Noise-induced volatility of collective dynamics

Harras, Georges; Tessone, Claudio J.; Sornette, Didier

doi:10.1103/physreve.85.011150

Cited by 27 publications

(26 citation statements)

References 54 publications

(71 reference statements)

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“…Models built on the analogy with the Ising model to capture social influences between investors are reviewed in the next section, which often provide explanations for the excess volatility puzzle. Let us mention in particular our own candidate in terms of the "noise-induced volatility" phenomenon (Harras et al, 2012).…”

Section: The Excess Volatility Puzzle: Thinking As An Economistmentioning

confidence: 99%

Physics and financial economics (1776–2014): puzzles, Ising and agent-based models

2014

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This short review presents a selected history of the mutual fertilization between physics and economics, from Isaac Newton and Adam Smith to the present. The fundamentally different perspectives embraced in theories developed in financial economics compared with physics are dissected with the examples of the volatility smile and of the excess volatility puzzle. The role of the Ising model of phase transitions to model social and financial systems is reviewed, with the concepts of random utilities and the logit model as the analog of the Boltzmann factor in statistic physics. Recent extensions in term of quantum decision theory are also covered. A wealth of models are discussed briefly that build on the Ising model and generalize it to account for the many stylized facts of financial markets. A summary of the relevance of the Ising model and its extensions is provided to account for financial bubbles and crashes. The review would be incomplete if it would not cover the dynamical field of agent based models (ABMs), also known as computational economic models, of which the Ising-type models are just special ABM implementations. We formulate the "Emerging Market Intelligence hypothesis" to reconcile the pervasive presence of "noise traders" with the near efficiency of financial markets. Finally, we note that evolutionary biology, more than physics, is now playing a growing role to inspire models of financial markets.

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Section: The Excess Volatility Puzzle: Thinking As An Economistmentioning

confidence: 99%

Physics and financial economics (1776–2014): puzzles, Ising and agent-based models

2014

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“…Some randomness is also due to the stochastic realisations of the clusters in the percolation network. The overall resulting dynamics is stationary at long times since it is easy to check from (27) that E[p rice (t)] = E[p rice (t − 1)], which results from the fact that h(t)∆t = E[∆j(t)] by definition, as explained in the above sub-section providing a summary of the mathematical formulation of the JLS model.…”

Section: Synthetic Price Time Seriesmentioning

confidence: 99%

“…In agent-based models constructed on generalisations of the Ising model [8,27], it was proposed that a natural dynamics of the control parameter p(t) is not deterministic but random with persistence in order to represent the overall social sentiment of the market. The simplest process that conveniently captures this is the Ornstein-Uhlenbeck process [52], which is a mean-reverting Wiener process (or mean-reverting random walk in discrete time).…”

Section: Illustrations By Numerical Simulations Using a Ornstein-uhlementioning

confidence: 99%

“…This form was motivated on the basis of an analogy with critical phenomena, in which imitative Ising-like agents exhibit global coordinated behaviors when the forces of imitation increase to overcome the amplitude of randomness (or idiosyncratic opinions). See [24][25][26][27] for specific implementation of Ising-like traders. A large shift in the market book, leading to a crash according to the Kyle model [28], is possible in this herding phase.…”

Section: Introductionmentioning

confidence: 99%

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Micro-foundation using percolation theory of the finite time singular behavior of the crash hazard rate in a class of rational expectation bubbles

Seyrich

Sornette

2016

Int. J. Mod. Phys. C

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We present a plausible micro-founded model for the previously postulated power law finite time singular form of the crash hazard rate in the Johansen-Ledoit-Sornette model of rational expectation bubbles. The model is based on a percolation picture of the network of traders and the concept that clusters of connected traders share the same opinion. The key ingredient is the notion that a shift of position from buyer to seller of a sufficiently large group of traders can trigger a crash. This provides a formula to estimate the crash hazard rate by summation over percolation clusters above a minimum size of a power s a (with a > 1) of the cluster sizes s, similarly to a generalized percolation susceptibility. The power s a of cluster sizes emerges from the super-linear dependence of group activity as a function of group size, previously documented in the literature. The crash hazard rate exhibits explosive finite-time singular behaviors when the control parameter (fraction of occupied sites, or density of traders in the network) approaches the percolation threshold pc. Realistic dynamics are generated by modelling the density of traders on the percolation network by an Ornstein-Uhlenbeck process, whose memory controls the spontaneous excursion of the control parameter close to the critical region of bubble formation. Our numerical simulations recover the main stylized properties of the JLS model with intermittent explosive super-exponential bubbles interrupted by crashes.

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“…In a broader context, diversity-induced resonance can be generalized to other sources of disorder in the internal dynamics of the system constituents. Interestingly, even repulsive and evolving patterns of interactions can trigger a common collective behavior, be it synchronization [19,20], an amplification of an external signal [17,21] or a nonlinear increase in the volatility of the global dynamics [22]. In a social context, these repulsive interactions would represent contrarians, i.e.…”

Section: Introductionmentioning

confidence: 99%

Diversity-induced resonance in the response to social norms

2013

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In this paper we focus on diversity-induced resonance, which was recently found in bistable, excitable and other physical systems. We study the appearance of this phenomenon in a purely economic model of cooperating and defecting agents. Agent's contribution to a public good is seen as a social norm. So defecting agents face a social pressure, which decreases if free-riding becomes widespread. In this model, diversity among agents naturally appears because of the different sensitivity towards the social norm. We study the evolution of cooperation as a response to the social norm (i) for the replicator dynamics, and (ii) for the logit dynamics by means of numerical simulations. Diversity-induced resonance is observed as a maximum in the response of agents to changes in the social norm as a function of the degree of heterogeneity in the population. We provide an analytical, mean-field approach for the logit dynamics and find very good agreement with the simulations. From a socio-economic perspective, our results show that, counter-intuitively, diversity in the individual sensitivity to social norms may result in a society that better follows such norms as a whole, even if part of the population is less prone to follow them.

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Noise-induced volatility of collective dynamics

Cited by 27 publications

References 54 publications

Physics and financial economics (1776–2014): puzzles, Ising and agent-based models

Physics and financial economics (1776–2014): puzzles, Ising and agent-based models

Micro-foundation using percolation theory of the finite time singular behavior of the crash hazard rate in a class of rational expectation bubbles

Diversity-induced resonance in the response to social norms

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