- 1 December 2002
- WORKING PAPER SERIES - No. 198Extracting risk neutral probability densities by fitting implied volatility smiles: some methodological points and an application to the 3M Euribor futures option pricesDetails
- Following Shimko (1993), a large amount of research has evolved around the problem of extracting risk neutral densities from options prices by interpolating the Balck-Scholes implied volatility smile. Some of the methods recently proposed use variants of the cubic spline. Thesee methods have the property of producing 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 with a relatively low number of knot points. In the estimations we opt for a measure of roughness penalty, which is more appropriate than the plain second partial derivative often used. We apply this technique to the LIFFE three-month Euribor future option proces. Constant horizon risk neutral densities are calculated and summary statistics from these densities are 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.
- JEL Code
- C14 : Mathematical and Quantitative Methods→Econometric and Statistical Methods and Methodology: General→Semiparametric and Nonparametric Methods: General
F33 : International Economics→International Finance→International Monetary Arrangements and Institutions
G15 : Financial Economics→General Financial Markets→International Financial Markets