Decomposing market impact into diffusive components
problem Market impact scaling
method Decomposing impact into realized and counterfactual returns
result Implication of square-root law in information-neutral regime
On-device research index
arXiv research
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.
168,695 papers · 148 categories
Trend · papers per month
48 results for “square-root diffusion”
We develop an efficient method to calibrate CDS spreads using asymptotic approximations.
problem Calibrating CDS spreads in the SSRD model with correlated processes.
method Asymptotic coefficient expansion to approximate solutions of nonlinear PDEs.
result Our approximation does not require uncorrelated interest rate and default intensity processes.
Anomalous impact in reaction-diffusion modelscond-mat.stat-mech
We generalize the reaction-diffusion model A + B -> 0 in order to study the impact of an excess of A (or B) at the reaction front. We provide an exact solution of the model, which shows that linear response breaks down: the average displacement of the reaction front grows as the square-root of the imbalance. We argue t…
Impact is not just volatilityq-fin.TR
The notion of market impact is subtle and sometimes misinterpreted. Here we argue that impact should not be misconstrued as volatility. In particular, the so-called ``square-root impact law'', which states that impact grows as the square-root of traded volume, has nothing to do with price diffusion, i.e. that typical p…
This paper explains how predictable order flow can lead to Brownian motion in financial prices.
problem Why financial prices exhibit Brownian motion despite predictable order flow.
method Generalized Lillo-Mike-Farmer model to nonlinear price-impact dynamics, mapping to Lévy-walk model.
result Price dynamics remain diffusive under the square-root law, even with persistent order flow.
The Volterra square-root process shows non-uniqueness of limiting distributions and regularity of its law.
problem Non-uniqueness of limiting distributions in the Volterra square-root process.
method Establishing existence of limiting distributions using integrability of the Volterra convolution kernel and exponential-affine transformation.
result The limiting distributions of the Volterra square-root process depend on the initial state and belong to weighted Besov spaces.
We prove strong existence and uniqueness, and Hölder regularity, of a large class of stochastic Volterra equations, with singular kernels and non-Lipschitz diffusion coefficient. Extending Yamada-Watanabe's theorem, our proof relies on an approximation of the process by a sequence of semimartingales with regularised ke…
New law predicts first extinction in resampling processes.
problem Intractable extinction times in resampling processes.
method Modeling multinomial updates as independent square-root diffusions.
result Closed-form law for first-extinction time with linear cost.
We present an extended version of the recently proposed "LLOB" model for the dynamics of latent liquidity in financial markets. By allowing for finite cancellation and deposition rates within a continuous reaction-diffusion setup, we account for finite memory effects on the dynamics of the latent order book. We compute…
Revisiting Trade-sign Long-memory and Square-root Law price impact
problem Revisiting the Lillo-Mike-Farmer (LMF) theory and the square-root law (SQRL) of meta-order impact
method Using a coupled discrete reaction-diffusion formulation
result Long-memory of trade signs and square-root law of meta-order impact
Statistical mixing and aggregation in Feller diffusioncond-mat.stat-mech
We consider Feller mean-reverting square-root diffusion, which has been applied to model a wide variety of processes with linearly state-dependent diffusion, such as stochastic volatility and interest rates in finance, and neuronal and populations dynamics in natural sciences. We focus on the statistical mixing (or sup…
We confirm the square-root law of market impact on Apple Inc. using a large dataset.
problem Testing the square-root law of market impact on a single U.S. large-cap equity.
method Using a full market-by-order feed, we reconstruct metaorders and calibrate impact using the square-root formula.
result The square-root law is confirmed with a prefactor of 0.34, consistent with worldwide data.
