Symmetrical Bernstein Copula and the Empirical Analysis of Foreign Exchange

This paper studies the foreign exchange data whose dependence structure is approximate symmetry, such as Euro/Pound (euro/pound) and Dollar/Pound ($/pound). It fits their dependence structure by symmetrical Bernstein Copula, and estimates the marginal densities through Kernel density. Under the triangular no-arbitrage condition, the univariate distribution of Dollar / Euro ($/euro) exchange rate implied by the bivariate distribution of these two exchange rates is consistent with the univariate distribution which is estimated by the Kernel density.