Market dynamics immediately before and after financial shocks: Quantifying the Omori, productivity, and Bath laws

Hidden jerk in universal creep and aftershocks

Most materials exhibit creep memory under the action of a constant load. The memory behavior is governed by Andrade's creep law, which also has an inherent connection with the Omori-Utsu law of earthquake aftershocks. Both empirical laws lack a deterministic interpretation. Coincidentally, the Andrade law is similar to the time-varying part of the creep compliance of the fractional dashpot in anomalous viscoelastic modeling. Consequently, fractional derivatives are invoked, but since they lack a physical interpretation, the physical parameters of the two laws extracted from curve fit lack confidence. In this Letter, we establish an analogous linear physical mechanism that underlies both laws and relates its parameters with the material's macroscopic properties. Surprisingly, the explanation does not require the property of viscosity. Instead, it necessitates the existence of a rheological property that relates strain with the first order time derivative of stress, which involves jerk. Further, we justify the constant quality factor model of acoustic attenuation in complex media. The obtained results are validated in light of the established observations.

Evolution of Cohesion between USA Financial Sector Companies before, during, and Post-Economic Crisis: Complex Networks Approach

Various mathematical frameworks play an essential role in understanding the economic systems and the emergence of crises in them. Understanding the relation between the structure of connections between the system’s constituents and the emergence of a crisis is of great importance. In this paper, we propose a novel method for the inference of economic systems’ structures based on complex networks theory utilizing the time series of prices. Our network is obtained from the correlation matrix between the time series of companies’ prices by imposing a threshold on the values of the correlation coefficients. The optimal value of the threshold is determined by comparing the spectral properties of the threshold network and the correlation matrix. We analyze the community structure of the obtained networks and the relation between communities’ inter and intra-connectivity as indicators of systemic risk. Our results show how an economic system’s behavior is related to its structure and how the crisis is reflected in changes in the structure. We show how regulation and deregulation affect the structure of the system. We demonstrate that our method can identify high systemic risks and measure the impact of the actions taken to increase the system’s stability.

Financial earthquakes: SARS-CoV-2 news shock propagation in stock and sovereign bond markets

The SARS-CoV-2 epidemics outbreak has shocked global financial markets, inducing policymakers to put in place unprecedented interventions to inject liquidity and to counterbalance the negative impact on worldwide financial systems. Through the lens of statistical physics, we examine the financial volatility of the reference stock and bond markets of the United States, United Kingdom, Spain, France, Germany and Italy to quantify the effects of country-specific socio-economic and political announcements related to the epidemics. Main results show that financial markets exhibit heterogeneous behaviours towards news on the epidemics, with the Italian and German bond markets responding with major delays to shocks. Additionally, credit markets tend to be slower than equity markets in adjusting prices after shocks, hence being slower at incorporating the effects of such news.

The impact of the SARS-CoV-2 pandemic on financial markets: a seismologic approach

This work investigates financial volatility cascades generated by SARS-CoV-2 related news using concepts developed in the field of seismology. We analyze the impact of socio-economic and political announcements, as well as of financial stimulus disclosures, on the reference stock markets of the United States, United Kingdom, Spain, France, Germany and Italy. We quantify market efficiency in processing SARS-CoV-2 related news by means of the observed Omori power-law exponents and we relate these empirical regularities to investors' behavior through the lens of a stylized Agent-Based financial market model. The analysis reveals that financial markets may underreact to the announcements by taking a finite time to re-adjust prices, thus moving against the efficient market hypothesis. We observe that this empirical regularity can be related to the speculative behavior of market participants, whose willingness to switch toward better performing investment strategies, as well as their degree of reactivity to price trend or mispricing, can induce long-lasting volatility cascades.

On the Statistical Significance of the Variability Minima of the Order Parameter of Seismicity by Means of Event Coincidence Analysis

Natural time analysis has led to the introduction of an order parameter for seismicity when considering earthquakes as critical phenomena. The study of the fluctuations of this order parameter has shown that its variability exhibits minima before strong earthquakes. In this paper, we evaluate the statistical significance of such minima by using the recent method of event coincidence analysis. Our study includes the variability minima identified before major earthquakes in Japan and Eastern Mediterranean as well as in global seismicity.

