Working Paper presents research work by both Danmarks Nationalbank’s employees and our partners. The series is primarily targeted at professionals and people with an interest in central banking research as well as economics and finance in a broader sense.

# Extracting risk neutral probability densities by fitting implied volatility smiles: Some methodological points and an application to the 3M Euribor futures option prices.

Following Shimko (1993), a large amount of research has evolved around the problem of extracting risk neutral densities from options prices by interpolating the Black-Scholes implied volatility smile. Some of the methods recently proposed use variants of the cubic spline. These methods produce non-differentiable probability densities. We argue that this is an undesirable feature, and suggest circumventing the problem by fitting a smoothing spline of higher order polynomials. We apply this technique to the LIFFE three-month Euribor futures option prices. Summary statistics from constant horizon risk neutral densities are calculated and used to assess market uncertainty on a day-by-day basis. Finally, we analyse the impact of the 11 September attacks on the expectation of future Euribor interest rates.