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Testing the martingale restriction for option implied densities

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Abstract

This paper contributes to the forecasting literature by presenting a new evaluation method for density and probability estimates. This procedure is particularly well suited for analyzing time series of forecasts implied from option prices, although the results are very general and can be applied also outside this framework. A small scale simulation study documents that valid and accurate inference can be drawn for option implied densities with the proposed method. The new testing procedure is demonstrated in an empirical application on density estimates implied from $/£ currency options.

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Authors and Affiliations

  1. Danske Bank, Holmens Kanal 2-12, 1092, Copenhagen K, Denmark

    Thomas Busch

  2. CREATES, University of Aarhus, School of Economics and Management, Building 322, 8000, Aarhus C, Denmark

    Thomas Busch

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  1. Thomas Busch
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Correspondence to Thomas Busch.

Additional information

I am indebted to, Bent Jesper Christensen and Morten M. Christensen for their helpful comments, and to an anonymous referee for critiques that let to an improved version of this paper. I am especially grateful to Stewart Hodges who encouraged me to take on this project, and helped me with his insightful suggestions and guidance. I would also like to thank participants at the FMA European Conference 2005 in Siena, the 9th World Congress of the Econometric Society 2005 in London, the FMA Annual Meeting 2005 in Chicago, and seminar participants at University of Aarhus and Aarhus Business School for comments. For generously providing data I thank Mascia Bedendo.

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Busch, T. Testing the martingale restriction for option implied densities. Rev Deriv Res 11, 61–81 (2008). https://doi.org/10.1007/s11147-008-9024-z

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