A classic problem in physics is the origin of fat tailed distributions generated by complex systems. We study the distributions of stock returns measured over different time lags We find that destroying all correlations without changing the d distribution, by shuffling the order of the daily returns, causes…
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48 results for “Fat-tails”
New fat-tail normality test based on conditional second moments with applications to financeq-fin.ST
Paper introduces a new fat-tail test using conditional second moments.
problem Measuring and assessing the impact of fat-tails on data dispersion.
method Constructs a goodness-of-fit statistic based on conditional second moments.
result Shows superior performance of the new test compared to existing methods.
Fat Tails in Financial Return Distributions Revisited: Evidence from the Korean Stock Marketq-fin.GN
Study finds recent Korean stock returns have fatter tails than before, especially for smaller companies.
problem Understanding the fat tails in financial return distributions.
method Empirical analysis of Korean stock market data, controlling for the 1997 foreign currency crisis and volatility clustering.
result Fat tails in stock return distributions persist even after controlling for market crashes and volatility clustering.
Study on Gini estimation for fat-tailed data, showing bias and proposing corrections.
problem Estimating Gini index under infinite variance data.
method Analysis of nonparametric and maximum likelihood estimators, focusing on phase transitions and tail index effects.
result Maximum likelihood estimation outperforms nonparametric methods for fat-tailed data.
The Origin of Fat Tailsq-fin.GN
We propose a random walk model of asset returns where the parameters depend on market stress. Stress is measured by, e.g., the value of an implied volatility index. We show that model parameters including standard deviations and correlations can be estimated robustly and that all distributions are approximately normal.…
Leverage and Uncertaintyq-fin.RM
Investor success hinges on managing risk, uncertainty, and leverage effectively.
problem Managing risk, uncertainty, and leverage in investment decisions.
method Adaptive skills and quantitative probabilistic methods.
result Derivation of the fractional Kelly criterion for assets with fat tails and insights into Risk Parity strategies.
Where Do Thin Tails Come From?q-fin.RM
The literature of heavy tails (typically) starts with a random walk and finds mechanisms that lead to fat tails under aggregation. We follow the inverse route and show how starting with fat tails we get to thin-tails when deriving the probability distribution of the response to a random variable. We introduce a general…
Optimal portfolios for fat-tailed risks using a new tail risk measure.
problem Optimizing portfolios for pension funds and insurance liabilities with extreme risk sensitivity.
method Developed a new tail risk measure (Extreme Deviation, XD) and optimized portfolios based on this measure.
result Optimal portfolios maximize return per unit of XD, balancing hedging and risk contributions.
Superstatistics with cut-off tails models financial data with fat tails and cutoffs.
problem Capturing the fat-tailed and cutoff shapes in financial time series.
method Incorporates cut-off effects into superstatistics to model financial data.
result The model accurately describes real financial time series properties.
Elliptical processes generalize Gaussian and Student-t models with fat tails and computational efficiency.
problem Need for models with fat tails and computational tractability.
method Represent elliptical distributions as continuous mixtures of Gaussian distributions, derive closed-form expressions for marginal and conditional distributions.
result Elliptical processes offer advantages in robust regression compared to Gaussian processes.
Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applicationsstat.OT
The book examines statistical issues with fat-tailed distributions and proposes remedies.
problem Misapplication of conventional statistical techniques to fat-tailed distributions.
method Investigates the limitations of traditional asymptotics and proposes remedies.
result Traditional statistical techniques often fail when applied to fat-tailed distributions.
New model simulates financial market price dynamics with realistic fat tails.
problem Simulate price evolution in financial markets with realistic features.
method Self-Organized Criticality (SOC) model on multilayer network of traders, considering order book dynamics.
result Fat tails in return distributions observed, matching real markets.
Quantitative approach to multifractality induced by correlations and broad distribution of dataq-fin.CP
Analyzes multifractality caused by fat-tailed distributions in time series.
problem Quantifying multifractality induced by fat-tailed distributions in time series data.
method Examines different types of fat-tailed distributions using Tsallis statistics and nonextensive analysis.
result Developed semi-analytical formulas to distinguish true multifractality from spurious multifractality.
Study finds sales forecasters overreact to extreme news.
problem Understanding how forecasters react to sales growth news.
method Proposes a framework with fat-tailed dynamics and linear forecasting rule.
result Forecasters overreact to significant sales growth news.
News and price returns from threshold behaviour and vice-versa: exact solution of a simple agent-based market modelphysics.soc-ph
Starting from an exact relationship between news, threshold and price return distributions in the stationary state, I discuss the ability of the Ghoulmie-Cont-Nadal model of traders to produce fat-tailed price returns. Under normal conditions, this model is not able to transform Gaussian news into fat-tailed price retu…
A new method makes Gaussian filters robust to outliers.
problem Outliers in sensor measurements disrupt Gaussian filters.
method Apply a pseudo measurement derived from a feature function.
result The method effectively handles outliers in both linear and nonlinear systems.
