In this paper, we obtain asymptotic formulas with error estimates for the implied volatility associated with a European call pricing function. We show that these formulas imply Lee's moment formulas for the implied volatility and the tail-wing formulas due to Benaim and Friz. In addition, we analyze Pareto-type tails o…
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48 results for “asymptotic formulae”
We extend asymptotic formulas for saddle connections on translation surfaces.
problem Counting saddle connections on translation surfaces with large genus.
method Recursive formulas and asymptotic analysis for all strata and multiplicities.
result Asymptotics for all saddle connections on translation surfaces of growing genus.
We derive formulas for F measures' standard error and confidence intervals.
problem Estimating F measures' accuracy with confidence.
method Analytic formulas based on asymptotic normality.
result Valid formulas for sample size planning.
In this note, we answer a question of Mirzakhani on asymptotic behavior of the one-point volume polynomial of moduli spaces of curves. We also present some applications of Mirzakhani's asymptotic formulae of Weil-Petersson volumes.
Abstract: Characterizes frontals and wavefronts with formulas.
problem Characterizing frontals and wavefronts.
method Representation formulas for frontals and wavefronts.
result Representation formulas for various types of frontals and wavefronts.
We prove a graph theoretic closed formula for coefficients in the Tian-Yau-Zelditch asymptotic expansion of the Bergman kernel. The formula is expressed in terms of the characteristic polynomial of the directed graphs representing Weyl invariants. The proof relies on a combinatorial interpretation of a recursive formul…
The BBF, SABR, and rough SABR formulas provide nearly arbitrage-free implied vol approximations.
problem Arbitrage in implied volatility calculations.
method Analytical proofs for BBF, SABR, and rough SABR formulas under specific models.
result These formulas offer asymptotically arbitrage-free approximations of implied volatility.
The article provides formulas for homological blocks of Seifert fibered homology 3-spheres.
problem Calculating Witten-Reshetikhin-Turaev invariants for Seifert fibered homology 3-spheres.
method Explicit modular transformation formulas of homological blocks.
result New proof of Witten asymptotic conjecture for Seifert fibered homology 3-spheres.
Formula derived for torsion of modified Dirac operator.
problem Analyzing modified Dirac operator's torsion.
method Proved formula for asymptotic expansion.
result Leading term formula for torsion.
New method improves covariance estimation for weighted samples.
problem Improving covariance estimation for weighted sample data.
method Asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators of weighted sample covariances.
result Asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators of weighted sample covariances.
Formula derived for special q-hypergeometric series at roots of unity.
problem Asymptotic behavior of special q-hypergeometric series at complex roots of unity.
method Derivation of a formula for the radial asymptotics of Nahm sums at complex roots of unity.
result Formula for the radial asymptotics of Nahm sums at complex roots of unity.
Odaka and Wang proved the intersection formula for the Donaldson-Futaki invariant. In this paper, we generalize this result for the higher Futaki invariants which are obstructions to asymptotic Chow semistability.
New formulas for surface curvature when tangent vector points in asymptotic directions.
problem Formula limitations when tangent vector points in asymptotic directions.
method Analogous formulas for surfaces with cusp singular points.
result Invariants of cusp singular points of contour lines.
Formula found for energy slope in complex geometry.
problem Calculating the asymptotic slope of a K-energy.
method Established a formula for the asymptotic slope.
result Found a formula for the asymptotic slope of α-K-energy.
The paper calculates asymptotic Betti numbers and homology multiplicities for graph configuration spaces.
problem Understanding the homology of ordered configuration spaces of graphs.
method Explicit formulas for asymptotic Betti numbers and homology multiplicities in characteristic zero.
result Explicit formulas for asymptotic multiplicities in homology of irreducible representations of the symmetric group.
Volume renormalization for conformally compact asymptotically hyperbolic manifolds in dimension fourmath.DG
New formula for volume in 4D hyperbolic manifolds.
problem Volume calculation for specific geometric manifolds.
method Derive new renormalized volume formula.
result Generalizes existing formulas for Poincare-Einstein manifolds.
We provide a proof and analyze the asymptotic behavior of a formula for the linking number of line segments.
problem The invariant formula for the linking number of line segments and its asymptotic behavior.
method Detailed proof and asymptotic analysis of the formula.
result We provide a proof and analyze the asymptotic behavior of the formula for the linking number of line segments.
