Quantifying reflexivity in financial markets: toward a prediction of flash crashes

Identifying new classes of financial price jumps with wavelets

We introduce an unsupervised classification framework that leverages a multiscale wavelet representation of time-series and apply it to stock price jumps. In line with previous work, we recover the fact that time-asymmetry of volatility is the major feature that separates exogenous, news-induced jumps from endogenously generated jumps. Local mean-reversion and trend are found to be two additional key features, allowing us to identify new classes of jumps. Using our wavelet-based representation, we investigate the endogenous or exogenous nature of cojumps, which occur when multiple stocks experience price jumps within the same minute. Perhaps surprisingly, our analysis suggests that a significant fraction of cojumps result from an endogenous contagion mechanism.

Exogenous and endogenous factors affecting stock market transactions: A Hawkes process analysis of the Tokyo Stock Exchange during the COVID-19 pandemic

Transactions in financial markets are not evenly spaced but can be concentrated within a short period of time. In this study, we investigated the factors that determine the transaction frequency in financial markets. Specifically, we employed the Hawkes process model to identify exogenous and endogenous forces governing transactions of individual stocks in the Tokyo Stock Exchange during the COVID-19 pandemic. To enhance the accuracy of our analysis, we introduced a novel EM algorithm for the estimation of exogenous and endogenous factors that specifically addresses the interdependence of the values of these factors over time. We detected a substantial change in the transaction frequency in response to policy change announcements. Moreover, there is significant heterogeneity in the transaction frequency among individual stocks. We also found a tendency where stocks with high market capitalization tend to significantly respond to external news, while their excitation relationship between transactions is weak. This suggests the capability of quantifying the market state from the viewpoint of the exogenous and endogenous factors generating transactions for various stocks.

Modelling time-varying interactions in complex systems: the Score Driven Kinetic Ising Model

A common issue when analyzing real-world complex systems is that the interactions between their elements often change over time. Here we propose a new modeling approach for time-varying interactions generalising the well-known Kinetic Ising Model, a minimalistic pairwise constant interactions model which has found applications in several scientific disciplines. Keeping arbitrary choices of dynamics to a minimum and seeking information theoretical optimality, the Score-Driven methodology allows to extract from data and interpret the presence of temporal patterns describing time-varying interactions. We identify a parameter whose value at a given time can be directly associated with the local predictability of the dynamics and we introduce a method to dynamically learn its value from the data, without specifying parametrically the system's dynamics. We extend our framework to disentangle different sources (e.g. endogenous vs exogenous) of predictability in real time, and show how our methodology applies to a variety of complex systems such as financial markets, temporal (social) networks, and neuronal populations.

The excess volatility puzzle explained by financial noise amplification from endogenous feedbacks

The arguably most important paradox of financial economics-the excess volatility puzzle-first identified by Robert Shiller in 1981 states that asset prices fluctuate much more than information about their fundamental value. We show that this phenomenon is associated with an intrinsic propensity for financial markets to evolve towards instabilities. These properties, exemplified for two major financial markets, the foreign exchange and equity futures markets, can be expected to be generic in other complex systems where excess fluctuations result from the interplay between exogenous driving and endogenous feedback. Using an exact mapping of the key property (volatility/variance) of the price diffusion process onto that of a point process (arrival intensity of price changes), together with a self-excited epidemic model, we introduce a novel decomposition of the volatility of price fluctuations into an exogenous (i.e. efficient) component and an endogenous (i.e. inefficient) excess component. The endogenous excess volatility is found to be substantial, largely stable at longer time scales and thus provides a plausible explanation for the excess volatility puzzle. Our theory rationalises the remarkable fact that small stochastic exogenous fluctuations at the micro-scale of milliseconds to seconds are renormalised into long-term excess volatility with an amplification factor of around 5 for equity futures and 2 for exchange rates, in line with models including economic fundamentals explicitly.

