Abstract
In this paper we investigate the relationship between the information entropy of the distribution of intraday returns and intraday and daily measures of market risk. Using data on the EUR/JPY exchange rate, we find a negative relationship between entropy and intraday Value-at-Risk, and also between entropy and intraday Expected Shortfall. This relationship is then used to forecast daily Value-at-Risk, using the entropy of the distribution of intraday returns as a predictor.
Highlights
Entropy, as a measure of uncertainty of a system, is widely used in many applications, from physics to social sciences
This paper investigates the link between entropy and various measures of market risk such as
Based on the result of Lorentz [25], we developed the concept of entropy of a distribution function and we applied this concept to estimate the entropy of the distribution of intraday returns
Summary
As a measure of uncertainty of a system, is widely used in many applications, from physics to social sciences. As stated by the second law of thermodynamics, “this entropy cannot decrease in any process in which the system remains adiabatically isolated, i.e., shielded from heat exchange with its environment” [1]. From this point of view, the stock market could be regarded as a non-isolated system, subject to a constant information exchange process with the real economy. An application in the foreign exchange markets is that of Oh et al [5], who use the approximate entropy as a measure of the relative efficiency of the FX markets. Their results suggest that market efficiency measured by approximate entropy is correlated with the liquidity level of foreign exchange markets
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