Dr Emese Lazar, Dr Alfonso Dufour and Daniel Traian Pele publish new paper 'Information entropy and measures of market risk', which describes how entropy as a financial model can be used to forecast value-at-risk (VaR). Dr Emese Lazar discusses the paper below:
Entropy is a measure of uncertainty. In some ways it is similar to volatility. So, when there is more uncertainty about the financial returns, then entropy increases. It reaches its minimum value when a distribution has no uncertainty (when the outcome is known), and it reaches its maximum value when a distribution is uniform (when all outcomes are equally likely).
Entropy is calculated using the following equation, which uses probabilities only, ignoring the sizes of the possible outcomes:
As we depart from normality to distributions with heavier tails (that represent returns with higher tail risk, as in the case of financial returns), the entropy generally decreases.
As such, there is a suspected negative relationship between entropy and measures of risk such as Value-at-Risk (VaR) and Expected Shortfall (ES), and we investigate this relationship in our paper. For FX returns, we found evidence of a strong (negative) relationship between entropy and intraday measures of risk. Finally, we used entropy to forecast daily VaR. Our backtest results show that the entropy-based VaR forecasts perform better than competing models.