In this paper, using the Greiner's approach to heat kernel asymptotics, we give new proofs of the equivariant Gauss-Bonnet-Chern formula and the variation formulas for the equivariant Ray-Singer metric, which are originally due to J. M. Bismut and W. Zhang.
Study on hyperbolic manifolds with special boundaries.
problem Characterizing geometric properties of hyperbolic manifolds with specific boundaries.
method Analyzing asymptotically hyperbolic manifolds with a horospherical boundary.
result Derived geometric formulas for the model case of horoballs and their complements.
Proves formula for unique Kähler-Einstein metric on quasi-projective manifolds.
problem Finding unique Kähler-Einstein metrics on quasi-projective manifolds.
method Elementary proof using ODE solutions and spectral theory.
result Asymptotic expansion formula for unique complete Kähler-Einstein metric.
The paper calculates the asymptotic of holomorphic analytic torsion forms for line bundles.
problem Calculating the asymptotic of holomorphic analytic torsion forms for line bundles.
method Using asymptotic formula and Toeplitz operators, the paper generalizes the results for direct images of line bundles.
result Generalized asymptotic formula for holomorphic torsion forms of line bundles and direct images.
We consider the asymptotic behavior of the implied volatility in stochastic asset price models with atoms. In such models, the asset price distribution has a singular component at zero. Examples of models with atoms include the constant elasticity of variance model, jump-to-default models, and stochastic models describ…
The paper connects eigenvalue problems for various operators and establishes inequalities and asymptotic formulas for heat traces.
problem Eigenvalue problems and heat trace asymptotics for different operators.
method Establishes connections and inequalities for eigenvalues and heat traces.
result Eigenvalue inequalities and three-term asymptotic formulas for heat traces of various operators.
Paper derives asymptotic formula for conjugacy classes in groups with contracting elements.
problem Counting conjugacy classes in groups with contracting elements.
method Statistical convex-cocompact actions with contracting elements.
result Asymptotic formula for conjugacy classes, showing transcendental conjugacy growth series for certain groups.
New formulas for hyperbolic mass using horospheres.
problem Mass calculation of asymptotically hyperbolic manifolds.
method Geometric formulas derived using coordinate horospheres.
result Improved rigidity results of hyperbolic space.
Paper derives a formula for the determinant of Dirichlet-to-Neumann operator on Riemann surfaces.
problem Bounding asymptotics of a conformal invariant under degeneration of Riemann surfaces.
method Meyer-Vietoris formula, gluing, height function on moduli space, properness of height function, Steklov isospectral metrics, Laplacian with Dirichlet/Neumann boundary conditions.
result Properness of height function on moduli space of genus zero hyperbolic surfaces implies compactness theorem for Steklov isospectral metrics.
Proves a conjecture about 3-manifold invariants using trees and asymptotic formulas.
problem Proving the holomorphy of certain rational functions for plumbed 3-manifolds.
method Induction on a sequence of trees, using the Euler-Maclaurin summation formula.
result Proves the conjecture about Witten-Reshetikhin-Turaev invariants and homological blocks.
We discuss asymptotic behavior of the eigenvalue distribution of the differential form Laplacian on a Riemannian foliated manifold when the metric on the ambient manifold is blown up in directions normal to the leaves (in the adiabatic limit). Motivated by analogies with semiclassical spectral asymptotics, we use ideas…
Formula found for Calabi-Yau metrics on flag variety bundles.
problem Finding unique asymptotically conical Calabi-Yau metrics on flag variety canonical bundles.
method Generalizing the Calabi Ansatz to Kähler classes, deriving a simple formula.
result Explicit formula for metrics on canonical bundles of flag varieties.
In this paper, by a new method we establish the Weyl-type asymptotic formula for the counting function of biharmonic Stekloff eigenvalues with Neumann boundary condition in a bounded domain of an -dimensional Riemannian manifold.
Formula derived for a magnetic line invariant.
problem Solving MHD problems with two-scale mean fields.
method Combinatorial definition of invariant for three-component links.
result Proven formula for invariant verified for simple cases.
The study examines the asymptotic behavior of extremal length in Teichmüller space.
problem Understanding the asymptotic behavior of extremal length along Teichmüller rays.
method Analyzing the limit of extremal length and deriving formulas for limiting Teichmüller distance and detour metric.
result An explicit formula for the limiting Teichmüller distance and a necessary and sufficient condition for Teichmüller rays to be asymptotic.
