Estimating Tipping Points in Feedback-Driven Financial Networks

Abstract

Much research has been conducted arguing that tipping points at which complex systems experience phase transitions are difficult to identify. To test the existence of tipping points in financial markets, based on the alternating offer strategic model we propose a network of bargaining agents who mutually either cooperate or compete, where the feedback mechanism between trading and price dynamics is driven by an external “hidden” variable R that quantifies the degree of market overpricing. Due to the feedback mechanism, R fluctuates and oscillates over time, and thus periods when the market is underpriced and overpriced occur repeatedly. As the market becomes overpriced, bubbles are created that ultimately burst as the market reaches a crash tipping point R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> . The market starts recovering from the crash as a recovery tipping point R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> is reached. The probability that the index will drop in the next year exhibits a strong hysteresis behavior very much alike critical transitions in other complex systems. The probability distribution function of R has a bimodal shape characteristic of small systems near the tipping point. By examining the S&P500 index we illustrate the applicability of the model and demonstrate that the financial data exhibit tipping points that agree with the model. We report a cointegration between the returns of the S&P 500 index and its intrinsic value.