages Posted: 15 Aug 2017 Last revised: 1 Dec 2018

See all articles by Peter Løchte Jørgensen

Peter Løchte Jørgensen

University of Aarhus - Business and Social Sciences

Date Written: August 10, 2018


In the European Union financial regulation requires that life and pension (L&P) companies use the Smith and Wilson (2000) model for the term structure of risk-free interest rates when valuing their liabilities and long term guarantees. Some key features of this model are that it allows for a perfect fit to market observed bond prices, and that its extrapolated long rates converge towards a constant level, the Ultimate Forward Rate (UFR). Both this level and the rate at which convergence towards it takes place are directly specified via parameters of the model. Since the Smith-Wilson model is not one of finance theory's standard term structure models, we introduce the model and summarize its most important mathematical properties. We also describe how the European Solvency II regulation came to embrace this particular model.

The paper moves on to document how the regulation also imposes quite detailed and tight restrictions on how the Smith-Wilson model should be parameterized and applied. We argue that many of these implementation instructions - one of which is the regulator's specification of a very high UFR - seem biased in the same direction and that this could indicate a systematic attempt to "lift" the term structure curve up and away from its true location whereby artificially high discount rates are induced. The result of the bias is not only significant undervaluation of L&P liabilities but also a peculiar contradiction of the Solvency II overall objective of enhancing financial stability and of protecting policyholders via the promotion of economic valuation in accordance with market consistent principles.

The paper's analysis is accompanied by valuation illustrations based on data on the liability composition of an actual medium-sized Danish pension fund. The results suggest that the undervaluation of liabilities resulting from use of the regulation compliant Smith-Wilson model can be massive compared to results obtained from some alternative and more freely calibrated models.

Keywords: Solvency II, financial regulation, term structure of interest rates, calibration, market valuation

JEL Classification: G12, G22, G28

Suggested Citation

Jørgensen, Peter Løchte, An Analysis of the Solvency II Regulatory Framework's Smith-Wilson Model for the Term Structure of Risk-Free Interest Rates (August 10, 2018). Journal of Banking and Finance, Vol. 97, 2018, Available at SSRN: or

Peter Løchte Jørgensen (Contact Author)

University of Aarhus - Business and Social Sciences ( email )

Finance Research Group
Fuglesangs Allé 4
DK-8210 Aarhus, 8210
+4587165117 (Phone)


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