Analytic torsion formula generalized for CR manifolds with S^1 action.
problem Generalizing the asymptotic formula of analytic torsion to CR manifolds.
method Introducing Fourier components and establishing asymptotic formula.
result Asymptotic formula for analytic torsion on CR manifolds with S^1 action.
In this paper, we introduce a monotonicity formula for the mean curvature flow. We also apply this monotonicity formula to study the asymptotic behavior of eternal solutions.
The paper calculates factor loading and unique variance covariances for various factor analysis methods.
problem Estimating the asymptotic covariances of unrotated factor loading and unique variance estimates.
method Explicit formulas derived from sample covariances or correlations, using least square, principal, iterative principal component, alpha, or image factor analysis.
result The formulas produce reasonable standard errors for rotated loading estimates in multivariate normal populations.
In this paper, we establish sharp inequalities for four kinds of classical eigenvalues on a bounded domain of a Riemannian manifold. We also establish asymptotic formulas for the eigenvalues of the buckling and clamped plate problems. In addition, we give a negative answer to the Payne conjecture for the one-dimensiona…
The paper calculates the full asymptotics of analytic torsions for compact orbifolds.
problem Analytic torsions of compact locally symmetric orbifolds.
method Using Selberg's trace formula and geometric localization, the paper evaluates the heat trace and orbital integrals.
result Explicit formula for the asymptotic Ray-Singer analytic torsion of compact orbifolds.
We conjecture that the Joyce-Song wall-crossing formula for Donaldson-Thomas invariants arises naturally from an asymptotic expansion in the field theoretic work of Gaiotto, Moore and Neitzke. This would also give a new perspective on how the formulae of Joyce-Song and Kontsevich-Soibelman are related. We check the con…
Motivated by recent interest in the spectrum of the Laplacian of incomplete surfaces with isolated conical singularities, we consider more general incomplete m-dimensional manifolds with singularities on sets of codimension at least 2. With certain restrictions on the metric, we establish that the spectrum is discrete …
The study finds uniform bounds for Black-Scholes implied volatility.
problem Finding uniform bounds for Black-Scholes implied volatility.
method Expressed in terms of optimisation problems, derived upper and lower bounds, exploited symmetries.
result Uniform bounds for Black-Scholes implied volatility are derived and used to reprove asymptotic formulae.
The asymptotic behavior of the implied volatility associated with a general call pricing function has been extensively studied in the last decade. The main topics discussed in this paper are Lee's moment formulas for the implied volatility, and Piterbarg's conjecture, describing how the implied volatility behaves in th…
Sharp criterion for Chern-Gauss-Bonnet integral using Q curvature.
problem Quantifying the Chern-Gauss-Bonnet integral using Q curvature.
method New approach involving singular integral estimation.
result Derivation of asymptotic formula for Q curvature equation.
We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process and the density of the stock price process in the Stein-Stein and the Heston model…
Study on implied volatility of Asian options with stochastic volatility.
problem Understanding the implied volatility of Asian options under stochastic volatility models.
method Using Malliavin calculus and anticipating Ito's formula, the paper computes and finds asymptotic formulas for the implied volatility and skew.
result Developed short-maturity asymptotic formulas for the skew of the implied volatility, which depends on the roughness of the volatility model.
Formula for fixed points on noncompact spaces.
problem Calculating fixed points on noncompact manifolds.
method Equivariant index theorem, localised functional, asymptotically local operators.
result Obtained a new Lefschetz fixed-point formula.
Paper studies second order tail probabilities in risk models.
problem Analyzing tail probabilities in risk models with constant interest force.
method Asymptotic expansion and weighted Kesten-type inequality for second order subexponential random variables.
result Second order asymptotic formulae for continuous-time renewal risk models are derived.
Formulae count square-tiled surfaces in genus two.
problem Counting square-tiled surfaces in genus two.
method Parametrized classification into four diagrams, provided formulae for enumeration.
result Formulae for enumeration of square-tiled surfaces in four diagrams, completing the count for genus two.
The article calculates asymptotic expansions for quantum invariants from surgeries on Whitehead link components.
problem Calculating quantum invariants for 3-manifolds resulting from surgeries on Whitehead link components.
method Asymptotic expansion of relative Reshetikhin-Turaev and Turaev-Viro invariants.
result Asymptotic formulas for both invariants are derived.