We suggest that the broad distribution of time scales in financial markets could be a crucial ingredient to reproduce realistic price dynamics in stylised Agent-Based Models. We propose a fractional reaction-diffusion model for the dynamics of latent liquidity in financial markets, where agents are very heterogeneous i…
We revisit the "epsilon-intelligence" model of Toth et al.(2011), that was proposed as a minimal framework to understand the square-root dependence of the impact of meta-orders on volume in financial markets. The basic idea is that most of the daily liquidity is "latent" and furthermore vanishes linearly around the cur…
We develop and test a fast and accurate semi-analytical formula for single-name default swaptions in the context of a shifted square root jump diffusion (SSRJD) default intensity model. The model can be calibrated to the CDS term structure and a few default swaptions, to price and hedge other credit derivatives consist…
We describe general multilevel Monte Carlo methods that estimate the price of an Asian option monitored at fixed dates. Our approach yields unbiased estimators with standard deviation in expected time for a variety of processes including the Black-Scholes model, Merton's jump-diffusion mod…
We propose a minimal theory of non-linear price impact based on a linear (latent) order book approximation, inspired by diffusion-reaction models and general arguments. Our framework allows one to compute the average price trajectory in the presence of a meta-order, that consistently generalizes previously proposed pro…
In this paper we solve the dividend optimization problem for a corporation or a financial institution when the managers of the corporation are facing (regulatory) implementation delays. We consider several cash reservoir models for the firm including two mean-reverting processes, Ornstein-Uhlenbeck and square-root proc…
The aim of this paper is to examine the time scaling of the semivariance when returns are modeled by various types of jump-diffusion processes, including stochastic volatility models with jumps in returns and in volatility. In particular, we derive an exact formula for the semivariance when the volatility is kept const…
Study differential properties of matrix square roots in specific cases.
problem Understanding matrix square roots in semi-simple, symmetric, and orthogonal cases.
method Analysis of differential and metric structures of real square roots of matrices under specific conditions.
result Differential properties of matrix square roots in semi-simple, symmetric, and orthogonal cases.
The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerat…
Gaussian prior and likelihood improve bandit learning performance.
problem Improving bandit learning with misspecified Gaussian distributions.
method An agent with a bounded information ratio interacts with a Bernoulli bandit based on a Gaussian prior and likelihood.
result The regret increase is at most linear in the square-root of the time horizon for diffuse distributions.
A new method simulates square-root processes efficiently.
problem Simulating square-root processes accurately and efficiently.
method Simulate the integrated square-root process instead of the square-root process itself.
result High precision with low number of time steps, and exact limiting Inverse Gaussian distributions.
The Subtle Interplay between Square-root Impact, Order Imbalance & Volatility: A Unifying Frameworkq-fin.TR
New framework explains market volatility and metaorder impact.
problem Reconciling contradictory observations in market microstructure.
method Introducing a new theoretical framework to describe metaorders with different signs, sizes, and durations.
result Price diffusion is ensured by long memory of cross-correlations between metaorders.
Guarantees uniform convergence for square-root Lipschitz losses.
problem Uniform convergence guarantees for square-root Lipschitz losses.
method Using Rademacher complexity and square root of scalar loss function Lipschitz constant.
result Generalizes previous results and handles non-smooth loss functions.
The Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance, is a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this p…
Through the direct study of the analysis estimator we derive oracle inequalities with fast and slow rates by adapting the arguments involving projections by Dalalyan, Hebiri and Lederer (2017). We then extend the theory to the square root analysis estimator. Finally, we focus on (square root) total variation regularize…
Study finds price impact follows a 'double' square-root law, suggesting mechanical origin.
problem Understanding the origin of price impact in markets.
method Detailed dataset of Tokyo Stock Exchange orders, analyzing single and metaorders.
result Price impact follows a 'double' square-root law, indicating mechanical origin rather than information.
The Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance, is a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this p…
A new method solves large-scale sparse group square-root Lasso problems efficiently.
problem Large-scale linearly constrained sparse group square-root Lasso problems.
method Dual semismooth Newton based augmented Lagrangian method (ALM).
result The proposed method efficiently solves the problem with numerical experiments demonstrating its effectiveness.
Square-root natural-gradient improves variational inference convergence.
problem Challenges in establishing theoretical convergence guarantees for natural-gradient descent.
method Square-root parameterization for Gaussian covariance.
result Establishes novel convergence guarantees for natural-gradient Gaussian inference.
SrvfNet aligns multiple functional data to templates without supervision.
problem Aligning large collections of functional data to templates without labeled data.
method Generative deep learning framework using SRVF and fully-connected layers.
result Framework achieves alignment and optimal template prediction without supervision.
