Zerotopia – Bounded and Unbounded Pension Adventures (Term Structure Modelling with and without Negative Short Rates)

Abstract

Pension funds often use Gaussian interest rates model – such as those used and validated by the Dutch central bank – which assign a large probability of rates falling below their current levels, deep into negative territory. However, since 2008, Central Banks resorted mostly to quantitative easing instead of deep cuts in short rates to expand monetary policy. The ECB (Draghi, 2014) has even stated that the short interest rates could 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 – tends to buy bonds or derivatives 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, made through quantitative easing, can impact equity prices more than liability prices, overall benefitting pension funds. By contrast, higher interest rates, would be a bigger risk if liabilities are over-hedged. A Gaussian pension fund may fail to recognise the unusual risks near the lower bound.