Investigates cross-impact kernels for financial asset prices.
problem Understanding and parameterizing cross-impact kernels for financial asset prices.
method Examined martingale-admissible and no-statistical-arbitrage-admissible kernels, determined their overlap, and provided calibration formulas.
result Identified the overlap between martingale-admissible and no-statistical-arbitrage-admissible kernels and provided formulas for their calibration.
We extend the "No-dynamic-arbitrage and market impact"-framework of Jim Gatheral [Quantitative Finance, 10(7): 749-759 (2010)] to the multi-dimensional case where trading in one asset has a cross-impact on the price of other assets. From the condition of absence of dynamical arbitrage we derive theoretical limits for t…
Estimates self- and cross-impact concavity and decay patterns in financial markets.
problem Understanding the impact of financial transactions on market dynamics.
method Nonparametric estimation of concave multi-asset propagator models using metaorders and order flow data.
result Concave self-impact with shifted power-law decay, significant gain from cross-impact, and improved predictive accuracy.
Two models are identified for robust cross-impact analysis.
problem Developing and validating cross-impact models that fit data and are well-behaved.
method Classified cross-impact models according to desirable properties and evaluated them on three asset classes.
result Only one model satisfies all desirable properties and is suitable for applications.
Estimates cross-impact on derivatives markets using E-Mini futures and options.
problem Empirical estimation of cross-impact on complex financial instruments like derivatives.
method Modeling derivatives prices as a function of stochastic factors and trades on both factors and derivatives.
result Simple framework successfully captures cross-impact on derivatives markets.
Study shows integrating OFI from multiple levels improves price impact explanation but not forecasting.
problem Explaining and forecasting price movements in equity markets using OFI.
method Systematic approach to combine OFIs from multiple levels into an integrated variable, testing multi-asset models with and without cross-impact terms.
result Lagged cross-asset OFIs improve future return forecasting but not contemporaneous price impact.
Optimal portfolio choice with cross-impact propagators, solving complex equations.
problem Maximizing revenue-risk in a continuous-time portfolio choice problem with cross-impact.
method Formulated as a maximization problem, solved explicitly using operator resolvents and stochastic Fredholm equations.
result Sufficient conditions for the absence of price manipulation, providing financial insights.
The study identifies features making cross-impact relevant in explaining price variance of US assets.
problem Understanding the relevance of cross-impact in explaining price variance of US assets.
method Using tick-by-tick data spanning 5 years for 500 US assets, the study investigates the features making cross-impact relevant.
result Price formation is endogenous within highly liquid assets, influencing less liquid correlated products with a constrained impact velocity.
We extend the framework of trading strategies of Gatheral [2010] from single stocks to a pair of stocks. Our trading strategy with the executions of two round-trip trades can be described by the trading rates of the paired stocks and the ratio of their trading periods. By minimizing the potential cost arising from cros…
We model the impact costs of a strategy that trades a basket of correlated instruments, by extending to the multivariate case the linear propagator model previously used for single instruments. Our specification allows us to calibrate a cost model that is free of arbitrage and price manipulation. We illustrate our resu…
We reconsider the multivariate Kyle model in a risk-neutral setting with a single, perfectly informed rational insider and a rational competitive market maker, setting the price of n correlated securities. We prove the unicity of a symmetric, positive definite solution for the impact matrix and provide insights on its …
We construct a price impact model between stocks in a correlated market. For the price change of a given stock induced by the short-run liquidity of this stock itself and of the information about other stocks, we introduce a self- and a cross-impact function of the time lag. We model the average cross-response function…
Model explains yield curve dynamics using order flow shocks.
problem Understanding the yield curve's fluctuations and their relation to order flows.
method Relates exogenous shocks to order flow surprises, creating a microstructural model that incorporates price and order flow dynamics.
result The model explains yield curve dynamics with fewer parameters and generates liquidity-dependent correlations.
A risk-averse agent hedges her exposure to a non-tradable risk factor U using a correlated traded asset S and accounts for the impact of her trades on both factors. The effect of the agent's trades on U is referred to as cross-impact. By solving the agent's stochastic control problem, we obtain a closed-form expr…
Study optimizes trading in multiple assets with cross-effects.
problem Optimizing trade execution in multiple assets with cross-impact effects.
method Formulated as a stochastic control problem, extended to progressively measurable controls, solved using linear-quadratic control theory.
result Cross-hedging effects can be optimal, e.g., trading in an asset without an initial position.
