arXiv research

Rough and Hodge Laplacians eigenvalues approach zero with fixed volume.

We establish a uniform comparison between the spectrum of the rough Laplacian (acting on sections of a vector bundle of complex rank one or of harmonic curvature) with the spectrum of a discrete operator (a generalization of a discrete magnetic Laplacian added with a potential) acting on a finite dimensional space comi…

The paper finds a geometric lower bound for the first positive eigenvalue of the rough Laplacian on 1-forms.

We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are Hölder continuous locally in space and time. This is done via local parabolic Harnack estimates for weak solutions of operators in divergence form with b…

Study large deviations for hypoelliptic diffusion on sub-Riemannian manifolds.

More than forty years ago J. H. Samson has defined the Laplacian $Δ_{sym}$ acting on the space of symmetric covariant $p$-tensors on an $n$-dimensional Riemannian manifold $(M, g)$. This operator is an analogue of the well known Hodge-de Rham Laplacian $Δ$ which acts on the space of exterior differential $p$-forms ($1 …

Our topological setting is a smooth compact manifold of dimension two or higher with smooth boundary. Although this underlying topological structure is smooth, the Riemannian metric tensor is only assumed to be bounded and measurable. This is known as a rough Riemannian manifold. For a large class of boundary condition…

Solves Yamabe problem for 3D metrics of Sobolev class $W^{2,q}$.

Unified framework for multi-user bandits using Laplacian kernels.

Paper explores rough path theory for frictionless markets, linking NCFL to unbiased rough integrators.

Model rough volatility using RDEs with correlated Brownian motion and fractional Brownian motion.

Derives a rough SABR formula for short maturities.

Study finds roughness in volatility despite diffusive instantaneous volatility.

We are concerned about the coarse and precise aspects of a priori estimates for Green's function of a regular domain for the Laplacian-Betrami operator on any $3\le n$-dimensional complete non-compact boundary-free Riemannian manifold through the square Sobolev/Nash/logarithmic-Sobolev inequalities plus the rough and s…

We present a number of related comparison results, which allow to compare moment explosion times, moment generating functions and critical moments between rough and non-rough Heston models of stochastic volatility. All results are based on a comparison principle for certain non-linear Volterra integral equations. Our u…

Develops a new method for quantizing rough volatility for volatility derivatives pricing.

Researchers compute Greeks for rough Volterra SV models using Malliavin calculus.

Measures of implied volatility roughness corrected for bias.

Study finds rough volatility models underperform in SPX option pricing.

New methods price American options in rough volatility models.

Study approximates weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.

Integrates rough geometric forms on manifolds.

Study approximates rough stochastic volatility models using diffusion processes.

A submanifold $M^m$ of a Euclidean space $R^{m+p}$ is said to have harmonic mean curvature vector field if $Δ\vec{H}=0$, where $\vec{H}$ is the mean curvature vector field of $M\hookrightarrow R^{m+p}$ and $Δ$ is the rough Laplacian on $M$. There is a conjecture named after Bangyen Chen which states that submanifolds o…

Estimates roughness of volatility from discrete variance data.

We introduce a notion of p-rough integrator on any Banach manifolds, for any $p\geq 1$, which plays the role of weak geometric Holder p-rough paths in the usual Banach space setting. The awaited results on rough differential equations driven by such objects are proved, and a canonical representation is given if the man…

Volatility roughness studied using fractional noise-driven models.

A hybrid framework for American option pricing under time-varying rough volatility.

New method analyzes volatility models for option prices, especially in rough volatility.

Novel approach to financial derivatives pricing using rough path theory.

Efficient simulation scheme for rough Heston model reduces computational cost.

Foundation for robust finance using rough path theory.

Sharp bounds on weak convergence rate for rough volatility models.

The paper develops a new model for rough volatility in commodity markets.

Bitcoin volatility shows multifractal structure, contradicting rough volatility models.

Perfect hedging of options with a dynamic portfolio in rough volatility models.

The paper explores how score-driven models can approximate rough volatility.

Unified approach to stochastic control, filtering, and stopping using rough paths.

Analyzes how rough volatility affects stock pricing and risk premium.

The BBF, SABR, and rough SABR formulas provide nearly arbitrage-free implied vol approximations.

The paper proves signatures of non-geometric rough paths can approximate functionals uniformly.

This paper optimizes portfolio selection for multivariate affine and quadratic Volterra models with rough volatilities.

Study tests rough fractional volatility model across different time scales, revealing new volatility patterns.

Rough volatility models are known to reproduce the behavior of historical volatility data while at the same time fitting the volatility surface remarkably well, with very few parameters. However, managing the risks of derivatives under rough volatility can be intricate since the dynamics involve fractional Brownian mot…

Extends pricing methods for index options under rough volatility.

Establishes a microstructural foundation for a rough log-normal volatility model.

Study on CVA in volatility models, including rough volatility.

Study improves weak error estimates for rough volatility models.