Nonequilibrium phase transitions in competitive markets caused by network effects

Network effects are the added value derived solely from the popularity of a product in an economic market. Using agent-based models inspired by statistical physics, we propose a minimal theory of a competitive market for (nearly) indistinguishable goods with demand-side network effects, sold by statistically identical sellers. With weak network effects, the model reproduces conventional microeconomics: there is a statistical steady state of (nearly) perfect competition. Increasing network effects, we find a phase transition to a robust nonequilibrium phase driven by the spontaneous formation and collapse of fads in the market. When sellers update prices sufficiently quickly, an emergent monopolist can capture the market and undercut competition, leading to a symmetry- and ergodicity-breaking transition. The nonequilibrium phase simultaneously exhibits three empirically established phenomena not contained in the standard theory of competitive markets: spontaneous price fluctuations, persistent seller profits, and broad distributions of firm market shares.

Volatility as a Transmitter of Systemic Risk: Is there a Structural Risk in Finance?

This article discusses the role of volatility in the context of systemic risk in finance. The main argument is that volatility transmits risks within the financial system and beyond, shaking the financial system and threatening in particular small or vulnerable clients (SMEs, households, and also low- and middle-income countries). In addition, it is argued that volatility-induced threats result from structural characteristics of the financial markets themselves (reactivity, reflexivity, and recursivity). The article introduces the concept of volatility, and different approaches to understanding risks related to the financial system (e.g., financial analysis, systems analysis). Two cases related to systemic risk are presented. The first concerns the role of volatility in three major financial crises (stock crash 1987, Asian crisis 1996-1997, global banking crisis 2007-2008), documenting that volatility spillovers have become a "new normal." The second case concerns the moderate reflection of systemic risk within The Journal of Finance (the leading financial journal). The two cases show that volatility plays a role in systemic risks, but that this role has not yet been examined in detail by the scientific community.

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.

Significant hot hand effect in the game of cricket

We investigate the predictability and persistence of individual and team performance (hot-hand effect) by analyzing the complete recorded history of international cricket. We introduce an original temporal representation of performance streaks, which is suitable to be modelled as a self-exciting point process. We confirm the presence of predictability and hot-hands across the individual performance and the absence of the same in team performance and game outcome. Thus, Cricket is a game of skill for individuals and a game of chance for the teams. Our study contributes to recent historiographical debates concerning the presence of persistence in individual and collective productivity and success. The introduction of several metrics and methods can be useful to test and exploit clustering of performance in the study of human behavior and design of algorithms for predicting success.

Analysis of Individual High-Frequency Traders’ Buy–Sell Order Strategy Based on Multivariate Hawkes Process

Traders who instantly react to changes in the financial market and place orders in milliseconds are called high-frequency traders (HFTs). HFTs have recently become more prevalent and attracting attention in the study of market microstructures. In this study, we used data to track the order history of individual HFTs in the USD/JPY forex market to reveal how individual HFTs interact with the order book and what strategies they use to place their limit orders. Specifically, we introduced an 8-dimensional multivariate Hawkes process that included the excitations due to the occurrence of limit orders, cancel orders, and executions in the order book change, and performed maximum likelihood estimations of the limit order processes for 134 HFTs. As a result, we found that the limit order generation processes of 104 of the 134 HFTs were modeled by a multivariate Hawkes process. In this analysis of the EBS market, the HFTs whose strategies were modeled by the Hawkes process were categorized into three groups according to their excitation mechanisms: (1) those excited by executions; (2) those that were excited by the occurrences or cancellations of limit orders; and (3) those that were excited by their own orders.

