Applications of entropy on financial markets

Abstract

Financial markets have been attracting over the past years an increasing attention amongst physicists, computer scientists, and other researchers devoted to studies of complex systems, due to their intricate phenomenological behavior which makes cause-effect prediction extremely difficult. Complementing traditional statistical and econometric methods, an interdisciplinary field of research named "econophysics" has emerged, advancing techniques that originate from statistical physics in order to shed new light on the phenomenological observations. The success of these methods is reflected upon the discovery of universal laws that prevail in diverse markets. For example, the presence of power laws in the unconditional distribution of asset returns revolutionized the way we perceive rare events in the market. Likewise, correlations in the absolute value of returns (volatility) suggest the desirable property of long term memory. Formally, econophysics encompasses the collection of these empirical laws and their respective methods. One of the most studied topics in econophysics is the nature of price fluctuations in financial markets, because they are fundamental for many real-life applications such as risk and portfolio management (besides the evident theoretical value of their better understanding). Among the econophysics tools, entropy represents an important concept for quantifying the disorder and uncertainty in dynamical systems. In particular, the concept of entropy (in many different existing formulations) has been extensively used in finance to quantify the diversity and regularity of movements in price across a variety of markets (i.e. stock, currency, future, commodity). The goal of the current work is to explore ways entropy can be useful in the study of financial markets through a strictly empirical approach. Our contributions focus on the application of entropy on the foreign exchange (FX) market and take the form of two articles. The first paper studies the impact of financial crises in the FX market using Shannon entropy, and the second introduces a novel algorithm (based on the concept of Approximate entropy) for analyzing the global behavior of the FX.