Bayesian realized-GARCH models forecast financial tail risks using two-sided Weibull distribution.
problem Forecasting financial tail risks in volatile markets.
method Adaptive Bayesian Markov Chain Monte Carlo for estimation and forecasting, incorporating sub-sampled realized range and variance.
result Realized-GARCH models with two-sided Weibull distribution outperform other models in tail risk forecasting.
New framework estimates VaR and ES jointly using Bayesian methods.
problem Joint estimation of Value-at-Risk (VaR) and Expected Shortfall (ES).
method Bayesian Markov Chain Monte Carlo method with measurement equation.
result Proposed models outperform other methods in VaR and ES forecasting.
Bayesian realized EGARCH models improve tail risk forecasting.
problem Forecasting tail risks in financial markets.
method Developed a Bayesian framework for realized EGARCH models, incorporating multiple realized volatility measures and using robust adaptive Metropolis algorithm for estimation.
result Standardized skewed Student-t distribution and sub-sampled realized range models outperform other models in tail risk forecasting.
A new model framework called Realized Conditional Autoregressive Expectile (Realized-CARE) is proposed, through incorporating a measurement equation into the conventional CARE model, in a manner analogous to the Realized-GARCH model. Competing realized measures (e.g. Realized Variance and Realized Range) are employed a…
Improved tail risk forecasting using realized measures and Bayesian methods.
problem Forecasting tail risk in financial markets.
method Extended Taylor's model with realized measures, using maximum likelihood and Bayesian MCMC methods.
result Bayesian approach outperforms maximum likelihood in forecasting accuracy.
VOLARE provides standardized realized volatility measures from financial data.
problem Lack of standardized realized volatility measures from ultra-high-frequency data.
method Asset-specific pipeline for cleaning and sampling data, providing a wide range of realized estimators.
result Comprehensive set of realized estimators for equities, exchange rates, and futures.
A new model forecasts financial risks using multiple realized measures.
problem Forecasting financial risks using multiple realized measures.
method Developed a semi-parametric joint VaR and ES forecasting framework using realized measures.
result The proposed model outperformed other models in forecasting financial risks.
Enhanced volatility model using LSTM and realized volatility.
problem Volatility modeling in financial markets.
method Combining deep learning (LSTM) and realized volatility measures in a Bayesian framework.
result Superior predictive performance compared to benchmark models.
Paper explores variable skipping to speed up range density estimation.
problem Efficiently estimating range densities over high-dimensional data.
method Variable skipping technique to accelerate range density estimation.
result 10-100x efficiency improvements in challenging high-quantile error metrics.
Fitting models for non-Poisson point processes is complicated by the lack of tractable models for much of the data. By using large samples of independent and identically distributed realizations and statistical learning, it is possible to identify absence of fit through finding a classification rule that can efficientl…
For a specific class of 4-manifolds, random isometries cannot lift to orientation-preserving diffeomorphisms.
problem When does a finite group of isometries of a specific 4-manifold lift to orientation-preserving diffeomorphisms?
method Combination of equivariant connected-sum constructions, fixed-point theory, finite group actions on surfaces, analytic combinatorics, and previous work.
result Random subgroups of isometries are asymptotically almost never realizable in orientation-preserving diffeomorphisms.
In this paper we consider the realization of DE attractors by self-diffeomorphisms of manifolds. For any expanding self-map φ:M→M of a connected, closed p-dimensional manifold M, one can always realize a (p,q)-type attractor derived from φ by a compactly-supported self-diffeomorphsm of $\RR^{p+q}$, as long…
We consider the problem of the statistical uncertainty of the correlation matrix in the optimization of a financial portfolio. We show that the use of clustering algorithms can improve the reliability of the portfolio in terms of the ratio between predicted and realized risk. Bootstrap analysis indicates that this impr…
New algorithms reduce collaborative PAC learning sample complexity.
problem Collaborative PAC learning with reduced sample complexity.
method Design of new algorithms for both realizable and non-realizable settings.
result Sample complexity is O(ln(k)) times the worst-case sample complexity for learning a single task. A chord diagram consists of a circle, called the backbone, with line segments, called chords, whose endpoints are attached to distinct points on the circle. The genus of a chord diagram is the genus of the orientable surface obtained by thickening the backbone to an annulus and attaching bands to the inner boundary cir…
New integrators preserve geometric structure in Hamiltonian systems.
problem Preserving geometric structure in Hamiltonian systems on Jacobi manifolds.
method Combining Poissonization and symplectic bi-realizations to construct structure-preserving integrators.
result Explicit construction and application of Jacobi Hamiltonian integrators.