Many independent studies on stocks and futures contracts have established that market impact is proportional to the square-root of the executed volume. Is market impact quantitatively similar for option markets as well? In order to answer this question, we have analyzed the impact of a large proprietary data set of opt…
In this paper we investigate the asymptotics of forward-start options and the forward implied volatility smile in the Heston model as the maturity approaches zero. We prove that the forward smile for out-of-the-money options explodes and compute a closed-form high-order expansion detailing the rate of the explosion. Fu…
Classical solvable stochastic volatility models (SVM) use a CEV process for instantaneous variance where the CEV parameter takes just few values: 0 - the Ornstein-Uhlenbeck process, 1/2 - the Heston (or square root) process, 1- GARCH, and 3/2 - the 3/2 model. Some other models were discovered in \cite{Labordere2009…
The study confirms that market volatility can be explained by correlated metaorders impacting prices in a square-root fashion.
problem Explaining market volatility using metaorders and their impact.
method Generated synthetic market data and analyzed the correlation between order flow and returns.
result The square-root law of market impact is confirmed and can be measured from anonymized trade data.
We apply an asymmetric version of Kirman's herding model to volatile financial markets. In the relation between returns and agent concentration we use the square root law proposed by Zhang. This can be derived by extending the idea of a critical mean field theory suggested by Plerou et al. We show that this model is eq…
We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V-shaped and {\it vanishes} around the current price. This result is generic, and only relies on mild assumptions about the order flow and on the fact that prices are (to a first approximation) diffusive. This natu…
Solves non-Abelian Rainich problem for SU(2) gauge fields.
problem Existence of local SU(2) Yang-Mills fields with prescribed stress-energy tensor.
method Canonically identifying tensors with Hermitian forms and defining internal square roots of stress-energy tensors.
result Existence of local SU(2) Yang-Mills field is equivalent to a single differential condition on internal square roots of stress-energy tensor.
Square-Root Price Impact Is Necessary for Endogenous Manipulation Cycles in Learning-Agent Marketsq-fin.CP
Agent-based market shows herding cycles with square-root price impact.
problem Understanding herding cycles in agent-based markets.
method Agent-based model with 20,000 retail traders interacting with a single institutional agent.
result Agent discovers multi-cycle predatory strategy with 8-11 complete cycles over 2000 trading days.
The square root velocity framework is a method in shape analysis to define a distance between curves and functional data. Identifying two curves if they differ by a reparametrisation leads to the quotient space of unparametrised curves. In this paper we study analytical and topological aspects of this construction for …
Efficiently computes matrix square roots and their inverses for large matrices.
problem Computing matrix square roots and inverses for large matrices efficiently.
method Combines Krylov subspace methods with rational approximation for quadratic-time computation.
result Achieves 4 decimal places of accuracy with fewer than 100 matrix-vector multiplications.
Paper connects surface shape analysis and unbalanced optimal transport.
problem Computing the SRNF shape distance on piecewise linear surfaces.
method Characterizes SRNF shape distance as WFR distance pullback, proposes new algorithm for WFR distance computation.
result Direct computation of SRNF shape distance on piecewise linear surfaces.
Novel approach integrates Multivariate Square-root Lasso into Synthetic Control for high-dimensional data.
problem Challenges in practical implementation and computational efficiency of Synthetic Control method for high-dimensional disaggregated data.
method Integrates Multivariate Square-root Lasso into Synthetic Control framework.
result Demonstrates superior computational efficiency without compromising estimation accuracy.
This thesis examines the accuracy of scaling VaR estimates for longer holding periods.
problem The accuracy of VaR estimates for longer holding periods using the square root of time rule.
method Examined VaR scaling for longer holding periods using empirical analysis.
result Scaling can provide good estimates of VaR but may lead to significant losses over time.
TPSQRs model longitudinal event data, detecting ADRs from EHRs.
problem Detecting adverse drug reactions from longitudinal event data.
method Learned by estimating a collection of interrelated PSQRs, using Poisson pseudo-likelihood for estimation.
result TPSQRs effectively and efficiently recover ADR signals from EHRs.
Improved survival analysis using square root Cox's models and neural networks.
problem Feature selection in survival analysis.
method Square root Cox's survival analysis by the fittest linear and neural networks model, directly tuning penalty parameter λ.
result Substantially improved over traditional methods, achieving phase transition in feature selection.
The paper establishes a uniform Lipschitz bound on the square root of the systole function in Teichmüller space.
problem Uniform Lipschitz bounds on geometric functions in Teichmüller space.
method Injectivity radius analysis and Lipschitz bounds on systole function.
result Uniform Lipschitz constant for the square root of the systole function on Teichmüller space.