Working Paper: CEPR ID: DP5114
Authors: Matthew Hurd; Mark Salmon; Christoph Schleicher
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: copulae; exchange rates; option implied pdfs; triangular arbitrage
JEL Codes: F31; G12
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| euro-sterling exchange rates (F36) | dollar-sterling exchange rates (F31) |
| Bernstein copula (C46) | joint distribution of the simplified sterling exchange rate index (ERI) (F31) |
| option-implied marginal distributions (D39) | joint distribution of the simplified sterling exchange rate index (ERI) (F31) |
| joint distribution of the simplified sterling exchange rate index (ERI) (F31) | conditional densities (C46) |
| standard deviation of the sterling ERI (F36) | risk associated with currency fluctuations (F31) |
| asymmetry in foreign exchange rates (F31) | failure of standard parametric copula functions (C46) |