The relationship between risk and incomplete states uncertainty: A tsallis entropy perspective

Abstract

This paper provides a 'non-extensive' information theoretic perspective on the relationship between risk and incomplete states uncertainty. Theoretically and empirically, we demonstrate that a substitution effect between the latter two may take place. Theoretically, the 'non-extensive' volatility measure is concave with respect to the standard (based on normal distribution) volatility measure. With the degree of concavity depending on an incomplete states uncertainty parameter-The Tsallis-q. Empirically, the latter negatively causes the normal measure of volatility, positively affecting the tails of the distribution of realised log-returns.