Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/82362
Authors: 
Andersen, Allan Bødskov
Wagener, Tom
Year of Publication: 
2002
Series/Report no.: 
Danmarks Nationalbank Working Papers 9
Abstract: 
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 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 futures option prices. 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.
Subjects: 
Implied volatility
risk neutral density estimation
interest rate expectation
JEL: 
C14
F33
G15
Document Type: 
Working Paper

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