The paper analyzes skewness and kurtosis measures for skew-elliptical distributions.
problem Examining skewness and kurtosis measures for skew-elliptical distributions.
method Deriving exact expressions for skewness and kurtosis measures for skew-elliptical distributions, constructing test statistics, and comparing measures through simulations and real data analysis.
result Exact expressions and test statistics for skewness and kurtosis measures for various skew-elliptical distributions.
Kurtosis is seen as a measure of the discrepancy between the observed data and a Gaussian distribution and is defined when the 4th moment is finite. In this work an empirical study is conducted to investigate the behaviour of the sample estimate of kurtosis with respect to sample size and the tail index when applied to…
We find a remarkable time persistence of various proxies for the kurtosis (p-kurtosis) of the intraday returns distribution for the S&P500 index and this permits a significant measure of their evolution from 1983 to 2004. There appears a long time scale dramatic variation of the p-kurtosis uncorrelated with the variati…
This paper investigates the common intuition suggesting that during crises the shape of the financial market clearly differentiates from that of random walk processes. In this sense, it challenges the analysis of the nature of financial markets proposed by Fama and his associates. For this, a geometric approach is prop…
FAMDAD detects anomalies in mixed data using kurtosis-weighted Factor Analysis.
problem Detecting anomalies in high-dimensional mixed data.
method kurtosis-weighted Factor Analysis of Mixed Data (FAMDAD).
result Anomalies are highly separable in the first and last few dimensions of the FAMDAD embedding.
Study finds time-varying volatility and multifractality in Bitcoin, with asymmetry weakening as market efficiency increases.
problem Investigating time-varying properties of Bitcoin's volatility and multifractality.
method Rolling window method to examine daily Bitcoin returns and multifractal properties over time.
result Volatility asymmetry in Bitcoin changes over time, becoming less pronounced as market efficiency increases.
A new law limits kurtosis contrast in balanced mixtures.
problem Kurtosis-based ICA fails in wide, balanced mixtures.
method Proved a redundancy law and showed purification restores contrast.
result Kurtosis contrast obeys O(κmax/Reff) in balanced mixtures. Existing strategies for finite-armed stochastic bandits mostly depend on a parameter of scale that must be known in advance. Sometimes this is in the form of a bound on the payoffs, or the knowledge of a variance or subgaussian parameter. The notable exceptions are the analysis of Gaussian bandits with unknown mean and…
Proposes a new method for big portfolio selection using graph-based conditional moments.
problem Challenges in selecting portfolios for thousands of stocks.
method Graph-based Conditional Moments (GRACE) method: learns quantiles, means, variances, skewness, and kurtosis of stock returns.
result Shows superior performance compared to competitors, especially in measures of conditional variance, skewness, and kurtosis.
Study shows how cryptocurrency market skewness and kurtosis interact during pandemic.
problem Understanding the dynamics of cryptocurrency markets during the pandemic.
method Examined skewness and kurtosis interactions in cryptocurrency market data.
result More observations cluster around extremes during pandemic, indicating volatile behavior.
We establish several new stylised facts concerning the intra-day seasonalities of stock dynamics. Beyond the well known U-shaped pattern of the volatility, we find that the average correlation between stocks increases throughout the day, leading to a smaller relative dispersion between stocks. Somewhat paradoxically, t…
Extended Jarrow-Rudd model with skewness and kurtosis for option pricing.
problem Valuation of options with non-normal market dynamics.
method Introduced a generalized Jarrow-Rudd (GJR) model with skewness and kurtosis, incorporating transaction costs and market driver influences.
result Demonstrated the GJR pricing model's effectiveness in fitting market data.
Novel method prices call options using Pearson diffusion processes.
problem Pricing European call options with skewness and kurtosis.
method Modeling asset returns with Pearson diffusion processes.
result Proposed method outperforms Black-Scholes and Heston models.
Paper defines new risk measures for elliptical distributions.
problem Risk measurement for elliptical distributions.
method DTM, DTS, DTK definitions and formula derivation for specific distributions.
result Explicit formulas for DTE, DTV, DTS, and DTK for various distributions.
