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Extracting expectations from currency option prices: a comparison of methods

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Author Info
Marian Micu () (Research and Policy Analysis Bank for International Settlements)
Abstract

This paper compares the goodness-of-fit and the stability of six methods used to extract risk-neutral probability density functions from currency option prices. We first compare five existing methods commonly employed to recover risk-neutral density functions from option prices. Specifically, we compare the methods introduced by Shimko (1993), Madan and Milne (1994), Malz (1996), Melick and Thomas (1997) and Bliss and Panigirtzoglou (2002). In addition, we propose a new method based on the piecewise cubic Hermite interpolation of the implied volatility function. We use data on 12 emerging market currencies against the US dollar and find that the piecewise cubic Hermite interpolation method is by far the method with the best accuracy in fitting observed option prices. We also find that there is a relative tradeoff between the goodness-of-fit and the stability of the methods. Thus, methods which have a better accuracy in fitting observed option prices appear to be more sensitive to option pricing errors, while the most stable methods have a fairly disappointing fitting. However, for the first two PDF moments as well as the quartiles of the risk-neutral distributions we find that the estimates do not differ significantly across methods. This suggests that there is a large scope for selection between these methods without essentially sacrificing the accuracy of the analysis. Nonetheless, depending on the particular use of these PDFs, some methods may be more suitable than others

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Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2005 with number 226.

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Date of creation: 11 Nov 2005
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Handle: RePEc:sce:scecf5:226

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Keywords: Risk-neutral probability density functions; option pricing; exchange rate expectations;

Find related papers by JEL classification:
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing
F31 - International Economics - - International Finance - - - Foreign Exchange
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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