Inflation and Liqiudity Premia in Indexed-Linked Bonds: An Extended Kalman Filter Approach

Abstract

In a framework of an equilibrium pricing model, the dynamics of real interest rates and expected inflation are estimated. Unlike previous models, we allow the existence of a liquidity premium. The model is estimated using observations on French index-linked and nominal bonds of various maturities. In order to fit coupon bearing bonds in an affine structure context, we utilize the extended Kalman filter to linearize the state equations. Our findings are as follows: in the absence of liquidity, the inflation premium runs from 113 basis points to some 250 basis points across the curve. These results are somewhat larger than the premia found for the UK market but comparable with US TIPS. The liquidity premium in real bonds equals some 6 basis points for bonds maturing in 2009 and is slightly humped shaped with a peak at the 10-year bond. For short-term bonds, the liquidity premium accounts for some 5% of the total real risk premium. For long-term bonds, this premium equals 10%. The inflation premium is a prominent factor in nominal bonds as it account for more than 50% of the total risk premium across the term structure for nominal interest rates. Although the contribution of the liquidity premium to total premium is small, it has a large impact on the expected nominal yield spread through the expected liquidity level. We find that this yield spread is upward sloping as it runs from 5 basis points to some 135 basis points for the 2032 bond.