In a recent paper [\textit{M. Cristelli, A. Zaccaria and L. Pietronero, Phys. Rev. E 85, 066108 (2012)}], Cristelli \textit{et al.} analysed relation between skewness and kurtosis for complex dynamical systems and identified two power-law regimes of non-Gaussianity, one of which scales with an exponent of 2 and the oth…
Cross-sectional signatures of market panic were recently discussed on daily time scales in [1], extended here to a study of cross-sectional properties of stocks on intra-day time scales. We confirm specific intra-day patterns of dispersion and kurtosis, and find that the correlation across stocks increases in times of …
We derive new approximations for the Value at Risk and the Expected Shortfall at high levels of loss distributions with positive skewness and excess kurtosis, and we describe their precisions for notable ones such as for exponential, Pareto type I, lognormal and compound (Poisson) distributions. Our approximations are …
The paper uses the variance-gamma model to price options and explain excess kurtosis.
problem Explaining excess kurtosis in stock price data.
method Random-time subordination, Laplace distribution, Esscher transform.
result The variance-gamma model explains excess kurtosis in log-returns data.
Independent Component Analysis (ICA) - one of the basic tools in data analysis - aims to find a coordinate system in which the components of the data are independent. Most popular ICA methods use kurtosis as a metric of non-Gaussianity to maximize, such as FastICA and JADE. However, their assumption of fourth-order mom…
Exact tail probability bounds for bounded kurtosis.
problem Determining worst-case tail probabilities under kurtosis constraints.
method AI-guided search and certifying pipeline to compute bounds.
result A four-regime map of tail probabilities with explicit formulas.
We find the exact worst-case tail probability for bounded kurtosis.
problem Determining the worst-case tail probability under bounded kurtosis constraints.
method AI-guided search and certificate verification around the certifying pipeline.
result A four-regime map of tail probabilities with explicit formulas and dual certificates.
New method models portfolios with leptokurtic risk factors using Gram-Charlier expansions.
problem Modeling portfolios with excess kurtosis.
method GC-like expansions of the hyperbolic-secant law to account for leptokurtosis.
result Portfolio distribution with risk factors modeled as GC-like expansions of the HS law.
We present a novel notion of outlier, called the Concentration Free Outlier Factor, or CFOF. As a main contribution, we formalize the notion of concentration of outlier scores and theoretically prove that CFOF does not concentrate in the Euclidean space for any arbitrary large dimensionality. To the best of our knowled…
In this study we suggest a portfolio selection framework based on option-implied information and multivariate non-Gaussian models. The proposed models incorporate skewness, kurtosis and more complex dependence structures among stocks log-returns than the simple correlation matrix. The two models considered are a multiv…
This paper investigates the hedging effectiveness of a dynamic moving window OLS hedging model, formed using wavelet decomposed time-series. The wavelet transform is applied to calculate the appropriate dynamic minimum-variance hedge ratio for various hedging horizons for a number of assets. The effectiveness of the dy…
This paper provides an insight to the time-varying dynamics of the shape of the distribution of financial return series by proposing an exponential weighted moving average model that jointly estimates volatility, skewness and kurtosis over time using a modified form of the Gram-Charlier density in which skewness and ku…
We apply a quadratic hedging scheme developed by Foellmer, Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process and show that local risk-minimizing strategies with respect to the physical measure do exist, even though an associated minimal martingale measure …
Stress shocks are often calculated as multiples of the standard deviation of a history set. This paper investigates how many standard deviations are required to guarantee that this shock exceeds any observation within the history set, given the additional constraint of kurtosis. The results of this analysis are then us…
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.
We demonstrate the potential of Deep Learning methods for measurements of cosmological parameters from density fields, focusing on the extraction of non-Gaussian information. We consider weak lensing mass maps as our dataset. We aim for our method to be able to distinguish between five models, which were chosen to lie …
We find a nonlinear dependence between an indicator of the degree of multiscaling of log-price time series of a stock and the average correlation of the stock with respect to the other stocks traded in the same market. This result is a robust stylized fact holding for different financial markets. We investigate this re…
We solve a portfolio selection problem with four objectives, finding convex scalarizations for part of the Pareto front.
problem Portfolio selection with four objectives: mean, variance, skewness, and kurtosis.
method Linearly scalarize MVSK objectives into a convex polynomial Fλ over the probability simplex, compute optimizers for each λ. result Identify a set of hyper-parameters for which the scalarization is convex, allowing computation of part of the Pareto front.
