Taylor, S J and Wang, Y (2010) Option prices and risk-neutral densities for currency cross-rates. Journal of Futures Markets, 30. pp. 324-360. ISSN 0270-7314
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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