Analysis of global stock index data during crisis period via complex network approach

Considerable research has been done on the complex stock market, however, there is very little systematic work on the impact of crisis on global stock markets. For filling in these gaps, we propose a complex network method, which analyzes the effects of the 2008 global financial crisis on global main stock index from 2005 to 2010. Firstly, we construct three weighted networks. The physics-derived technique of minimum spanning tree is utilized to investigate the networks of three stages. Regional clustering is found in each network. Secondly, we construct three average threshold networks and find the small-world property in the network before and during the crisis. Finally, the dynamical change of the network community structure is deeply analyzed with different threshold. The result indicates that for large thresholds, the network before and after the crisis has a significant community structure. Though this analysis, it would be helpful to investors for making decisions regarding their portfolios or to regulators for monitoring the key nodes to ensure the overall stability of the global stock market.

Impact and recovery process of mini flash crashes: An empirical study

In an Ultrafast Extreme Event (or Mini Flash Crash), the price of a traded stock increases or decreases strongly within milliseconds. We present a detailed study of Ultrafast Extreme Events in stock market data. In contrast to popular belief, our analysis suggests that most of the Ultrafast Extreme Events are not necessarily due to feedbacks in High Frequency Trading: In at least 60 percent of the observed Ultrafast Extreme Events, the largest fraction of the price change is due to a single market order. In times of financial crisis, large market orders are more likely which leads to a significant increase of Ultrafast Extreme Events occurrences. Furthermore, we analyze the 100 trades following each Ultrafast Extreme Events. While we observe a tendency of the prices to partially recover, less than 40 percent recover completely. On the other hand we find 25 percent of the Ultrafast Extreme Events to be almost recovered after only one trade which differs from the usually found price impact of market orders.

Fluctuation-driven price dynamics and investment strategies

Investigation of the driven mechanism of the price dynamics in complex financial systems is important and challenging. In this paper, we propose an investment strategy to study how dynamic fluctuations drive the price movements. The strategy is successfully applied to different stock markets in the world, and the result indicates that the driving effect of the dynamic fluctuations is rather robust. We investigate how the strategy performance is influenced by the market states and optimize the strategy performance by introducing two parameters. The strategy is also compared with several typical technical trading rules. Our findings not only provide an investment strategy which extends investors’ profits, but also offer a useful method to look into the dynamic properties of complex financial systems.

Measuring critical transitions in financial markets

Tipping points in complex systems are structural transitions from one state to another. In financial markets these critical points are connected to systemic risks, which have led to financial crisis in the past. Due to this, researchers are studying tipping points with different methods. This paper introduces a new method which bridges the gap between real-world portfolio management and statistical facts in financial markets in order to give more insight into the mechanics of financial markets.

Power-law rheology controls aftershock triggering and decay

The occurrence of aftershocks is a signature of physical systems exhibiting relaxation phenomena. They are observed in various natural or experimental systems and usually obey several non-trivial empirical laws. Here we consider a cellular automaton realization of a nonlinear viscoelastic slider-block model in order to infer the physical mechanisms of triggering responsible for the occurrence of aftershocks. We show that nonlinear viscoelasticity plays a critical role in the occurrence of aftershocks. The model reproduces several empirical laws describing the statistics of aftershocks. In case of earthquakes, the proposed model suggests that the power-law rheology of the fault gauge, underlying lower crust, and upper mantle controls the decay rate of aftershocks. This is verified by analysing several prominent aftershock sequences for which the rheological properties of the underlying crust and upper mantle were established.

Self-similar aftershock rates

In many important systems exhibiting crackling noise-an intermittent avalanchelike relaxation response with power-law and, thus, self-similar distributed event sizes-the "laws" for the rate of activity after large events are not consistent with the overall self-similar behavior expected on theoretical grounds. This is particularly true for the case of seismicity, and a satisfying solution to this paradox has remained outstanding. Here, we propose a generalized description of the aftershock rates which is both self-similar and consistent with all other known self-similar features. Comparing our theoretical predictions with high-resolution earthquake data from Southern California we find excellent agreement, providing particularly clear evidence for a unified description of aftershocks and foreshocks. This may offer an improved framework for time-dependent seismic hazard assessment and earthquake forecasting.