Quantifying the Endogeneity in Online Donations

Charitable crowdfunding provides a new channel for people and families suffering from unforeseen events, such as accidents, severe illness, and so on, to seek help from the public. Thus, finding the key determinants which drive the fundraising process of crowdfunding campaigns is of great importance, especially for those suffering. With a unique data set containing 210,907 crowdfunding projects covering a period from October 2015 to June 2020, from a famous charitable crowdfunding platform, specifically Qingsong Chou, we will reveal how many online donations are due to endogeneity, referring to the positive feedback process of attracting more people to donate through broadcasting campaigns in social networks by donors. For this aim, we calibrate three different Hawkes processes to the event data of online donations for each crowdfunding campaign on each day, which allows us to estimate the branching ratio, a measure of endogeneity. It is found that the online fundraising process works in a sub-critical state and nearly 70-90% of the online donations are endogenous. Furthermore, even though the fundraising amount, number of donations, and number of donors decrease rapidly after the crowdfunding project is created, the measure of endogeneity remains stable during the entire lifetime of crowdfunding projects. Our results not only deepen our understanding of online fundraising dynamics but also provide a quantitative framework to disentangle the endogenous and exogenous dynamics in complex systems.

Continuous Time Random Walk with Correlated Waiting Times. The Crucial Role of Inter-Trade Times in Volatility Clustering

In many physical, social, and economic phenomena, we observe changes in a studied quantity only in discrete, irregularly distributed points in time. The stochastic process usually applied to describe this kind of variable is the continuous-time random walk (CTRW). Despite the popularity of these types of stochastic processes and strong empirical motivation, models with a long-term memory within the sequence of time intervals between observations are rare in the physics literature. Here, we fill this gap by introducing a new family of CTRWs. The memory is introduced to the model by assuming that many consecutive time intervals can be the same. Surprisingly, in this process we can observe a slowly decaying nonlinear autocorrelation function without a fat-tailed distribution of time intervals. Our model, applied to high-frequency stock market data, can successfully describe the slope of decay of the nonlinear autocorrelation function of stock market returns. We achieve this result without imposing any dependence between consecutive price changes. This proves the crucial role of inter-event times in the volatility clustering phenomenon observed in all stock markets.

Impact of Governmental interventions on epidemic progression and workplace activity during the COVID-19 outbreak

In the first quarter of 2020, the COVID-19 pandemic brought the world to a state of paralysis. During this period, humanity saw by far the largest organized travel restrictions and unprecedented efforts and global coordination to contain the spread of the SARS-CoV-2 virus. Using large scale human mobility and fine grained epidemic incidence data, we develop a framework to understand and quantify the effectiveness of the interventions implemented by various countries to control epidemic growth. Our analysis reveals the importance of timing and implementation of strategic policy in controlling the epidemic. We also unearth significant spatial diffusion of the epidemic before and during the lockdown measures in several countries, casting doubt on the effectiveness or on the implementation quality of the proposed Governmental policies.

Detection of Mutual Exciting Structure in Stock Price Trend Dynamics

We investigated a comprehensive analysis of the mutual exciting mechanism for the dynamic of stock price trends. A multi-dimensional Hawkes-model-based approach was proposed to capture the mutual exciting activities, which take the form of point processes induced by dual moving average crossovers. We first performed statistical measurements for the crossover event sequence, introducing the distribution of the inter-event times of dual moving average crossovers and the correlations of local variation (LV), which is often used in spike train analysis. It was demonstrated that the crossover dynamics in most stock sectors are generally more regular than a standard Poisson process, and the correlation between variations is ubiquitous. In this sense, the proposed model allowed us to identify some asymmetric cross-excitations, and a mutually exciting structure of stock sectors could be characterized by mutual excitation correlations obtained from the kernel matrix of our model. Using simulations, we were able to substantiate that a burst of the dual moving average crossovers in one sector increases the intensity of burst both in the same sector (self-excitation) as well as in other sectors (cross-excitation), generating episodes of highly clustered burst across the market. Furthermore, based on our finding, an algorithmic pair trading strategy was developed and backtesting results on real market data showed that the mutual excitation mechanism might be profitable for stock trading.

