The Empirical Performance of Option-Based Densities of Foreign Exchange

30 Pages Posted: 31 Oct 2007

See all articles by Ben R. Craig

Ben R. Craig

Federal Reserve Bank of Cleveland; Deutsche Bundesbank

Joachim Keller

Deutsche Bundesbank - Economic Research Centre

Multiple version iconThere are 2 versions of this paper

Date Written: November 2003


In this paper, the authors calculate risk-neutral densities (RND) by estimating the daily diffusion process of the underlying futures contract for foreign exchange, based on the price of the American puts and calls reported on the Chicago Mercantile Exchange for the end of the day. Their quick and accurate method of calculating the prices of the American options uses higher-order lattices and smoothing of the option's value function at the boundaries to mitigate the nondifferentiability of the payoff boundary at expiration and the early exercise boundary. The authors estimate the diffusion process by minimizing the squared distance between the calculated prices and the observed prices in the data. They also test whether the densities provided from American options provide a good forecasting tool. They use a nonparametric test of the densities that depends on inverse probabilities. They modify the test to compensate for an inherent problem that arises from the time-series nature of the transformed variables when the forecasting windows overlap. They find that the densities based on the American option prices for foreign exchange do considerably well for the longer time horizons.

Keywords: risk-neutral density, option prices, diffusion process

JEL Classification: G13, G15

Suggested Citation

Craig, Ben R. and Keller, Joachim, The Empirical Performance of Option-Based Densities of Foreign Exchange (November 2003). FRB of Cleveland Working Paper No. 03-13, Available at SSRN: or

Ben R. Craig (Contact Author)

Federal Reserve Bank of Cleveland ( email )

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Deutsche Bundesbank

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Joachim Keller

Deutsche Bundesbank - Economic Research Centre ( email )

Wilhelm-Epstein-Strasse 14
Frankfurt/Main D-60431

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