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.