A Financial Market Model Incorporating Herd Behaviour

Herd behaviour in financial markets is a recurring phenomenon that exacerbates asset price volatility, and is considered a possible contributor to market fragility. While numerous studies investigate herd behaviour in financial markets, it is often considered without reference to the pricing of financial instruments or other market dynamics. Here, a trader interaction model based upon informational cascades in the presence of information thresholds is used to construct a new model of asset price returns that allows for both quiescent and herd-like regimes. Agent interaction is modelled using a stochastic pulse-coupled network, parametrised by information thresholds and a network coupling probability. Agents may possess either one or two information thresholds that, in each case, determine the number of distinct states an agent may occupy before trading takes place. In the case where agents possess two thresholds (labelled as the finite state-space model, corresponding to agents’ accumulating information over a bounded state-space), and where coupling strength is maximal, an asymptotic expression for the cascade-size probability is derived and shown to follow a power law when a critical value of network coupling probability is attained. For a range of model parameters, a mixture of negative binomial distributions is used to approximate the cascade-size distribution. This approximation is subsequently used to express the volatility of model price returns in terms of the model parameter which controls the network coupling probability. In the case where agents possess a single pulse-coupling threshold (labelled as the semi-infinite state-space model corresponding to agents’ accumulating information over an unbounded state-space), numerical evidence is presented that demonstrates volatility clustering and long-memory patterns in the volatility of asset returns. Finally, output from the model is compared to both the distribution of historical stock returns and the market price of an equity index option.

Quantifying Stock Return Distributions in Financial Markets

Being able to quantify the probability of large price changes in stock markets is of crucial importance in understanding financial crises that affect the lives of people worldwide. Large changes in stock market prices can arise abruptly, within a matter of minutes, or develop across much longer time scales. Here, we analyze a dataset comprising the stocks forming the Dow Jones Industrial Average at a second by second resolution in the period from January 2008 to July 2010 in order to quantify the distribution of changes in market prices at a range of time scales. We find that the tails of the distributions of logarithmic price changes, or returns, exhibit power law decays for time scales ranging from 300 seconds to 3600 seconds. For larger time scales, we find that the distributions tails exhibit exponential decay. Our findings may inform the development of models of market behavior across varying time scales.

Abrupt rise of new machine ecology beyond human response time

Society's techno-social systems are becoming ever faster and more computer-orientated. However, far from simply generating faster versions of existing behaviour, we show that this speed-up can generate a new behavioural regime as humans lose the ability to intervene in real time. Analyzing millisecond-scale data for the world's largest and most powerful techno-social system, the global financial market, we uncover an abrupt transition to a new all-machine phase characterized by large numbers of subsecond extreme events. The proliferation of these subsecond events shows an intriguing correlation with the onset of the system-wide financial collapse in 2008. Our findings are consistent with an emerging ecology of competitive machines featuring ‘crowds' of predatory algorithms, and highlight the need for a new scientific theory of subsecond financial phenomena.

Can Google Trends search queries contribute to risk diversification?

Portfolio diversification and active risk management are essential parts of financial analysis which became even more crucial (and questioned) during and after the years of the Global Financial Crisis. We propose a novel approach to portfolio diversification using the information of searched items on Google Trends. The diversification is based on an idea that popularity of a stock measured by search queries is correlated with the stock riskiness. We penalize the popular stocks by assigning them lower portfolio weights and we bring forward the less popular, or peripheral, stocks to decrease the total riskiness of the portfolio. Our results indicate that such strategy dominates both the benchmark index and the uniformly weighted portfolio both in-sample and out-of-sample.

