Zerotopia – bounded and unbounded pension adventures: term structure modelling with and without negative short rates

Pension funds often use Gaussian interest rate models – such as those used and validated by the Dutch central bank – which assign a high probability to rates falling below their current levels, deep into negative territory. However, since 2008, central banks have resorted mostly to quantitative easing instead of deep cuts in short rates to expand monetary policy. The ECB (Draghi, 2014) has even stated that short interest rates could not fall further (than -0.50%), thus suggesting that the Gaussian models used by pension funds lack realism. If a lower bound exists, a Gaussian pension fund – one that uses a Gaussian model – will tend to buy bonds or derivatives in order to hedge the risk of negative rates, although this risk is small. The funds used to hedge the risk of negative rates could be best invested elsewhere. Finally, monetary expansion close to the lower bound, realised through quantitative easing, can impact equity prices more than liability prices, thus benefitting pension funds overall. By contrast, higher interest rates would be a bigger risk if liabilities are overhedged. A Gaussian pension fund may fail to recognize the unusual risks near the lower bound.


Netspar, Network for Studies on Pensions, Aging and Retirement, is a thinktank and knowledge network. Netspar is dedicated to promoting a wider understanding of the economic and social implications of pensions, aging and retirement in the Netherlands and Europe.


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