The crash of October 1987 seen as a phase transition: amplitude and universality

We analyze the evolution of several financial indices before the crash of October 1987. The amplitude of the crash varies from one index to another. However, assuming that the crash is similar to a phase transition and particularly to a specific heat jump, we find that the crash amplitude can be well estimated by assuming a simple background which differs from market to market. We show that the divergence near the crash event is logarithmic and extends between 2 weeks and 4 years before the october 1987 crash on both S&P500 and Dow Jones indices. The behavior is like that found for the d = 2 Ising model specific heat. The latter result is in contrast to previous works which have considered a power law behavior of the index near the crash. Finally, we confirm the presence of log-periodic oscillations and discuss briefly their origin.