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

35 Pages Posted: 10 Aug 2005

See all articles by Matthew Hurd

Matthew Hurd

Bank of England - Monetary Analysis

Mark Salmon

University of Cambridge - Faculty of Economics and Politics

Christoph Schleicher

Bank of England

Multiple version iconThere are 2 versions of this paper

Date Written: June 2005

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: Exchange rates, copulae, option implied pdfs, triangular arbitrage

JEL Classification: F31, G12

Suggested Citation

Hurd, Matthew and Salmon, Mark Howard and Schleicher, Christoph, Using Copulas to Construct Bivariate Foreign Exchange Distributions with an Application to the Sterling Exchange Rate Index (June 2005). CEPR Discussion Paper No. 5114, Available at SSRN: https://ssrn.com/abstract=781205

Matthew Hurd (Contact Author)

Bank of England - Monetary Analysis ( email )

Threadneedle Street
London EC2R 8AH
United Kingdom

Mark Howard Salmon

University of Cambridge - Faculty of Economics and Politics ( email )

Austin Robinson Building
Sidgwick Avenue
Cambridge, CB3 9DD
United Kingdom

Christoph Schleicher

Bank of England ( email )

Threadneedle Street
London EC2R 8AH
United Kingdom
+44 0207 601 4115 (Phone)
+44 0207 601 5953 (Fax)

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