Asymmetric excitation of left- and right-tail extreme events probed using a Hawkes model: Application to financial returns

We construct a two-tailed peaks-over-threshold Hawkes model that captures asymmetric self- and cross-excitation in and between left- and right-tail extreme values within a time series. We demonstrate its applicability by investigating extreme gains and losses within the daily log-returns of the S&P 500 equity index. We find that the arrivals of extreme losses and gains are described by a common conditional intensity to which losses contribute twice as much as gains. However, the contribution of the former decays almost five times more quickly than that of the latter. We attribute these asymmetries to the different reactions of market traders to extreme upward and downward movements of asset prices: an example of negativity bias, wherein trauma is more salient than euphoria.

Nonuniversal Power Law Distribution of Intensities of the Self-Excited Hawkes Process: A Field-Theoretical Approach

The Hawkes self-excited point process provides an efficient representation of the bursty intermittent dynamics of many physical, biological, geological, and economic systems. By expressing the probability for the next event per unit time (called "intensity"), say of an earthquake, as a sum over all past events of (possibly) long-memory kernels, the Hawkes model is non-Markovian. By mapping the Hawkes model onto stochastic partial differential equations that are Markovian, we develop a field theoretical approach in terms of probability density functionals. Solving the steady-state equations, we predict a power law scaling of the probability density function of the intensities close to the critical point n=1 of the Hawkes process, with a nonuniversal exponent, function of the background intensity ν_{0} of the Hawkes intensity, the average timescale of the memory kernel and the branching ratio n. Our theoretical predictions are confirmed by numerical simulations.

Modeling aggressive market order placements with Hawkes factor models

Price changes are induced by aggressive market orders in stock market. We introduce a bivariate marked Hawkes process to model aggressive market order arrivals at the microstructural level. The order arrival intensity is marked by an exogenous part and two endogenous processes reflecting the self-excitation and cross-excitation respectively. We calibrate the model for a Shenzhen Stock Exchange stock. We find that the exponential kernel with a smooth cut-off (i.e. the subtraction of two exponentials) produces much better calibration than the monotonous exponential kernel (i.e. the sum of two exponentials). The exogenous baseline intensity explains the U-shaped intraday pattern. Our empirical results show that the endogenous submission clustering is mainly caused by self-excitation rather than cross-excitation.

Modeling stochastic processes in disease spread across a heterogeneous social system

This study infers probabilistic infection routes of a vector-borne disease, by modeling internal dynamics of metapopulations driven by human mobility as multivariate stochastic processes. In this way, our proposed model uncovers the self-excitation and mutual excitation nature of disease spread across a heterogeneous social system with rich context. Our model is a general extension of networked Hawkes processes, providing flexibilities to add constraints (presence of diffusion medium) and to use domain knowledge (cross-metapopulation connectivity), enabling covering of direct and indirect diffusion processes such as contact-based and vector-borne disease spread. Our model is readily applicable to a wide range of intragroup and intergroup diffusion processes in social and natural systems and can infer probabilistic causality between discrete events.

Diffusion processes are governed by external triggers and internal dynamics in complex systems. Timely and cost-effective control of infectious disease spread critically relies on uncovering underlying diffusion mechanisms, which is challenging due to invisible infection pathways and time-evolving intensity of infection cases. Here, we propose a new diffusion framework for stochastic processes, which models disease spread across metapopulations by incorporating human mobility as topological pathways in a heterogeneous social system. We apply Bayesian inference with the stochastic Expectation–Maximization algorithm to quantify underlying diffusion dynamics in terms of exogeneity and endogeneity and estimate cross-regional infection flow based on Granger causality. The effectiveness of our proposed model is shown by using comprehensive simulation procedures (robustness tests with noisy data considering missing or delayed human case reporting in real situations) and by applying the model to real data from 15-y dengue outbreaks in Australia.

