Extended correlations, i.e. correlations that can take values less than − 1 and/or larger than 1, occur naturally in mathematical models of financial processes. Extended correlations also occur in financial practice, especially in dispersion trading, implying arbitrage opportunities. Based on theoretical and practical emergence of extended correlations, we derive a mathematical framework for extended correlations explaining interpretations and applications. We develop a broader mathematical approach, which can model conventional as well as extended correlations.