Super-Exponential Endogenous Bubbles in an Equilibrium Model of Fundamentalist and Chartist Traders

2018

PLoS ONE

Self Cite

Since the 2008 financial crisis, agent-based models (ABMs), which account for out-of-equilibrium dynamics, heterogeneous preferences, time horizons and strategies, have often been envisioned as the new frontier that could revolutionise and displace the more standard models and tools in economics. However, their adoption and generalisation is drastically hindered by the absence of general reliable operational calibration methods. Here, we start with a different calibration angle that qualifies an ABM for its ability to achieve abnormal trading performance with respect to the buy-and-hold strategy when fed with real financial data. Starting from the common definition of standard minority and majority agents with binary strategies, we prove their equivalence to optimal decision trees. This efficient representation allows us to exhaustively test all meaningful single agent models for their potential anomalous investment performance, which we apply to the NASDAQ Composite index over the last 20 years. We uncover large significant predictive power, with anomalous Sharpe ratio and directional accuracy, in particular during the dotcom bubble and crash and the 2008 financial crisis. A principal component analysis reveals transient convergence between the anomalous minority and majority models. A novel combination of the optimal single-agent models of both classes into a two-agents model leads to remarkable superior investment performance, especially during the periods of bubbles and crashes. Our design opens the field of ABMs to construct novel types of advanced warning systems of market crises, based on the emergent collective intelligence of ABMs built on carefully designed optimal decision trees that can be reversed engineered from real financial data.

Section: Introductionmentioning

confidence: 99%

Calibrating emergent phenomena in stock markets with agent based models

Fievet

2018

PLoS ONE

Self Cite

“…Motivated by its applications to financial markets, we study an extended version of the dynamical mean-field equation of the Ising model in which the external (magnetic or news) field is endogenized to represent a smoothed moving average of the past state variable. This new model stands for a simplification of the interplay between instantaneous social imitation and past trends in social coordinations [Harras et al, 2012;Kaizoji et al, 2015;Sornette & Zhou, 2006;Zhou & Sornette, 2007]. We show the existence of a rich set of bifurcations as a function of the two parameters quantifying the relative importance of immediate versus past social opinions on the formation of the next value of the state variable.…”

Section: Introductionmentioning

confidence: 89%

“…We generalize map (2) by introducing a dynamics on the field H. In the standard map (2), as already mentioned, H is considered to be exogenous, and is taken to represent the influence of outside news on the opinion or decision s(t) of the typical agent. Motivated by models of financial price dynamics [Kaizoji et al, 2015;Ollikainen, 2016], we propose to interpret H as a measure of momentum of the opinion dynamics. To reduce the dynamics to arguably the simplest model without the need for specifying the price evolution, one can consider that the opinion dynamics momentum is a proxy for the price momentum included in the asset price dynamics of [Kaizoji et al, 2015].…”

Section: Extended Mean-field Ising Modelmentioning

confidence: 99%

“…Motivated by models of financial price dynamics [Kaizoji et al, 2015;Ollikainen, 2016], we propose to interpret H as a measure of momentum of the opinion dynamics. To reduce the dynamics to arguably the simplest model without the need for specifying the price evolution, one can consider that the opinion dynamics momentum is a proxy for the price momentum included in the asset price dynamics of [Kaizoji et al, 2015]. Let us recall that the logic of the initial model [Kaizoji et al, 2015] is that the so-called noise traders or technical analysts come to their investment decisions based on the information they gather from the opinions of their fellow noise traders and on their measure of the strength of the price trends.…”

Section: Extended Mean-field Ising Modelmentioning

confidence: 99%

See 1 more Smart Citation

A Generalized 2D-Dynamical Mean-Field Ising Model with a Rich Set of Bifurcations (Inspired and Applied to Financial Crises)

Smug

Int. J. Bifurcation Chaos

Ashwin

2018

Self Cite

We analyze an extended version of the dynamical mean-field Ising model. Instead of classical physical representation of spins and external magnetic field, the model describes traders' opinion dynamics. The external field is endogenized to represent a smoothed moving average of the past state variable. This model captures in a simple set-up the interplay between instantaneous social imitation and past trends in social coordinations. We show the existence of a rich set of bifurcations as a function of the two parameters quantifying the relative importance of instantaneous versus past social opinions on the formation of the next value of the state variable. Moreover, we present a thorough analysis of chaotic behavior, which is exhibited in certain parameter regimes. Finally, we examine several transitions through bifurcation curves and study how they could be understood as specific market scenarios. We find that the amplitude of the corrections needed to recover from a crisis and to push the system back to “normal” is often significantly larger than the strength of the causes that led to the crisis itself.

“…Previous models developed by our group implementing the concept of positive feedbacks to characterize bubbles have emphasized mostly the influence of past prices level on future returns [Sornette and Andersen, 2002;Lin and Sornette, 2013;Hüsler et al, 2013;Corsi and Sornette, 2014;Lin et al, 2014;Sornette and Cauwels, 2015a] and the reinforcing role of social influence of the price formation process [Kaizoji et al, 2015]. The role of a nonlinear response to momentum [Ide and Sornette, 2002] has been suggested to be at the origin of the super-exponential price growth characterising bubbles [Sornette and Cauwels, 2015a;Leiss et al, 2015] and also as a model of hyperinflation [Sornette et al, 2003].…”

Section: Introductionmentioning

confidence: 99%

A simple mechanism for financial bubbles: time-varying momentum horizon

Schätz

2018

Quantitative Finance

Building on the notion that bubbles are transient self-fulfilling prophecies created by positive feedback mechanisms, we construct the simplest continuous price process whose expected returns and volatility are functions of momentum only. The momentum itself is measured by a simple continuous moving average of past prices over a given time horizon. We introduce a simple dynamics of the time horizon used by the representative investor, which is motivated by the race of trend following agents to forerun their competitors. We provide the full set of solutions, which includes an explosive regime where the price and momentum explodes stochastically in finite time to infinity, transient price dynamics escaping to infinity and recurrent behaviors, where the momentum remains either strictly positive or undergoes instantaneous reflections at the origin. The proposed price generating process produces price dynamics that are in agreement with the main qualitative properties of empirical financial time series. Moreover, it produces realistic regime shifts between non bubble and bubble regimes. We construct a quasi-likelihood methodology to calibrate the model to empirical financial time series, which is applied to an Internet index and a "brick and mortar" index, over the period of the dotcom bubble and its subsequent crash, from Jan. 1998 to Dec. 2002. The Wilks test of nested hypotheses shows a very strong skill in diagnosing the bubble of the Internet index and in disqualifying a bubble in the "brick and mortar" index.