Inferring collective dynamical states from widely unobserved systems

When assessing spatially extended complex systems, one can rarely sample the states of all components. We show that this spatial subsampling typically leads to severe underestimation of the risk of instability in systems with propagating events. We derive a subsampling-invariant estimator, and demonstrate that it correctly infers the infectiousness of various diseases under subsampling, making it particularly useful in countries with unreliable case reports. In neuroscience, recordings are strongly limited by subsampling. Here, the subsampling-invariant estimator allows to revisit two prominent hypotheses about the brain’s collective spiking dynamics: asynchronous-irregular or critical. We identify consistently for rat, cat, and monkey a state that combines features of both and allows input to reverberate in the network for hundreds of milliseconds. Overall, owing to its ready applicability, the novel estimator paves the way to novel insight for the study of spatially extended dynamical systems.

From infectious diseases to brain activity, complex systems can be approximated using autoregressive models. Here, the authors show that incomplete sampling can bias estimates of the stability of such systems, and introduce a novel, unbiased metric for use in such situations.

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.

Detection of intensity bursts using Hawkes processes: An application to high-frequency financial data

Given a stationary point process, an intensity burst is defined as a short time period during which the number of counts is larger than the typical count rate. It might signal a local nonstationarity or the presence of an external perturbation to the system. In this paper we propose a procedure for the detection of intensity bursts within the Hawkes process framework. By using a model selection scheme we show that our procedure can be used to detect intensity bursts when both their occurrence time and their total number is unknown. Moreover, the initial time of the burst can be determined with a precision given by the typical interevent time. We apply our methodology to the midprice change in foreign exchange (FX) markets showing that these bursts are frequent and that only a relatively small fraction is associated with news arrival. We show lead-lag relations in intensity burst occurrence across different FX rates and we discuss their relation with price jumps.

Theory of nonstationary Hawkes processes

We expand the theory of Hawkes processes to the nonstationary case, in which the mutually exciting point processes receive time-dependent inputs. We derive an analytical expression for the time-dependent correlations, which can be applied to networks with arbitrary connectivity, and inputs with arbitrary statistics. The expression shows how the network correlations are determined by the interplay between the network topology, the transfer functions relating units within the network, and the pattern and statistics of the external inputs. We illustrate the correlation structure using several examples in which neural network dynamics are modeled as a Hawkes process. In particular, we focus on the interplay between internally and externally generated oscillations and their signatures in the spike and rate correlation functions.

Hawkes process model with a time-dependent background rate and its application to high-frequency financial data

A Hawkes process model with a time-varying background rate is developed for analyzing the high-frequency financial data. In our model, the logarithm of the background rate is modeled by a linear model with a relatively large number of variable-width basis functions, and the parameters are estimated by a Bayesian method. Our model can capture not only the slow time variation, such as in the intraday seasonality, but also the rapid one, which follows a macroeconomic news announcement. By analyzing the tick data of the Nikkei 225 mini, we find that (i) our model is better fitted to the data than the Hawkes models with a constant background rate or a slowly varying background rate, which have been commonly used in the field of quantitative finance; (ii) the improvement in the goodness-of-fit to the data by our model is significant especially for sessions where considerable fluctuation of the background rate is present; and (iii) our model is statistically consistent with the data. The branching ratio, which quantifies the level of the endogeneity of markets, estimated by our model is 0.41, suggesting the relative importance of exogenous factors in the market dynamics. We also demonstrate that it is critically important to appropriately model the time-dependent background rate for the branching ratio estimation.

Financial Knudsen number: Breakdown of continuous price dynamics and asymmetric buy-and-sell structures confirmed by high-precision order-book information

We generalize the description of the dynamics of the order book of financial markets in terms of a Brownian particle embedded in a fluid of incoming, exiting, and annihilating particles by presenting a model of the velocity on each side (buy and sell) independently. The improved model builds on the time-averaged number of particles in the inner layer and its change per unit time, where the inner layer is revealed by the correlations between price velocity and change in the number of particles (limit orders). This allows us to introduce the Knudsen number of the financial Brownian particle motion and its asymmetric version (on the buy and sell sides). Not being considered previously, the asymmetric Knudsen numbers are crucial in finance in order to detect asymmetric price changes. The Knudsen numbers allows us to characterize the conditions for the market dynamics to be correctly described by a continuous stochastic process. Not questioned until now for large liquid markets such as the USD-JPY and EUR-USD exchange rates, we show that there are regimes when the Knudsen numbers are so high that discrete particle effects dominate, such as during market stresses and crashes. We document the presence of imbalances of particles depletion rates on the buy and sell sides that are associated with high Knudsen numbers and violent directional price changes. This indicator can detect the direction of the price motion at the early stage while the usual volatility risk measure is blind to the price direction.

