arXiv research

Gaussian limit for small-time fluctuations of sub-Riemannian diffusion.

Study small-time fluctuations for sub-Riemannian diffusion loops.

Quantum theory explains financial market price fluctuations.

We provide a microfoundation for linear price impact models in a stationary market.

Optimizes portfolio in volatile markets with jumps, providing accurate formulas.

Researchers found a Weyl law for Liouville quantum gravity eigenvalues.

Study on small-time behavior of rough Bergomi model using large deviations principle.

We derive a small-time expansion for out-of-the-money call options under an exponential Levy model, using the small-time expansion for the distribution function given in Figueroa-Lopez & Houdre (2009), combined with a change of numéraire via the Esscher transform. In particular, we quantify find that the effect of a no…

The paper analyzes small-time asset price and volatility behaviors in Gaussian models.

Study calculates small-time basket option pricing under bi-variate SABR model.

Study describes heat kernel expansion for hypoelliptic operators.

In this paper we investigate the small time heat kernel asymptotics on the cut locus on a class of surfaces of revolution, which are the simplest 2-dimensional Riemannian manifolds different from the sphere with non trivial cut-conjugate locus. We determine the degeneracy of the exponential map near a cut-conjugate poi…

The article derives small-time expansions for jump-diffusion models with infinite jump activity.

This study examines abnormal geodesics in 2D-Zermelo navigation problems, revealing their role in separating time minimal and maximal curves.

In this paper we study the small time asymptotics for the heat kernel on a sub-Riemannian manifold, using a perturbative approach. We then explicitly compute, in the case of a 3D contact structure, the first two coefficients of the small time asymptotics expansion of the heat kernel on the diagonal, expressing them in …

Researchers calculate entropy of heat kernel on manifolds for very small times.

We consider a Markov process $X$, which is the solution of a stochastic differential equation driven by a Lévy process $Z$ and an independent Wiener process $W$. Under some regularity conditions, including non-degeneracy of the diffusive and jump components of the process as well as smoothness of the Lévy density of $Z…

Study small-time CLTs for stochastic Volterra equations with various kernels.

We find a simple strategy approximating optimal portfolio for short time horizons.

Study the heat kernel on quaternionic anti-de Sitter spaces and related spaces.

We consider a stochastic volatility model with Lévy jumps for a log-return process $Z=(Z_{t})_{t\geq 0}$ of the form $Z=U+X$, where $U=(U_{t})_{t\geq 0}$ is a classical stochastic volatility process and $X=(X_{t})_{t\geq 0}$ is an independent Lévy process with absolutely continuous Lévy measure $ν$. Small-time expansio…

The paper solves heat kernel asymptotics on non-degenerate CR manifolds.

We compute the small time asymptotic of the fundamental solution of Hörmander's type hypoelliptic operators with drift, at a stationary point, $x_0$, of the drift field. We show that the order of the asymptotic depends on the controllability of an associated control problem and of its approximating system. If the contr…

We study the small time asymptotics of the gradient and Hessian of the logarithm of the heat kernel at the cut locus, giving, in principle, complete expansions for both quantities. We relate the leading terms of the expansions to the structure of the cut locus, especially to conjugacy, and we provide a probabilistic in…

Proves heat expansion for Laplacian on a singularity.

Study option pricing near expiry for moderately out-of-the-money calls.

Researchers compute heat kernel coefficients for 2D diffusion operators.

Study on diffusion in non-complete sub-Riemannian manifolds with specific conditions.

We study the leading term in the small-time asymptotics of at-the-money call option prices when the stock price process $S$ follows a general martingale. This is equivalent to studying the first centered absolute moment of $S$. We show that if $S$ has a continuous part, the leading term is of order $\sqrt{T}$ in time $…

Motivated by marginals-mimicking results for Itô processes via SDEs and by their applications to volatility modeling in finance, we discuss the weak convergence of the law of a hypoelliptic diffusions conditioned to belong to a target affine subspace at final time, namely $\mathcal{L}(Z_t|Y_t = y)$ if $X_{\cdot}=(Y_\cd…

Improved option pricing for SABR model using Gauss-Hermite quadrature.

Study derives CEV volatility for SABR model, reducing approximation error.

Extends moderate deviations for a randomised Heston model.

We characterize the small-time asymptotic behavior of the exit probability of a Lévy process out of a two-sided interval and of the law of its overshoot, conditionally on the terminal value of the process. The asymptotic expansions are given in the form of a first-order term and a precise computable error bound. As an …

We extend and test empirically the multifractal model of asset returns based on a multiplicative cascade of volatilities from large to small time scales. The multifractal description of asset fluctuations is generalized into a multivariate framework to account simultaneously for correlations across times scales and bet…

We prove certain generalization of Hardy's inequality where the "boundary defining function" is replaced by a polynomial defining a singular algebraic variety. An application is given on the existence of a small time heat trace expansion for a Schrödinger operator with mild singularities along this algebraic set.

We study the dynamics of the normal implied volatility in a local volatility model, using a small-time expansion in powers of maturity T. At leading order in this expansion, the asymptotics of the normal implied volatility is similar, up to a different definition of the moneyness, to that of the log-normal volatility. …

New tests for identifying the number of latent factors in short panels with small time dimensions.

Study shows cryptocurrency price fluctuations become more similar to national currencies over time.

Bayesian models' singular fluctuation is shown to be akin to specific heat, influencing model complexity and generalization.

Paper develops a new method for calculating the probability density of a fractional SABR model.

Study heat traces for drifting Laplacian and Schrödinger operators on manifolds.

Analyzed Guyon's volatility model for existence and uniqueness.

New method recovers curvature from heat diffusion data.

Study spectral properties of sub-Riemannian Laplacians, proving quantum ergodicity and heat kernel asymptotics.

This paper studies the properties of discrete time stochastic optimal control problems associated with portfolio selection. We investigate if optimal continuous time strategies can be used effectively for a discrete time market after a straightforward discretization. We found that Merton's strategy approximates the per…

We study the nature of fluctuations in variety of price indices involving companies listed on the New York Stock Exchange. The fluctuations at multiple scales are extracted through the use of wavelets belonging to Daubechies basis. The fact that these basis sets satisfy vanishing moments conditions makes them ideal to …

New spectral functionals for Dirac operators with inner fluctuations computed.