Abstract
Capturing comovement between financial asset returns with linear correlation has been the staple approach in modern finance since the birth of Harry Markowitz’s portfolio theory. Linear correlation is the appropriate measure of dependence if asset returns follow a multivariate normal (or elliptical) distribution. However, the statistical analysis of the distribution of individual asset returns frequently finds fat tails, skewness, and other non-normal features. If the normal distribution is not adequate, then it is not clear how to appropriately measure the dependence between multiple asset returns. Fortunately, the theory of copulas provides a flexible methodology for the general modeling of multivariate dependence. As Cherubini, Luciano, and Vecchiato (2004) state the following in the introduction to their book: “the copula function methodology has become the most significant new technique to handle the co-movement between markets and risk factors in a flexible way.”
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(2006). Copulas. In: Modeling Financial Time Series with S-PLUS®. Springer, New York, NY. https://doi.org/10.1007/978-0-387-32348-0_19
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