Using copulas to construct bivariate foreign exchange distributions with an application to the sterling exchange rate index
Hurd, Matthew, Salmon, Mark H. and Schleicher, Christoph (2005) Using copulas to construct bivariate foreign exchange distributions with an application to the sterling exchange rate index. Discussion Paper. London: Centre for Economic Policy Research (Great Britain). Discussion paper (Centre for Economic Policy Research (Great Britain)) (No.511).
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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.
|Item Type:||Working or Discussion Paper (Discussion Paper)|
|Subjects:||H Social Sciences > HB Economic Theory|
|Divisions:||Faculty of Social Sciences > Warwick Business School|
|Library of Congress Subject Headings (LCSH):||Copulas (Mathematical statistics), Distribution (Probability theory), Foreign exchange rates -- Mathematical models, Arbitrage|
|Series Name:||Discussion paper (Centre for Economic Policy Research (Great Britain))|
|Publisher:||Centre for Economic Policy Research (Great Britain)|
|Place of Publication:||London|
|Official Date:||June 2005|
|Number of Pages:||35|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
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