A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Elliptical processes generalize Gaussian and Student-t models with fat tails and computational efficiency.
Study finds sales forecasters overreact to extreme news.
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…
We study the problems related to the estimation of the Gini index in presence of a fat-tailed data generating process, i.e. one in the stable distribution class with finite mean but infinite variance (i.e. with tail index ). We show that, in such a case, the Gini coefficient cannot be reliably estimated usin…
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…
The paper revisits classical competition theory to explain speculative asset price dynamics.
This paper investigates multiscaling in the rough Bergomi model, finding it primarily due to fat-tailed returns.
Arguably the most important problem in quantitative finance is to understand the nature of stochastic processes that underlie market dynamics. One aspect of the solution to this problem involves determining characteristics of the distribution of fluctuations in returns. Empirical studies conducted over the last decade …
This study empirically re-examines fat tails in stock return distributions by applying statistical methods to an extensive dataset taken from the Korean stock market. The tails of the return distributions are shown to be much fatter in recent periods than in past periods and much fatter for small-capitalization stocks …
A model of fluctuations in the market price including many deterministic dealers, who predict their buying and selling prices from the latest price change, is developed. We show that price changes of the model is approximated by ARCH(1) process. We conclude that predictions of dealers affected by the past price changes…
We introduce and establish the main properties of QHawkes ("Quadratic" Hawkes) models. QHawkes models generalize the Hawkes price models introduced in E. Bacry et al. (2014), by allowing all feedback effects in the jump intensity that are linear and quadratic in past returns. A non-parametric fit on NYSE stock data sho…
The paper combines Bitcoin price models with expert corrections for better predictions.
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.…
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.
We call attention against what seems to a widely held misconception according to which large crashes are the largest events of distributions of price variations with fat tails. We demonstrate on the Dow Jones Industrial index that with high probability the three largest crashes in this century are outliers. This result…
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…
New method models fat-tailed distributions with anisotropic tail-adaptive flows.
Risk and uncertainty will always be a matter of experience, luck, skills, and modelling. Leverage is another concept, which is critical for the investor decisions and results. Adaptive skills and quantitative probabilistic methods need to be used in successful management of risk, uncertainty and leverage. The author ex…
New method estimates VaR and ES using high-frequency data, outperforming existing approaches.
Critical volatility triggers log-normal to power-law transitions in interconnected systems.
Modified lognormal distribution with flexible tails for skewed data.
Key to the imposition of appropriate minimum capital requirements on a daily basis requires accurate volatility estimation. Here, measures are presented based on discrete estimation of aggregated high frequency UK futures realisations underpinned by a continuous time framework. Squared and absolute returns are incorpor…
In this paper we introduce an efficient fat-tail measurement framework that is based on the conditional second moments. We construct a goodness-of-fit statistic that has a direct interpretation and can be used to assess the impact of fat-tails on central data conditional dispersion. Next, we show how to use this framew…
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…
Proposes NDIG model to capture bitcoin volatility and option pricing.
The SV-GARCH-EVT model improves risk assessment in financial markets.
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 self-organized model with social percolation process is proposed to describe the propagations of information for different trading ways across a social system and the automatic formation of various groups within market traders. Based on the market structure of this model, some stylized observations of real market can…
Many sensors, such as range, sonar, radar, GPS and visual devices, produce measurements which are contaminated by outliers. This problem can be addressed by using fat-tailed sensor models, which account for the possibility of outliers. Unfortunately, all estimation algorithms belonging to the family of Gaussian filters…
We investigate the general problem of how to model the kinematics of stock prices without considering the dynamical causes of motion. We propose a stochastic process with long-range correlated absolute returns. We find that the model is able to reproduce the experimentally observed clustering, power law memory, fat tai…
Deep forecasting models show output heads significantly improve performance on fat-tailed financial returns.
We analyze quantitatively the effect of spurious multifractality induced by the presence of fat-tailed symmetric and asymmetric probability distributions of fluctuations in time series. In the presented approach different kinds of symmetric and asymmetric broad probability distributions of synthetic data are examined s…
Continuous time models in the theory of real options give explicit formulas for optimal exercise strategies when options are simple and the price of an underlying asset follows a geometric Brownian motion. This paper suggests a general, computationally simple approach to real options in discrete time. Explicit formulas…
Study analyzes foreign exchange rates using MFDFA, revealing multifractality and its sources.
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…
Exact results on power-law distributions in systems with resets.
The third moment variation of a financial asset return process is defined by the quadratic covariation between the return and square return processes. The skew and fat tail risk of an underlying asset can be hedged using a third moment variation swap under which a predetermined fixed leg and the floating leg of the rea…
A new factor analysis method using ICA reduces portfolio concentration and diversifies excess kurtosis.
In stochastic finance, one traditionally considers the return as a competitive measure of an asset, {\it i.e.}, the profit generated by that asset after some fixed time span , say one week or one year. This measures how well (or how bad) the asset performs over that given period of time. It has been established tha…
New risk models use chaotic attractors to predict extreme events.
We present analytical investigations of a multiplicative stochastic process that models a simple investor dynamics in a random environment. The dynamics of the investor's budget, , depends on the stochasticity of the return on investment, , for which different model assumptions are discussed. The fat-tail d…
In this paper we present a novel approach to the determination of fat tails in financial data by studying the information contained in the limit order book. In an order-driven market buyers and sellers may submit limit orders, which are executed when the price touches a pre-specified lower, respectively higher, limit-p…
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 multifractal behavior for tick data of prices is investigated in Korean financial market. Using the rescaled range analysis(R/S analysis), we show the multifractal nature of returns for the won-dollar exchange rate and the KOSPI. We also estimate the Hurst exponent and the generalized th-order Hurst exponent in …
We propose a new method of measuring the third and fourth moments of return distribution based on quadratic variation method when the return process is assumed to have zero drift. The realized third and fourth moments variations computed from high frequency return series are good approximations to corresponding actual …
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 …