Copulas and time series with long-ranged dependencies

We review ideas on temporal dependencies and recurrences in discrete time series from several areas of natural and social sciences. We revisit existing studies and redefine the relevant observables in the language of copulas (joint laws of the ranks). We propose that copulas provide an appropriate mathematical framework to study nonlinear time dependencies and related concepts-like aftershocks, Omori law, recurrences, and waiting times. We also critically argue, using this global approach, that previous phenomenological attempts involving only a long-ranged autocorrelation function lacked complexity in that they were essentially monoscale.

Near-extreme statistics of Brownian motion

We study the statistics of near-extreme events of Brownian motion (BM) on the time interval [0,t]. We focus on the density of states near the maximum, ρ(r,t), which is the amount of time spent by the process at a distance r from the maximum. We develop a path integral approach to study functionals of the maximum of BM, which allows us to study the full probability density function of ρ(r,t) and obtain an explicit expression for the moments <[ρ(r,t)]k> for arbitrary integer k. We also study near extremes of constrained BM, like the Brownian bridge. Finally we also present numerical simulations to check our analytical results.

Exact statistics of the gap and time interval between the first two maxima of random walks and Lévy flights

We investigate the statistics of the gap G(n) between the two rightmost positions of a Markovian one-dimensional random walker (RW) after n time steps and of the duration L(n) which separates the occurrence of these two extremal positions. The distribution of the jumps η(i)'s of the RW, f(η), is symmetric and its Fourier transform has the small k behavior 1-f[over ^](k)~|k|(μ), with 0<μ≤2. For μ=2, the RW converges, for large n, to Brownian motion, while for 0<μ<2 it corresponds to a Lévy flight of index μ. We compute the joint probability density function (PDF) P(n)(g,l) of G(n) and L(n) and show that, when n→∞, it approaches a limiting PDF p(g,l). The corresponding marginal PDFs of the gap, p(gap)(g), and of L(n), p(time)(l), are found to behave like p(gap)(g)~g(-1-μ) for g>>1 and 0<μ<2, and p(time)(l)~l(-γ(μ)) for l>>1 with γ(1<μ≤2)=1+1/μ and γ(0<μ<1)=2. For l, g>>1 with fixed lg(-μ), p(g,l) takes the scaling form p(g,l)~g(-1-2μ)p[over ˜](μ)(lg(-μ)), where p[over ˜](μ)(y) is a (μ-dependent) scaling function. We also present numerical simulations which verify our analytic results.

Quantifying the behavior of stock correlations under market stress

Understanding correlations in complex systems is crucial in the face of turbulence, such as the ongoing financial crisis. However, in complex systems, such as financial systems, correlations are not constant but instead vary in time. Here we address the question of quantifying state-dependent correlations in stock markets. Reliable estimates of correlations are absolutely necessary to protect a portfolio. We analyze 72 years of daily closing prices of the 30 stocks forming the Dow Jones Industrial Average (DJIA). We find the striking result that the average correlation among these stocks scales linearly with market stress reflected by normalized DJIA index returns on various time scales. Consequently, the diversification effect which should protect a portfolio melts away in times of market losses, just when it would most urgently be needed. Our empirical analysis is consistent with the interesting possibility that one could anticipate diversification breakdowns, guiding the design of protected portfolios.

Scaling of seismic memory with earthquake size

It has been observed that discrete earthquake events possess memory, i.e., that events occurring in a particular location are dependent on the history of that location. We conduct an analysis to see whether continuous real-time data also display a similar memory and, if so, whether such autocorrelations depend on the size of earthquakes within close spatiotemporal proximity. We analyze the seismic wave form database recorded by 64 stations in Japan, including the 2011 "Great East Japan Earthquake," one of the five most powerful earthquakes ever recorded, which resulted in a tsunami and devastating nuclear accidents. We explore the question of seismic memory through use of mean conditional intervals and detrended fluctuation analysis (DFA). We find that the wave form sign series show power-law anticorrelations while the interval series show power-law correlations. We find size dependence in earthquake autocorrelations: as the earthquake size increases, both of these correlation behaviors strengthen. We also find that the DFA scaling exponent α has no dependence on the earthquake hypocenter depth or epicentral distance.