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Option prices and risk‐neutral densities for currency cross rates

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  • Stephen J. Taylor
  • Yaw‐Huei Wang

Abstract

The theoretical relationship between the risk‐neutral density (RND) of the euro/ pound cross rate and the bivariate RND of the dollar/euro and the dollar/pound rates is derived; the required bivariate RND is defined by the dollar‐rate marginal RNDs and a copula function. The cross‐rate RND can be used by banks, international businesses, and central bankers to assess market expectations, to measure risks, and to value options, without relying on over‐the‐counter markets, which may be either non‐existent or illiquid. Empirical comparisons are made between cross‐rate RNDs estimated from several data sets. Five one‐parameter copula functions are evaluated and it is found that the Gaussian copula is the only one‐parameter copula function that is ranked highly in all of the comparisons we have made. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:324–360, 2010

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  • Stephen J. Taylor & Yaw‐Huei Wang, 2010. "Option prices and risk‐neutral densities for currency cross rates," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(4), pages 324-360, April.
    • Handle: RePEc:wly:jfutmk:v:30:y:2010:i:4:p:324-360
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    Cited by:

    1. Kopaliani, R. & Denisov, N., 2023. "Composite option pricing and the volatility surface construction," Journal of the New Economic Association, New Economic Association, vol. 60(3), pages 27-48.
    2. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    3. Kenichiro Shiraya & Tomohisa Yamakami, 2023. "Constructing Copulas Using Corrected Hermite Polynomial Expansion for Estimating Cross Foreign Exchange Volatility," Papers 2301.10044, arXiv.org.
    4. Shiraya, Kenichiro & Yamakami, Tomohisa, 2024. "Constructing copulas using corrected Hermite polynomial expansion for estimating cross foreign exchange volatility," European Journal of Operational Research, Elsevier, vol. 314(3), pages 1195-1214.
    5. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 899-960, Elsevier.

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