Linear processes in high dimensions: Phase space and critical properties

In this work we investigate the generic properties of a stochastic linear model in the regime of high dimensionality. We consider in particular the vector autoregressive (VAR) model and the multivariate Hawkes process. We analyze both deterministic and random versions of these models, showing the existence of a stable phase and an unstable phase. We find that along the transition region separating the two regimes the correlations of the process decay slowly, and we characterize the conditions under which these slow correlations are expected to become power laws. We check our findings with numerical simulations showing remarkable agreement with our predictions. We finally argue that real systems with a strong degree of self-interaction are naturally characterized by this type of slow relaxation of the correlations.

Modeling foreign exchange market activity around macroeconomic news: Hawkes-process approach

We present a Hawkes-model approach to the foreign exchange market in which the high-frequency price dynamics is affected by a self-exciting mechanism and an exogenous component, generated by the pre-announced arrival of macroeconomic news. By focusing on time windows around the news announcement, we find that the model is able to capture the increase of trading activity after the news, both when the news has a sizable effect on volatility and when this effect is negligible, either because the news in not important or because the announcement is in line with the forecast by analysts. We extend the model by considering noncausal effects, due to the fact that the existence of the news (but not its content) is known by the market before the announcement.

Branching-ratio approximation for the self-exciting Hawkes process

We introduce a model-independent approximation for the branching ratio of Hawkes self-exciting point processes. Our estimator requires knowing only the mean and variance of the event count in a sufficiently large time window, statistics that are readily obtained from empirical data. The method we propose greatly simplifies the estimation of the Hawkes branching ratio, recently proposed as a proxy for market endogeneity and formerly estimated using numerical likelihood maximization. We employ our method to support recent theoretical and experimental results indicating that the best fitting Hawkes model to describe S&P futures price changes is in fact critical (now and in the recent past) in light of the long memory of financial market activity.

Unraveling hidden order in the dynamics of developed and emerging markets

The characterization of asset price returns is an important subject in modern finance. Traditionally, the dynamics of stock returns are assumed to lack any temporal order. Here we present an analysis of the autocovariance of stock market indices and unravel temporal order in several major stock markets. We also demonstrate a fundamental difference between developed and emerging markets in the past decade - emerging markets are marked by positive order in contrast to developed markets whose dynamics are marked by weakly negative order. In addition, the reaction to financial crises was found to be reversed among developed and emerging markets, presenting large positive/negative autocovariance spikes following the onset of these crises. Notably, the Chinese market shows neutral or no order while being regarded as an emerging market. These findings show that despite the coupling between international markets and global trading, major differences exist between different markets, and demonstrate that the autocovariance of markets is correlated with their stability, as well as with their state of development.

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

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 statistical physics. Recent extensions in terms 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 did 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 Intelligence Market 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.

Scaling symmetry, renormalization, and time series modeling: the case of financial assets dynamics

We present and discuss a stochastic model of financial assets dynamics based on the idea of an inverse renormalization group strategy. With this strategy we construct the multivariate distributions of elementary returns based on the scaling with time of the probability density of their aggregates. In its simplest version the model is the product of an endogenous autoregressive component and a random rescaling factor designed to embody also exogenous influences. Mathematical properties like increments' stationarity and ergodicity can be proven. Thanks to the relatively low number of parameters, model calibration can be conveniently based on a method of moments, as exemplified in the case of historical data of the S&P500 index. The calibrated model accounts very well for many stylized facts, like volatility clustering, power-law decay of the volatility autocorrelation function, and multiscaling with time of the aggregated return distribution. In agreement with empirical evidence in finance, the dynamics is not invariant under time reversal, and, with suitable generalizations, skewness of the return distribution and leverage effects can be included. The analytical tractability of the model opens interesting perspectives for applications, for instance, in terms of obtaining closed formulas for derivative pricing. Further important features are the possibility of making contact, in certain limits, with autoregressive models widely used in finance and the possibility of partially resolving the long- and short-memory components of the volatility, with consistent results when applied to historical series.