Unified framework for realizable and agnostic learning.
problem Lack of a unified theory for realizable and agnostic learnability.
method Three-line blackbox reduction.
result Unified understanding across various learning settings.
New embeddings found that are stable but not smooth.
problem Understanding the relationship between stable and smooth embeddings.
method Analyzing stable smooth maps and their compositions with embeddings.
result Found an example of a stable embedding that is not smooth.
The paper introduces a new method to detect rough volatility and market states using fractional derivatives.
problem Testing self-similarity in fractional processes from a single observed trajectory is difficult under long-range dependence.
method The paper introduces a regime-adaptive KS/GL--KS framework based on the discrete Grünwald--Letnikov (GL) fractional derivative.
result The method detects rough volatility and persistent, anti-persistent, or efficient market states in financial applications.
Modeling long-range context for multi-function utterances in dialogues.
problem Complex dependencies across dialogue turns in long utterances.
method Adapted Convolutional Recurrent Neural Network (CRNN) to model interactions between utterances.
result Significantly outperforms existing work on CDA recognition on a tech forum dataset.
New algorithms for interactive learning match minimax bounds efficiently.
problem Interactive learning in the realizable setting with computational efficiency.
method General framework, computationally efficient algorithms, Monte Carlo hit-and-run sampling.
result Sample complexities quantifiable in terms of combinatorial quantities, computationally efficient.
Study confirms rough volatility in financial data, independent of microstructure noise.
problem Characterizing volatility in financial markets, especially rough volatility.
method Used range-based volatility estimators to confirm findings from fractional behavior.
result Log-volatility behaves like fractional Brownian motion with an even lower Hurst exponent.
New microcanonical models approximate non-Gaussian processes with long-range correlations.
problem Approximating non-Gaussian stationary processes with long-range correlations.
method Microcanonical models conditioned by energy vector, gradient descent, multiscale energy vectors.
result Microcanonical gradient descent processes converge and capture sparsity.
The influence of the past price behaviour on the realized volatility is investigated in the present article. The results show that trending (drifting) prices lead to increased (decreased) realized volatility. This ``volatility induced by trend'' constitutes a new stylized fact. The past price behaviour is measured by a…
Inspired by the recent literature on aggregation theory, we aim at relating the long range correlation of the stocks return volatility to the heterogeneity of the investors' expectations about the level of the future volatility. Based on a semi-parametric model of investors' anticipations, we make the connection betwee…
We propose a general framework for constructing and describing infinite type flat surfaces of finite area. Using this method, we characterize the range of dynamical behaviors possible for the vertical translation flows on such flat surfaces. We prove a sufficient condition for ergodicity of this flow and apply the cond…
Geometric framework for signed multivariate tail-dependence compatibility at various thresholds.
problem Modeling and analyzing signed multivariate tail-dependence across different thresholds.
method Developed a geometric witness framework to represent and invert signed tail families, identifying nonnegative weights and normalized masses.
result Characterization and synthesis of signed multivariate tail-dependence at finite thresholds, preserving the complete signed tail family throughout.
In the first quarter of 2006 Chicago Board Options Exchange (CBOE) introduced, as one of the listed products, options on its implied volatility index (VIX). This created the challenge of developing a pricing framework that can simultaneously handle European options, forward-starts, options on the realized variance and …
Soap bubbles and foams have been extensively studied by scientists, engineers, and mathematicians as models for organisms and materials, with applications ranging from extinguishing fires to mining to baking bread. Here we provide some basic results on the space of planar clusters of n bubbles of fixed topology. We sho…
Since Hobson's seminal paper [D. Hobson: Robust hedging of the lookback option. In: Finance Stoch. (1998)] the connection between model-independent pricing and the Skorokhod embedding problem has been a driving force in robust finance. We establish a general pricing-hedging duality for financial derivatives which are s…
Measuring comodules are defined and shown to provide a useful generalization of the set of maps between modules with a broad range of applications. Three applications are described. Connections on bundles are described in terms of measuring comodules, enabling curvature to be defined under general algebraic circumstanc…
Statistical depth metrics help identify risky power grid scenarios.
problem Identifying extreme scenarios for risk mitigation in power grid planning.
method Functional depth metrics for sub-selecting outlying scenarios.
result The proposed approach effectively identifies risky scenarios for operational risk mitigation.
