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Using Copulas to Construct Bivariate Foreign Exchange Distributions with an Application to the Sterling Exchange Rate Index

Matthew Hurd, Mark Salmon () and Christoph Schleicher

No 5114, CEPR Discussion Papers from C.E.P.R. Discussion Papers

Abstract: We model the joint risk neutral distribution of the euro-sterling and the dollar-sterling exchange rates using option-implied marginal distributions that are connected via a copula function that satisfies the triangular no-arbitrage condition. We then derive a univariate distribution for a simplified sterling effective exchange rate index (ERI). Our results indicate that standard parametric copula functions, such as the commonly used Normal and Frank copulas, fail to capture the degree of asymmetry observed in the data. We overcome this problem by using a non-parametric dependence function in the form of a Bernstein copula, which is shown to produce a very close fit. We further give an example of how our approach can be used to price currency index options.

Keywords: copulae; exchange rates; option implied pdfs; triangular arbitrage (search for similar items in EconPapers)
JEL-codes: F31 G12 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-fin, nep-fmk, nep-ifn and nep-mon
Date: 2005-06
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Working Paper: Using copulas to construct bivariate foreign exchange distributions with an application to the sterling exchange rate index (2007) Downloads
Working Paper: Using Copulas to Construct Bivariate Foreign Exchange Distributions with an Application to the Sterling Exchange Rate Index (2005)
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