Using copulas to construct bivariate foreign exchange distributions with an application to the sterling exchange rate index
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. 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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- Jose M. Campa & P. H. Kevin Chang, 1997.
"The Forecasting Ability of Correlations Implied in Foreign Exchange Options,"
NBER Working Papers
5974, National Bureau of Economic Research, Inc.
- 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.
- Campa, J.M. & Chang, P.H.K., 1995. "The Forecasting Ability of Correlations Implied in Foreign Exchange Options," Papers 95-26, Columbia - Graduate School of Business.
- 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.
- 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.
- 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.
- 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 843-855, September.
- Robert R. Bliss & Nikolaos Panigirtzoglou, 2004. "Option-Implied Risk Aversion Estimates," Journal of Finance, American Finance Association, vol. 59(1), pages 407-446, 02.
- 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 621-651, October.
- Sancetta, A., 2003. "Nonparametric Estimation of Multivariate Distributions with Given Marginals," Cambridge Working Papers in Economics 0320, Faculty of Economics, University of Cambridge.
- Joshua V. Rosenberg, 2003. "Nonparametric pricing of multivariate contingent claims," Staff Reports 162, Federal Reserve Bank of New York.
- 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.
- 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.
- Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
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