Can Markets Undergo Phase Transitions?
Monday, November 9, 2009
Presented by the Quantitative Finance Discussion Group and the Columbia University Financial Engineering Practitioners Seminar
In partnership with Columbia University’s Financial Engineering Practitioners Seminar, the New York Academy of Sciences’ Quantitative Finance Discussion Group hosts a lecture by Lisa Borland. Dr. Borland applies her training in theoretical physics to understand the dynamics of financial markets for applications in trading strategies and risk control.
Statistical Signatures in Times of Panic: Markets as a Self-Organizing System
Lisa Borland, PhD, Evnine and Associates
We study properties of the cross-sectional distribution of returns. A significant anti-correlation between dispersion and cross-sectional kurtosis is found such that dispersion is high but kurtosis is low in panic times, and the opposite in normal times. The co-movement of stock returns also increases in panic times. We define a simple statistic s, the normalized sum of signs of returns on a given day, to capture the degree of correlation in the system. s can be seen as the order parameter of the system because if s = 0 there is no correlation (a disordered state), whereas for s different from 0 there is correlation among stocks (an ordered state).
We make an analogy to non-equilibrium phase transitions and hypothesize that financial markets undergo self-organization when the external volatility perception rises above some critical value. Indeed, the distribution of s is unimodal in normal times, shifting to bimodal in times of panic. This is consistent with a second order phase transition. Simulations of a joint stochastic process for stocks use a multi timescale process in the temporal direction and an equation for the order parameter s for the dynamics of the cross-sectional correlation. Numerical results show good qualitative agreement with the stylized facts of real data, in both normal and panic times.
Reception to Follow
Lisa Borland, PhD
Evnine and Associates
Lisa Borland is currently Director of Derivatives Strategies at Evnine and Associates, a San Francisco based hedge fund. She received her Doctorate in Theoretical Physics from the University of Stuttgart, Germany and after some years of working in academia in the United States (Berkeley) and abroad (Brazil), she moved into the field of finance. She has over 30 scientific publications and has been invited to speak at about as many international conferences.
Her most notable work in finance has been the development of a theory for non-Gaussian option pricing. However, her main interest is more general; namely to try and understand the dynamics of financial markets, and apply that knowledge to trading strategies and risk control.
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