Paper solves optimal portfolio deleveraging with cross asset impacts.
problem Maximize equity while meeting debt/equity requirement with cross asset price impacts.
method Developed successive convex optimization (SCO) and an effective global algorithm integrating SCO, convex relaxation, and branch-and-bound.
result Proposed algorithms find global optimal solutions efficiently.
We provide an asymptotic expansion of the value function of a multidimensional utility maximization problem from consumption with small non-linear price impact. In our model cross-impacts between assets are allowed. In the limit for small price impact, we determine the asymptotic expansion of the value function around …
The composition of natural liquidity has been changing over time. An analysis of intraday volumes for the S&P500 constituent stocks illustrates that (i) volume surprises, i.e., deviations from their respective forecasts, are correlated across stocks, and (ii) this correlation increases during the last few hours of the …
The vast majority of market impact studies assess each product individually, and the interactions between the different order flows are disregarded. This strong approximation may lead to an underestimation of trading costs and possible contagion effects. Transactions in fact mediate a significant part of the correlatio…
The price impact for a single trade is estimated by the immediate response on an event time scale, i.e., the immediate change of midpoint prices before and after a trade. We work out the price impacts across a correlated financial market. We quantify the asymmetries of the distributions and of the market structures of …
Many unsupervised kernel methods rely on the estimation of the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). Both kernel CO and kernel CCO are sensitive to contaminated data, even when bounded positive definite kernels are used. To the best of our knowledge, there are few well…
Survey of kernels, RKHS, and their applications in machine learning.
problem Understanding kernels and their applications in machine learning.
method Review of historical context, mathematical definitions, and practical applications of kernels.
result Comprehensive overview of kernels, RKHS, and their applications.
To the best of our knowledge, there are no general well-founded robust methods for statistical unsupervised learning. Most of the unsupervised methods explicitly or implicitly depend on the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). They are sensitive to contaminated data, …
Deep neural kernels and Laplace kernel have equivalent RKHS on spheres.
problem Comparing RKHS of deep neural tangent and Laplace kernels.
method Proof of RKHS equivalence using sphere restrictions and kernel properties.
result RKHS of deep neural tangent kernel and Laplace kernel are the same on Sd−1. Kernel methods linked to feature subspaces and maximal correlation kernels.
problem Understanding kernel methods and their relationship to feature extraction.
method Established a correspondence between feature subspaces and kernels, introduced maximal correlation kernels, and demonstrated their optimality.
result Kernel SVM on maximal correlation kernel achieves minimum prediction error.
PGF kernels analyze spherical data using generalized RBF kernels.
problem Analysis of spherical data.
method Introduced PGF kernels and a semi-parametric learning algorithm.
result PGF kernels generalize RBF kernels for spherical data.
Adapts manifold structure for better clustering performance.
problem Lack of consideration for local manifold structure in existing multiple kernel k-means methods.
method Adopts manifold adaptive kernel to integrate local manifold structure of kernels.
result Proposed method outperforms state-of-the-art methods.
Optimal kernel in KR can be data-dependent, improving model performance.
problem Fixed kernel in KR limits model performance.
method Considered data-dependent kernels for KR, using posterior covariance.
result Data-dependent kernel choice leads to optimal performance.
Quantum kernels can be efficiently embedded into classical feature spaces.
problem Can all quantum kernels be efficiently embedded into classical feature spaces?
method Invoking computational universality and using techniques like random Fourier features, the authors show that certain classes of quantum kernels can be efficiently embedded.
result For shift-invariant and composition kernels, embedding quantum kernels are universal and efficient.
New random feature maps for Laplacian and related kernels.
problem Challenges in approximating the Laplacian kernel and its generalizations.
method Developed random feature maps for Laplacian and related kernels, providing efficient sampling schemes.
result Demonstrated the efficacy of these random feature maps on real datasets.
New method for learning with non-Euclidean data using decomposable kernels.
problem Difficulty in using classical kernels for non-Euclidean data.
method Reproducing kernel Krein space (RKKS) methods for kernels that admit a positive decomposition.
result Invariant kernels can be used for learning in non-Euclidean spaces.
New estimator reduces kernel mean estimation error.
problem Kernel mean estimation in reproducing kernel Hilbert spaces.
method Corrupt data with known distributions and estimate kernel mean under the corrupted distribution.
result The marginalized kernel mean estimator achieves lower estimation error.
