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

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Author Info
Hurd, Matthew
Salmon, Mark
Schleicher, Christoph

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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.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 5114.

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Date of creation: Jun 2005
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Handle: RePEc:cpr:ceprdp:5114

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Related research
Keywords: copulae; exchange rates; option implied pdfs; triangular arbitrage;

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Find related papers by JEL classification:
F31 - International Economics - - International Finance - - - Foreign Exchange
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October. [Downloadable!] (restricted)
  2. Campa, Jose Manuel & Chang, P. H. Kevin, 1998. "The forecasting ability of correlations implied in foreign exchange options," Journal of International Money and Finance, Elsevier, vol. 17(6), pages 855-880, December. [Downloadable!] (restricted)
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  3. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179. [Downloadable!] (restricted)
  4. Sancetta, A., 2003. "Nonparametric Estimation of Multivariate Distributions with Given Marginals," Cambridge Working Papers in Economics 0320, Faculty of Economics, University of Cambridge. [Downloadable!]
  5. Bliss, Robert R. & Panigirtzoglou, Nikolaos, 2002. "Testing the stability of implied probability density functions," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 381-422, March. [Downloadable!] (restricted)
  6. Sancetta, Alessio & Satchell, Stephen, 2004. "The Bernstein Copula And Its Applications To Modeling And Approximations Of Multivariate Distributions," Econometric Theory, Cambridge University Press, vol. 20(03), pages 535-562, June. [Downloadable!]
  7. Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December. [Downloadable!] (restricted)
  8. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, 05. [Downloadable!] (restricted)
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  9. Eytan, T Hanan & Harpaz, Giora, 1986. " The Pricing of Futures and Options Contracts on the Value Line Index," Journal of Finance, American Finance Association, vol. 41(4), pages 843-55, September. [Downloadable!] (restricted)
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  1. Andrew J. Patton, 2008. "Copula-Based Models for Financial Time Series," OFRC Working Papers Series 2008fe21, Oxford Financial Research Centre. [Downloadable!]
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