The Relationship between Risk and Incomplete States Uncertainty: A Tsallis Entropy Perspective
11 Pages Posted: 11 Sep 2013
Date Written: September 11, 2013
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.
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