We present Random Partition Kernels, a new class of kernels derived by demonstrating a natural connection between random partitions of objects and kernels between those objects. We show how the construction can be used to create kernels from methods that would not normally be viewed as random partitions, such as Random…
The NNGP kernel's predictions closely match those of the Matern kernel under certain conditions.
problem Comparing NNGP kernels to Matern kernels in practical applications.
method Demonstrated the necessity of normalization for NNGP kernels, explored numerical challenges, and compared predictions and performance.
result NNGP kernel predictions closely match Matern kernel predictions under specific circumstances.
In this paper, we compare 5 different nonlinear kernels: min-max, RBF, fRBF (folded RBF), acos, and acos-χ2, on a wide range of publicly available datasets. The proposed fRBF kernel performs very similarly to the RBF kernel. Both RBF and fRBF kernels require an important tuning parameter (γ). Interestingly, for a …
New kernels allow learning from non-separable data.
problem Learning from non-separable data.
method Introducing entangled kernels and a two-step algorithm.
result Efficient algorithm for learning entangled kernels.
Laplace kernel and Neural Tangent Kernels are shown to be nearly identical for normalized data.
problem Understanding the similarity between Laplace and Neural Tangent Kernels.
method Theoretical analysis and experiments on normalized data.
result Laplace kernel and Neural Tangent Kernels have nearly identical eigenfunctions and RKHS for normalized data.
Kernel smoothing on unknown manifolds with bounds and asymptotic normality.
problem Data on unknown manifolds without boundaries.
method Finite sample bounds and asymptotic normality for kernel smoothing and its derivatives.
result Established finite sample bounds and asymptotic normality for kernel smoothing.
In this paper we propose a family of tractable kernels that is dense in the family of bounded positive semi-definite functions (i.e. can approximate any bounded kernel with arbitrary precision). We start by discussing the case of stationary kernels, and propose a family of spectral kernels that extends existing approac…
The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce a new algorithm for kernel learning that combines a {\em continuous set of base …
New kernels capture both local and non-local interactions efficiently.
problem Designing kernels that capture both local and non-local interactions while remaining computationally tractable.
method Spectral truncation kernels based on C∗-algebra. result Spectral truncation kernels induce interactions across the data function domain and reduce computational cost.
Quantum kernel machines need to use more complex kernels to fully exploit their potential.
problem Current quantum kernels struggle with complex learning tasks due to limited degrees of freedom.
method Propose using operator-valued kernels and C∗-algebraic representations to enhance quantum kernels. result Quantum operator-valued kernels can reveal structural dependencies that scalar-valued kernels miss.
Constructing the adjacency graph is fundamental to graph-based clustering. Graph learning in kernel space has shown impressive performance on a number of benchmark data sets. However, its performance is largely determined by the chosen kernel matrix. To address this issue, the previous multiple kernel learning algorith…
Optimal kernel improves estimation accuracy in modal statistical methods.
problem Estimation accuracy of kernel-based modal statistical methods depends on the kernel used.
method The study theoretically shows an optimal kernel that minimizes asymptotic error criterion.
result An optimal kernel minimizes the error criterion when using an optimal bandwidth.
Efficiently searches through Gaussian process kernels using symbolic representation and Bayesian optimization.
problem Manual selection of kernels in Gaussian processes is complex and computationally expensive.
method Proposes a novel method using symbolic representation and Bayesian optimization to search through a structured kernel space.
result Empirically shows a computationally more efficient way of searching through a discrete kernel space.
The term "CoRE kernel" stands for correlation-resemblance kernel. In many applications (e.g., vision), the data are often high-dimensional, sparse, and non-binary. We propose two types of (nonlinear) CoRE kernels for non-binary sparse data and demonstrate the effectiveness of the new kernels through a classification ex…
MKLpy simplifies Multiple Kernel Learning in Python.
problem Learning optimal kernel functions from data.
method Python-based framework for Multiple Kernel Learning algorithms.
result Maximizes usability and simplifies development of novel solutions.
Sparse Kernel Flows learns dynamical systems from data.
problem Learning dynamical systems from limited data.
method Sparse Kernel Flows: trains optimal kernel from a dictionary of kernels.
result Sparse Kernel Flows can learn from 132 chaotic systems.