High quality topic extraction from business news explains abnormal financial market volatility

Understanding the mutual relationships between information flows and social activity in society today is one of the cornerstones of the social sciences. In financial economics, the key issue in this regard is understanding and quantifying how news of all possible types (geopolitical, environmental, social, financial, economic, etc.) affects trading and the pricing of firms in organized stock markets. In this article, we seek to address this issue by performing an analysis of more than 24 million news records provided by Thompson Reuters and of their relationship with trading activity for 206 major stocks in the S&P US stock index. We show that the whole landscape of news that affects stock price movements can be automatically summarized via simple regularized regressions between trading activity and news information pieces decomposed, with the help of simple topic modeling techniques, into their “thematic” features. Using these methods, we are able to estimate and quantify the impacts of news on trading. We introduce network-based visualization techniques to represent the whole landscape of news information associated with a basket of stocks. The examination of the words that are representative of the topic distributions confirms that our method is able to extract the significant pieces of information influencing the stock market. Our results show that one of the most puzzling stylized facts in financial economies, namely that at certain times trading volumes appear to be “abnormally large,” can be partially explained by the flow of news. In this sense, our results prove that there is no “excess trading,” when restricting to times when news is genuinely novel and provides relevant financial information.

Fertility heterogeneity as a mechanism for power law distributions of recurrence times

We study the statistical properties of recurrence times in the self-excited Hawkes conditional Poisson process, the simplest extension of the Poisson process that takes into account how the past events influence the occurrence of future events. Specifically, we analyze the impact of the power law distribution of fertilities with exponent α, where the fertility of an event is the number of triggered events of first generation, on the probability distribution function (PDF) f(τ) of the recurrence times τ between successive events. The other input of the model is an exponential law quantifying the PDF of waiting times between an event and its first generation triggered events, whose characteristic time scale is taken as our time unit. At short-time scales, we discover two intermediate power law asymptotics, f(τ)~τ(-(2-α)) for τ<<τ(c) and f(τ)~τ(-α) for τ(c)<<τ<<1, where τ(c) is associated with the self-excited cascades of triggered events. For 1<<τ<<1/ν, we find a constant plateau f(τ)=/~const, while at long times, 1/ν</~τ, f(τ)=/~e(-ντ) has an exponential tail controlled by the arrival rate ν of exogenous events. These results demonstrate a novel mechanism for the generation of power laws in the distribution of recurrence times, which results from a power law distribution of fertilities in the presence of self-excitation and cascades of triggering.

Financial price dynamics and pedestrian counterflows: a comparison of statistical stylized facts

We propose and document the evidence for an analogy between the dynamics of granular counterflows in the presence of bottlenecks or restrictions and financial price formation processes. Using extensive simulations, we find that the counterflows of simulated pedestrians through a door display eight stylized facts observed in financial markets when the density around the door is compared with the logarithm of the price. Finding so many stylized facts is very rare indeed among all agent-based models of financial markets. The stylized properties are present when the agents in the pedestrian model are assumed to display a zero-intelligent behavior. If agents are given decision-making capacity and adapt to partially follow the majority, periods of herding behavior may additionally occur. This generates the very slow decay of the autocorrelation of absolute return due to an intermittent dynamics. Our findings suggest that the stylized facts in the fluctuations of the financial prices result from a competition of two groups with opposite interests in the presence of a constraint funneling the flow of transactions to a narrow band of prices with limited liquidity.