Econophysics of Stock and Foreign Currency Exchange Markets

Abstract

Econophysics is a science in its infancy, born about ten years ago at this time of writing, at the crossing roads of physics, mathematics, computing and of course economics and finance. It also covers human sciences, because all economics is ultimately driven by human decision. From this human factor, econophysics has no hope to achieve the status of an exact science, but it is interesting to discover what can be achieved, discovering potential limits and trying try to push further away these limits. A few data analysis techniques are described with emphasis on the Detrended Fluctuation Analysis ($DFA$) and the Zipf Analysis Technique ($ZAT$). Information about the original data aresketchy, but the data concerns mainly the foreign currency exchange market. The robustness of the $DFA$ technique is underlined. Additional remarks are given for suggesting further work. Models about financial value evolutions are recalled, again without going into elaborate work discussing typical agent behaviors, but rather with hopefully sufficient information such that the basic ingredients can be memorized before reading some of the vast literature on price formation. Crashes being spectacular phenomena retain our attention and do so through data analysis and basic intuitive models. A few statistical and microscopic models are outlined.