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

Abstract

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 dollarsterling 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.JEL Classification: F31 and G12

Modelling the bivariate dependence structure of exchange rates before and after the introduction of the euro: a semi-parametric approach

“…The use of copulas to study exchange rate dependence is more recent, and still very limited (see Patton 2006, Hurd, Salmon and Schleicher, 2005, Dias and Embrechts, 2007. Several suggestions on possible sources of asymmetric exchange rate dependence have been proposed in previous studies.…”

An Analytic Multi-Currency Model with Stochastic Volatility and Stochastic Interest Rates

“…Among others, we recall Bliss and Panigirtzoglou (2002) and Schlögl (2012) and Austing (2011). Copulas have been employed in Bennett and Kennedy (2004), Salmon and Schneider (2006) and Hurd et al (2005).…”

Factor Copula Models and Their Application in Studying the Dependence of the Exchange Rate Returns

“…These studies will in turn assist the risk management of the international investment portfolio that can be significantly affected by the fluctuations in currencies. Hurd, Salmon, and Schleicher (2007) applied copulas to construct bivariate foreign exchange distributions with a focus on the application of the Sterling Exchange Rate Index. Built on their study, Patton (2006) extended the copulas conditional on variables or common factors found through the factor approach, and constructed flexible models of the conditional dependence structure of the mark-dollar and yen-dollar exchange rates.…”