New method models fat-tailed distributions with anisotropic tail-adaptive flows.
problem Gaussian-based variational inference fails to accurately capture tail decay in fat-tailed distributions.
method Improved theory on tails of flows, developed anisotropic tail-adaptive flows (ATAF).
result ATAF models tail-anisotropy, outperforming prior work on synthetic and real-world targets.
On the concentration of large deviations for fat tailed distributions, with application to financial datacond-mat.stat-mech
Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated on a single variable. The regime of large deviations is separated from the regi…
It is well known that the distribution of returns from various financial instruments are leptokurtic, meaning that the distributions have "fatter tails" than a Normal distribution, and have skew toward zero. This paper presents a graceful micro-level explanation for such fat-tailed outcomes, using agents whose private …
The aim of this paper is to propose a heterogeneous agent model of stock markets that develop complicated endogenous price fluctuations. We find occurrences of non-stationary chaos, or speculative bubble, are caused by the heterogeneity of traders' strategies. Furthermore, we show that the distributions of returns gene…
The SV-GARCH-EVT model improves risk assessment in financial markets.
problem Inaccurate risk assessment in financial markets due to fat-tailed and leverage effects.
method Enhanced SV model with EVT for tail distribution, MCMC for parameter estimation.
result SV-EVT models outperform other models in backtesting and out-of-sample analysis.
In complex systems such as turbulent flows and financial markets, the dynamics in long and short time-lags, signaled by Gaussian and fat-tailed statistics, respectively, calls for a unified description. To address this issue we analyze a real dataset, namely, price fluctuations, in a wide range of temporal scales to em…
A financial swap reduces skew and fat tails in a portfolio's performance.
problem Managing skew and fat tails in portfolio performance.
method Used a third moment variation swap and partial differential equation approach.
result The hedged portfolio returns are more Gaussian-like with thin-tails.
Study finds inefficiency in Brazilian stock market through correlations and fat-tailed returns.
problem Inefficiency of the Brazilian stock market, particularly the IBOVESPA future contracts.
method Analysis of cross-correlations with foreign markets, examination of log-return distribution, and neural network forecasting.
result Strong dependence on foreign markets and fat-tailed returns indicate inefficiency.
Model shows how imitation and randomness stabilize financial markets.
problem Stabilizing financial markets with self-organized criticality.
method Simple order book mechanism with self-organized criticality dynamics.
result Imitation and randomness stabilize market fluctuations.
Deep forecasting models show output heads significantly improve performance on fat-tailed financial returns.
problem Improving deep learning models for forecasting fat-tailed financial returns.
method Comparison of backbone architectures and output heads (point, Gaussian, Gaussian mixture) on S&P 500 monthly log-returns.
result Switching from point to Gaussian heads improves CRPS by about 1.3 percent, and from Gaussian to mixture adds another 2.4 percent.
The condition for stationary increments, not scaling, detemines long time pair autocorrelations. An incorrect assumption of stationary increments generates spurious stylized facts, fat tails and a Hurst exponent H_s=1/2, when the increments are nonstationary, as they are in FX markets. The nonstationarity arises from s…
Fat Tailed Factorsq-fin.PM
A new factor analysis method using ICA reduces portfolio concentration and diversifies excess kurtosis.
problem Standard factor analysis suffers from issues with pairwise correlations of asset returns.
method Identifies factors based on non-Gaussianity instead of variance, using ICA.
result Fat-tailed portfolios significantly reduce portfolio concentration and winner-takes-all problem.
This paper investigates multiscaling in the rough Bergomi model, finding it primarily due to fat-tailed returns.
problem Understanding multiscaling in the rough Bergomi model to improve financial modelling and risk management.
method Introducing a two-stage statistical testing procedure: first, testing for multiscaling against uniscaling; second, using shuffled surrogates to preserve return distributions.
result Multiscaling in the rough Bergomi model arises primarily from fat-tailed return distributions, not memory effects.
New risk models use chaotic attractors to predict extreme events.
problem Predicting Black Swan events in financial markets.
method Combining heavy-tailed priors with chaotic dynamics (Lorenz and Rossler systems).
result Models generate volatility clustering, fat tails, and extreme events.
The standard Gini coefficient estimation is flawed for fat-tailed data, leading to inaccurate comparisons.
problem Inaccurate Gini coefficient estimation for fat-tailed variables.
method Comparison of standard methodologies to indirect methods via maximum likelihood estimation of tail exponent.
result Indirect methods provide more accurate Gini coefficient estimates for fat-tailed data.
