Symmetry/anti-symmetry phase transitions in crude oil markets

Daily records of international crude oil prices are studied by means of a Zipf-type analysis. By using simple up-down information on price fluctuations, we have observed phase transitions between symmetric states, where occurrence of up and down fluctuations are almost equal, to anti-symmetric states, where there is a significant imbalance between up and down occurrences. Symmetric phase provides a time-scale domain for risk-neutral transactions. On the other hand, anti-symmetric phase can be exploited by speculators and consumers to accommodate contracts that take advantage of the spread between up and down occurrences.