Realized moments of higher order computed from intraday returns are introduced in recent years. The literature indicates that realized skewness is an important factor in explaining future asset returns. However, the literature mainly focuses on the whole market and on the monthly or weekly scale. In this paper, we cond…
Electromyogram (EMG) classification is a key technique in EMG-based control systems. The existing EMG classification methods do not consider the characteristics of EMG features that the distribution has skewness and kurtosis, causing drawbacks such as the requirement of hyperparameter tuning. In this paper, we propose …
We calculate realized volatility of the Nikkei Stock Average (Nikkei225) Index on the Tokyo Stock Exchange and investigate the return dynamics. To avoid the bias on the realized volatility from the non-trading hours issue we calculate realized volatility separately in the two trading sessions, i.e. morning and afternoo…
Model financial time series using φ^4 quantum field theory.
problem Inaccuracies in Ising models for financial data.
method φ^4 quantum field theory with inhomogeneous couplings.
result Accurately reproduces higher-order statistics like market kurtosis.
Several statistical and machine learning methods are proposed to estimate the type and intensity of physical load and accumulated fatigue . They are based on the statistical analysis of accumulated and moving window data subsets with construction of a kurtosis-skewness diagram. This approach was applied to the data gat…
The problem of non-stationarity in financial markets is discussed and related to the dynamic nature of price volatility. A new measure is proposed for estimation of the current asset volatility. A simple and illustrative explanation is suggested of the emergence of significant serial autocorrelations in volatility and …
Proposes a new regression method using Lp-norms for non-Gaussian noise.
problem Non-Gaussian noise in residuals affects the performance of local least squares regression.
method Introduces local polynomial Lp-norm regression, replacing weighted least squares with weighted Lp-norm estimation. result Demonstrates superior performance over local least squares in one-dimensional data and higher dimensions.
Enhances reinforcement learning uncertainty estimation with a generalized Gaussian error model.
problem Inaccurate error representations and compromised uncertainty estimation in conventional uncertainty-aware TD learning.
method Introduces a novel framework for generalized Gaussian error modeling in deep reinforcement learning, incorporating higher-order moments, particularly kurtosis, to improve uncertainty estimation and mitigation.
result Significant performance gains in policy gradient algorithms with the proposed framework.
Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this paper, we provide a novel framework to obtain uniform deviation bounds for loss…
We revisit the problem of pricing options with historical volatility estimators. We do this in the context of a generalized GARCH model with multiple time scales and asymmetry. It is argued that the reason for the observed volatility risk premium is tail risk aversion. We parametrize such risk aversion in terms of thre…
A financial model without short-selling shows deviations from normality.
problem Modeling financial asset prices with constraints on short selling.
method Developed a binomial model with two types of investors (bulls and bears) and a market maker, proving moments and fitting parameters.
result The model can approximate skewness and excess kurtosis, demonstrated with real data.
Using 1-min returns of Bitcoin prices, we investigate statistical properties and multifractality of a Bitcoin time series. We find that the 1-min return distribution is fat-tailed, and kurtosis largely deviates from the Gaussian expectation. Although for large sampling periods, kurtosis is anticipated to approach the G…
The analysis of observed conditional distributions of both lagged and simultaneous intraday price increments of a basket of stocks reveals phenomena of dependence - induced volatility smile and kurtosis reduction. A model based on multivariate t-Student distribution shows that the observed effects are caused by colelct…
The statistical properties of the increments x(t+T) - x(t) of a financial time series depend on the time resolution T on which the increments are considered. A non-parametric approach is used to study the scale dependence of the empirical distribution of the price increments x(t+T) - x(t) of S&P Index futures, for time…
Study shows variance gamma model outperforms Black-Scholes for USD-INR currency options.
problem Complex pricing of currency options with multi-assets.
method Examined USD-INR currency options, tested several models, compared performance.
result Variance gamma model outperforms Black-Scholes model in various volatility regimes.
Estimates financial networks using high-frequency trade data.
problem Leverage high-resolution intraday trade data for financial network insights.
method Estimate financial networks using random forests with microstructure measures.
result Higher network density in 2007, with Lehman Brothers having high degree connectivity.