arXiv research

This paper explores the harmonic mean of implied volatility and its relation to local volatility.

We extend the model-free formula of [Fukasawa 2012] for $\mathbb E[Ψ(X_T)]$, where $X_T=\log S_T/F$ is the log-price of an asset, to functions $Ψ$ of exponential growth. The resulting integral representation is written in terms of normalized implied volatilities. Just as Fukasawa's work provides rigourous ground for Ch…

Characterizes smiles in delta satisfying specific conditions.

Characterizes no Butterfly arbitrage in SVI model parameters.

Sparked by Alòs, León, and Vives (2007); Fukasawa (2011, 2017); Gatheral, Jaisson, and Rosenbaum (2018), so-called rough stochastic volatility models such as the rough Bergomi model by Bayer, Friz, and Gatheral (2016) constitute the latest evolution in option price modeling. Unlike standard bivariate diffusion models s…

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

We investigate the structure of good deal bounds, which are subintervals of a no-arbitrage pricing bound, for financial market models with convex constraints as an extension of Arai and Fukasawa (2014). The upper and lower bounds of a good deal bound are naturally described by a convex risk measure. We call such a risk…

Monotonicity of normalized implied-volatility coordinates under no-arbitrage

In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkhäuser/Springer Basel AG] for continuous processes, we propose a framework enabling us to (asymptotically) optimize…

Classical (Itô diffusions) stochastic volatility models are not able to capture the steepness of small-maturity implied volatility smiles. Jumps, in particular exponential Lévy and affine models, which exhibit small-maturity exploding smiles, have historically been proposed to remedy this (see \cite{Tank} for an overvi…

We consider rough stochastic volatility models where the driving noise of volatility has fractional scaling, in the "rough" regime of Hurst parameter $H < 1/2$. This regime recently attracted a lot of attention both from the statistical and option pricing point of view. With focus on the latter, we sharpen the large de…

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

Revisits Lee's Moment Formula, relaxing moment assumptions for implied volatility.

Modeling price formation with interacting Hawkes processes leading to stochastic volatility with leverage.

The article explores the mapping class group using unicellular maps and provides filtrations.

Constructs a moment map flow for isotropic maps on surfaces.

Maps are an important medium that enable people to comprehensively understand the configuration of cultural activities and natural elements over different times and places. Although massive maps are available in the digital era, how to effectively and accurately access the required map remains a challenge today. Previo…

The paper constructs biharmonic maps between spheres using polynomial maps.

Both bi-harmonic map and $f$-harmonic map have nice physical motivation and applications. In this paper, by combination of these two harmonic maps, we introduce and study $f$-bi-harmonic maps as the critical points of the $f$-bi-energy functional $\frac{1}{2}\int_M f|τ(φ)|^2dv_{g}$. This class of maps generalizes both …

Research explores real algebraic realization of round fold maps of codimension -1.

The paper derives Liouville theorems for various generalized maps on Riemannian manifolds.

This paper shows semi-equivelar toroidal maps are vertex-transitive covers.

Paper defines and studies Clairaut warped product Riemannian maps.

The paper explores unique continuation properties for polyharmonic maps between Riemannian manifolds.

The hyperelliptic mapping class group has been studied in various contexts within topology and algebraic geometry. What makes this study tractable is that there is a surjective map from the hyperelliptic mapping class group to a mapping class group of a punctured sphere. The more general family of superelliptic mapping…

This paper constructs real algebraic maps that are topologically special generic maps.

A Reeb space is defined as the space of all the connected components of inverse images of a smooth map, which is a fundamental tool in studying smooth manifolds using generic smooth maps whose codimensions are not positive such as Morse functions, their higher dimensional versions including fold maps and general stable…

The paper constructs gluing maps for harmonic maps between Riemannian manifolds.

Characterizes a general range decreasing group homomorphism.

The paper examines $HM$-tensional and $HS$-tensional maps between Riemannian manifolds.

The paper proves a Liouville theorem for specific harmonic maps with free boundary.

Dirac-harmonic maps are uncoupled under certain conditions.

We introduce slant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds as a generalization of slant immersions, invariant Riemannian maps and anti-invariant Riemannian maps. We give examples, obtain characterizations and investigate the harmonicity of such maps. We also obtain necessary and sufficie…

Analyzes harmonic and biharmonic maps from gradient Ricci solitons.

The paper studies maps from pseudo-Hermitian to Kähler manifolds, proving harmonic map properties.

In this paper, we show that one can interrelate pluriharmonic maps with para-pluriharmonic maps by means of the loop group method. As an appendix, we give examples for the interrelation between pluriharmonic maps and para-pluriharmonic maps. Moreover, we investigate the relation among CMC-surfaces by use of such maps.

The article explores constructing biharmonic and conformal biharmonic maps to spheres.

Harmonic map flow preserves almost-holomorphic maps without singularities.

Method computes harmonic and conformal maps from point clouds.

New theorem proves convergence of various discrete conformal structures to conformal maps.

This paper classifies semi-equivelar maps on a special surface.

Constructs harmonic maps between special geometric shapes.

Study on harmonic maps between cones, linking degrees to graph Laplacian eigenvalues.

Study isotropic Riemannian maps and helices along them.

Study on harmonic maps on weighted Riemannian foliations.

Maps and measures on surfaces link best Lipschitz and least gradient functions.

The construction of topological index maps for equivariant families of Dirac operators requires factoring a general smooth map through maps of a very simple type: zero sections of vector bundles, open embeddings, and vector bundle projections. Roughly speaking, a normally non-singular map is a map together with such a …

Paper proves existence and gives construction of Symphonic map between ellipsoids.