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Getting real forecasts, state price densities and risk premium from Euribor options

In this paper we study the development of interest rate risk premium and option implied state price densities in the Euribor futures option market. Using parametric and non-parametric statistical calibration, we transform the risk-neutral option implied densities for the Euribor futures rate into real-world densities. We investigate the period from the introduction of the Euro in 1999 until December 2012. The estimated densities are used to provide a measure for the interest rate risk premium and state prices implicit in the futures market. We find that the real-world densities can be used to forecast the futures rate, while the forecasting ability of the risk-neutral distributions is rejected. The state price densities in the market show a U-shaped curve suggesting that in general investors price higher those states with high and low rates compared to the expected spot rate. However, we show that state prices have in general a more pronounced right tail, implying that investors are more risk averse to increasing interest rates. We also document a negative market price of interest rate risk which generates positive premium for the futures contract.