arXiv research

We study the short-time asymptotics of conditional expectations of smooth and non-smooth functions of a (discontinuous) Ito semimartingale; we compute the leading term in the asymptotics in terms of the local characteristics of the semimartingale. We derive in particular the asymptotic behavior of call options with sho…

Short proof of heat kernel asymptotics and convolution approximation.

Study short-time existence of conformal Ricci flow on hyperbolic manifolds.

Study on heat content for domains with fractal boundaries.

Study short maturity Asian options under CEV model, presenting an analytical approximation.

In this paper, we study short-time existence of static flow on complete noncompact asymptotically static manifolds from the point of view that the stationary points of the evolution equations can be interpreted as static solutions of the Einstein vacuum equations with negative cosmological constant. For a static vacuum…

Study short maturity Asian options in local volatility models.

We consider the fractional Heston model originally proposed by Comte, Coutin and Renault. Inspired by recent ground-breaking work on rough volatility, which showed that models with volatility driven by fractional Brownian motion with short memory allows for better calibration of the volatility surface and more robust e…

New method approximates quadratic-growth BSDEs with short-term expansions.

Study short-term behavior of up-and-in barrier options using Malliavin calculus.

Study provides short-time expansions for LETF options using Lévy models.

We consider a short time existence problem motivated by a conjecture of Joyce. Specifically we prove that given any compact Lagrangian $L\subset \mathbb{C}^n$ with a finite number of singularities, each asymptotic to a pair of non-area-minimising, transversally intersecting Lagrangian planes, there is a smooth Lagrangi…

Study examines short-term IVS dynamics using a model-independent approach.

Proves smoothness of conical singularities in mean curvature flow.

Approximates bond option volatilities using affine short-rate models.

Study short-maturity VIX and European option prices with jumps.

The paper analyzes hypoelliptic heat kernels near a manifold's cut locus.

Corrected an error in yield curve behavior models.

We consider the heat kernel (and the zeta function) associated with Laplace type operators acting on a general irreducible rank 1 locally symmetric space X. The set of Minakshisundaram- Pleijel coefficients {A_k(X)}_{k=0}^{\infty} in the short-time asymptotic expansion of the heat kernel is calculated explicitly.

We discuss a simple extension of the Ho and Lee model with generic time-dependent drift in which: 1) we compute bond prices analytically; 2) the yield curve is sensible and the asymptotic yield is positive; and 3) our analytical solution provides a clean and simple way of separating volatility from the drift in the sho…

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

Study short maturity Asian options in jump-diffusion models with local volatility.

The paper analyzes short maturity Asian options using large deviations theory.

Model optimal growth strategy in a market with short-lived assets.

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

New asymptotic formula for option prices with interest rates and dividend yield effects.

In this short note, we prove by an appropriate change of variables that the SVI implied volatility parameterization presented in Gatheral's book and the large-time asymptotic of the Heston implied volatility agree algebraically, thus confirming a conjecture from Gatheral as well as providing a simpler expression for th…

Asymptotic analysis of short-maturity options on realized variance in local-stochastic volatility models.

We consider the Cauchy problem associated with a general parabolic partial differential equation in $d$ dimensions. We find a family of closed-form asymptotic approximations for the unique classical solution of this equation as well as rigorous short-time error estimates. Using a boot-strapping technique, we also provi…

The paper studies asymptotics and zeta functions on compact nilmanifolds.

Game theory model shows optimal investment strategy for wealth growth.

We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both short-range and long-range behaviors of the metric and the perturbation at infinity…

We consider a model for interest rates, where the short rate is given by a time-homogenous, one-dimensional affine process in the sense of Duffie, Filipovic and Schachermayer. We show that in such a model yield curves can only be normal, inverse or humped (i.e. endowed with a single local maximum). Each case can be cha…

Study on implied volatility of Asian options with stochastic volatility.

In this short paper, we review recent progress on the positive mass theorem for spacelike hypersurfaces which approach to null infinity in asymptotically flat spacetimes. We use it to prove, if the functions $c(u, θ, ψ)$, $d(u, θ, ψ)$ vanish at certain retarded time in vacuum Bondi's radiating spacetimes, then the Bond…

We obtain new closed-form pricing formulas for contingent claims when the asset follows a Dupire-type local volatility model. To obtain the formulas we use the Dyson-Taylor commutator method that we have recently developed in [5, 6, 8] for short-time asymptotic expansions of heat kernels, and obtain a family of general…

New spectral invariants from two elliptic operators reveal manifold geometry.

Study of prescribed mean curvature flow on noncompact hypersurfaces in Lorentz manifolds.

In this note we study conformal Ricci flow introduced by Arthur Fischer. We use DeTurck's trick to rewrite conformal Ricci flow as a strong parabolic-elliptic partial differential equations. Then we prove short time existences for conformal Ricci flow on compact manifolds as well as on asymptotically flat manifolds. We…

Derives short-term option pricing asymptotics in local-stochastic volatility models.

Study short-maturity Asian option pricing in LSV models using large deviations theory.

Let $(M^n, g)$ be a complete Riemannian manifold with $Rc\geq -Kg$, $H(x, y, t)$ is the heat kernel on $M^n$, and $H= (4πt)^{-\frac{n}{2}}e^{-f}$. Nash entropy is defined as $N(H, t)= \int_{M^n} (fH) dμ(x)- \frac{n}{2}$. We studied the asymptotic behavior of $N(H, t)$ and $\frac{\partial}{\partial t}\Big[N(H, t)\Big]$ …

Method for factor analysis in short panels without assuming sphericity or Gaussianity.

Study on asset price density and option pricing under stochastic volatility models.

We study some asymptotic behavior of the first nonzero eigenvalue of the Lalacian along the normalized Ricci flow and give a direct short proof for an asymptotic upper limit estimate.

This text is a revised version of the authors Habilitationsschrift which was submitted to the University of Augsburg, 1993. Fuchs type differential operators are used to model the analysis on manifolds with cone--like singularities, or more general, stratified spaces. This book provides a self--contained treatment of t…

Study on implied volatility of Inverse options under stochastic volatility models.

De Sitter spacetime can be separated into two parts along two kinds of hypersurfaces and the half-de Sitter spacetimes are covered by the planar and hyperbolic coordinates respectively. Two positive energy theorems were proved previously for certain $¶$-asymptotically de Sitter and $\H$-asymptotically de Sitter initial…