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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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  • Christoph Schleicher
  • Matthew Hurd
  • Mark Salmon

Abstract

We model the joint distribution between the euro-sterling and the dollar-sterling exchange rate using option-implied markginal distributions that are connected via a copula function. We then derive univariate distributions for the simpliefied sterling effective exchange rate index (ERI). Our results indicate that simple 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

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2005 with number 215.

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Date of creation: 11 Nov 2005
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Handle: RePEc:sce:scecf5:215

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Keywords: copula functions; option implied densities; effective exchange rates;

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References

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  1. 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.
  2. Andrew Patton, 2004. "Modelling Asymmetric Exchange Rate Dependence," Working Papers wp04-04, Warwick Business School, Finance Group.
  3. Robert R. Bliss & Nikolaos Panigirtzoglou, 2004. "Option-Implied Risk Aversion Estimates," Journal of Finance, American Finance Association, vol. 59(1), pages 407-446, 02.
  4. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October.
  5. 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.
  6. Joshua V. Rosenberg, 2003. "Nonparametric pricing of multivariate contingent claims," Staff Reports 162, Federal Reserve Bank of New York.
  7. Vivek Bhargava & John M. Clark, 2003. "Pricing U.S. Dollar Index Futures Options: An Empirical Investigation," The Financial Review, Eastern Finance Association, vol. 38(4), pages 571-590, November.
  8. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
  9. Sancetta, A., 2003. "Nonparametric Estimation of Multivariate Distributions with Given Marginals," Cambridge Working Papers in Economics 0320, Faculty of Economics, University of Cambridge.
  10. 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.
  11. 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.
  12. 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.
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Cited by:
  1. Mendoza-Velázquez, Alfonso & Galvanovskis, Evalds, 2009. "Introducing the GED-Copula with an application to Financial Contagion in Latin America," MPRA Paper 46669, University Library of Munich, Germany, revised 01 Feb 2010.
  2. Mark Salmon & Christoph Schleicher, 2006. "Pricing Multivariate Currency Options with Copulas," Working Papers wpn06-10, Warwick Business School, Finance Group.
  3. Fabrizio Durante & Erich Klement & Carlo Sempi & Manuel Úbeda-Flores, 2010. "Measures of non-exchangeability for bivariate random vectors," Statistical Papers, Springer, vol. 51(3), pages 687-699, September.
  4. Alvise De Col & Alessandro Gnoatto & Martino Grasselli, 2012. "Smiles all around: FX joint calibration in a multi-Heston model," Papers 1201.1782, arXiv.org, revised Jun 2013.
  5. Alessandro Gnoatto & Martino Grasselli, 2013. "An analytic multi-currency model with stochastic volatility and stochastic interest rates," Papers 1302.7246, arXiv.org, revised Mar 2013.
  6. De Col, Alvise & Gnoatto, Alessandro & Grasselli, Martino, 2013. "Smiles all around: FX joint calibration in a multi-Heston model," Journal of Banking & Finance, Elsevier, vol. 37(10), pages 3799-3818.

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