A new bandit model with stochastic context distributions and UCB algorithm.
problem Learning optimal actions in a stochastic environment with hidden contexts.
method Stochastic contextual bandit model and UCB algorithm.
result Order-optimal high-probability bound on cumulative regret for linear and kernelized reward functions.
Develops statistical methods for rates of change on Riemannian manifolds.
problem Statistical inference for rates of change in spatial processes over non-Euclidean domains.
method Formalizes smoothness and constructs differential processes for Riemannian manifolds, derives conditions for kernel existence, and develops predictive inference.
result Validates theoretical findings through simulation experiments for derivatives over polyhedral meshes.
For every compact surface S of finite type (possibly with boundary components but without punctures), we show that when n is sufficiently large there is no lift σ of the surface braid group Bn(S) to Diff(S,n), the group of C1 diffeomorphisms preserving n marked points and restricting to t…
Extends Alexandrov's result to unbounded convex domains in hyperbolic 3-space.
problem Determining unbounded convex domains in hyperbolic 3-space from boundary data.
method Using conformal structure and induced metric on the boundary.
result A wide range of boundary data can be realized on unbounded convex domains in hyperbolic 3-space.
Criterion for realizing groups on Enriques manifolds.
problem Realizing groups on Enriques manifolds.
method Using recent developments in Birman-Hilden theory and Nielsen realization for hyper-Kähler manifolds.
result Numerical criterion for realizing groups on Enriques manifolds.
Paper introduces probabilistic forecasting methods for cryptocurrency volatility.
problem Inadequate point forecasting methods for capturing full spectrum of volatility outcomes.
method Combines multiple base models (statistical and machine learning) to estimate conditional quantiles of cryptocurrency realized variance.
result QRS method outperforms sophisticated alternatives for Bitcoin volatility forecasting.
PLoM learns stochastic solutions to PDEs with limited data.
problem Synthesizing solutions to nonlinear PDEs with scarce data.
method Probabilistic Learning on Manifolds constrained by PDEs.
result Learned stochastic solutions minimize PDE residuals.
We study realizations of Lie algebras by vector fields. A correspondence between classification of transitive local realizations and classification of subalgebras is generalized to the case of regular local realizations. A reasonable classification problem for general realizations is rigorously formulated and an algori…
The paper examines circle graphs of Gauss diagrams and finds counterexamples to previous descriptions.
problem Problems with previous descriptions of realizable Gauss diagrams.
method Experimental checking and formulation of new descriptions of realizable circle graphs.
result New descriptions of realizable circle graphs and an algorithm for checking realizability.
Paper speeds up GP inference by reducing precision matrix computation.
problem High computational complexity in computing kernel precision matrices.
method Splitting precision matrix into Hankel-Toeplitz matrices and computing only unique entries.
result Precision matrix computation reduced from O(NM2) to O(NM). Geometrically realizes Khovanov homology for semiadequate links.
problem Computing Khovanov homology for semiadequate links.
method Introducing partial presimplicial sets and their geometric realization.
result Concrete formula for homotopy type of geometric realization.
The abstract discusses convergent realizations of Lie subalgebras in control theory.
problem Characterizing Lie subalgebras that can be realized as convergent vector fields.
method Generalizations and reformulations of algebraic properties for output realization.
result Recovery and clarification of previous results on control-affine systems and realization of Chen-Fliess series.
Incorrect parity-based descriptions of realizable Gauss diagrams found, but bipartite graphs provide a valid approach.
problem Incorrect descriptions of realizable Gauss diagrams using parity conditions.
method Used bipartite graphs to describe realizable Gauss diagrams.
result Realizable Gauss diagrams can be accurately described using bipartite graphs.
Study on distributions of realized and implied volatility, using Generalized Beta distribution.
problem Understanding the differences and relationships between realized and implied volatility distributions.
method Used Generalized Beta distribution to fit distributions of realized variance and implied volatility (VIX, VXO). Analyzed differences and correlations.
result Generalized Beta distribution provides the best fit for realized variance but not for implied volatility indices (VIX, VXO).
Torelli group cannot be realized as area-preserving homeomorphisms.
problem Realization of the Torelli group as area-preserving homeomorphisms.
method Analysis of the Torelli group and its relationship with homeomorphisms.
result The Torelli group has no realization inside the area-preserving homeomorphisms.
New method selects features for sequential decision making.
problem Dynamic feature selection for instance-wise decisions.
method Latent variable model trained in a supervised manner; reasoning across stochastic latent space.
result Outperforms existing methods on various datasets.