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Copula-Based Models for Financial Time Series1
First version: 31 August 2006. This version: 19 November 2007.
Abstract This paper presents an overview of the literature on applications of copulas
in the modelling of …nancial time series. Copulas have been used both in multivariate
time series analysis, where they are used to charaterise the (conditional) cross-sectional
dependence between individual time series, and in univariate time series analysis, where
they are used to characterise the dependence between a sequence of observations of a scalar
time series process. The paper includes a broad, brief, review of the many applications of
copulas in …nance and economics.
1 Introduction
The central importance of risk in …nancial decision-making directly implies the importance
of dependence in decisions involving more than one risky asset. For example, the variance
of the return on a portfolio of risky assets depends on the variances of the individual assets
and also on the linear correlation between the assets in the portfolio. More generally, the
distribution of the return on a portfolio will depend on the univariate distributions of the
individual assets in the portfolio and on the dependence between each of the assets, which
is captured by a function called a ‘copula’.
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