I report a new statistical distribution formulated to confront the infamous, long-standing, computational/modeling challenge presented by highly skewed and/or leptokurtic ("fat- or heavy-tailed") data. The distribution is straightforward, flexible and effective. Even when working with far fewer data points than are rou…
The paper revisits classical competition theory to explain speculative asset price dynamics.
problem Understanding the dynamics of speculative asset prices and their volatility.
method Specialized classical model of competition with reservation prices, incorporating speculation.
result The model explains excess, fat-tailed, and clustered volatility in speculative asset prices.
Correlation Structure and Fat Tails in Finance: a New Mechanismcond-mat.stat-mech
Fat tails in financial time series and increase of stocks cross-correlations in high volatility periods are puzzling facts that ask for new paradigms. Both points are of key importance in fundamental research as well as in Risk Management (where extreme losses play a key role). In this paper we present a new model for …
Study compares VIX and VXO to historic market data volatility distributions.
problem Comparing implied and realized volatility distributions.
method Systematic comparison of VIX and VXO to historic market data, studying distributions and ratios.
result Ratio of implied to realized volatility best fits heavy-tailed and fat-tailed distributions.
We perform a systematic investigation on the components of the empirical multifractality of financial returns using the daily data of Dow Jones Industrial Average from 26 May 1896 to 27 April 2007 as an example. The temporal structure and fat-tailed distribution of the returns are considered as possible influence facto…
Introduces QHawkes models for financial prices, capturing non-linear feedback effects.
problem Modeling financial volatility with non-linear feedback effects.
method Develops QHawkes models with linear and quadratic feedback, fits to NYSE data.
result QHawkes models capture fat-tailed volatility and time-reversal asymmetry in financial data.
Bayesian framework for comparing trading algorithms using cost analysis.
problem Comparing trading algorithms using cost analysis.
method Bayesian framework, hierarchical models, standardized benchmarks, fat tails, skewness, heteroscedasticity.
result Effective calculation of trading benchmarks with limited data.
The paper combines Bitcoin price models with expert corrections for better predictions.
problem Improving Bitcoin price predictions using statistical and expert insights.
method Linear regression models combined with expert corrections, utilizing Bayesian approach for fat-tailed distributions.
result Better price prediction results compared to using either model or expert opinion alone.
SOC theory explains financial volatility and economic shocks.
problem Excess volatility and small shocks causing large disruptions.
method Explains system behavior at critical point with fat-tailed fluctuations.
result SOC theory offers a plausible solution to financial market volatility.
Develops price dynamics equations with symmetric supply/demand functions, affecting tail behavior of price distributions.
problem Understanding the tail behavior of price distributions based on supply and demand functions.
method Created price dynamics equations using a symmetric function of demand/supply, analyzing linear and nonlinear cases.
result The exponent of the tail behavior of price distributions depends on the function of supply and demand, with exponents approaching -1 for large exponents in the function.
Market simulation with hierarchical information fluxcond-mat.stat-mech
We assume the market price to diffuse in a hierarchical comb of barriers, the heights of which represent the importance of new information entering the market. We find fat tails with the desired exponent for the price change distribution, and effective multifractality for intermediate times.
Revisits granular models explaining firm growth rates and sizes.
problem Understanding the relationship between firm size and growth rate statistics.
method Developed new theoretical insights linking firm size and growth rate statistics within granular models.
result Growth volatility distribution is size-independent but fat-tailed, challenging granular models.
We introduce a deterministic dealer model which implements most of the empirical laws, such as fat tails in the price change distributions, long term memory of volatility and non-Poissonian intervals. We also clarify the causality between microscopic dealers' dynamics and macroscopic market's empirical laws.
Relativistic extension of Brownian motion explains volatility smiles.
problem Understanding volatility smiles in financial markets.
method Relativistic extension of Brownian motion to model financial processes.
result The model predicts volatility smiles due to relativistic effects.
We use the GARCH model with a fat-tailed error distribution described by a rational function and apply it for the stock price data on the Tokyo Stock Exchange. To determine the model parameters we perform the Bayesian inference to the model. The Bayesian inference is implemented by the Metropolis-Hastings algorithm wit…
We proposed a model of interacting market agents based on the Ising spin model. The agents can take three actions: "buy," "sell," or "stay inactive." We defined a price evolution in terms of the system magnetization. The model reproduces main stylized facts of real markets such as: fat-tailed distribution of returns an…
Model explains financial data patterns through investor misperceptions.
problem Understanding stylized facts in financial markets.
method Derives mean field limit of agent-based financial model.
result Kinetic model replicates fat-tails, uncorrelated returns, and volatility clustering.