arXiv research

Efficient numerical method for time-fractional Black-Scholes model.

In this paper, we show that the price of an European call option, whose underlying asset price is driven by the space-time fractional diffusion, can be expressed in terms of rapidly convergent double-series. The series formula can be obtained from the Mellin-Barnes representation of the option price with help of residu…

In this paper, we focus on option pricing models based on space-time fractional diffusion. We briefly revise recent results which show that the option price can be represented in the terms of rapidly converging double-series and apply these results to the data from real markets. We focus on estimation of model paramete…

We construct a three-point compact finite difference scheme on a non-uniform mesh for the time-fractional Black-Scholes equation. We show that for special graded meshes used in finance, the Tavella-Randall and the quadratic meshes the numerical solution has a fourth-order accuracy in space. Numerical experiments are di…

Improved options pricing for two assets using fractional calculus.

Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy tailed jumps, and the time-fractional version codes heavy tailed waiting times. Thi…

CFTM uses fractional Brownian motion for dynamic topic modeling.

Fractional porous media equations yield q-Gaussian solutions for stock price returns.

Paper applies subdiffusive dynamics to American and barrier options pricing.

Despite significant effort in understanding complex systems (CS), we lack a theory for modeling, inference, analysis and efficient control of time-varying complex networks (TVCNs) in uncertain environments. From brain activity dynamics to microbiome, and even chromatin interactions within the genome architecture, many …

Rough volatility models are continuous time stochastic volatility models where the volatility process is driven by a fractional Brownian motion with the Hurst parameter smaller than half, and have attracted much attention since a seminal paper titled "Volatility is rough" was posted on SSRN in 2014 showing that the log…

The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications in physics, but also in insurance, finance and economics. A definition is given for a class of stochastic integrals driven by a CTRW, that includes the Ito and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is…

Researchers found the Wigner derivative and its inverse are equal for spherical tetrahedra.

The paper shows objective derivatives are covariant derivatives on Riemannian metrics.

Computes derivatives of sections in vector bundles using Lie derivatives.

Paper proposes auction method for smart derivatives to avoid disputes.

Derivatives impact U.S. banking sector's systemic risk, but loan and leverage ratios are more significant.

This paper deals with the concept of curvature of framed space curves, their higher-order derivatives, variations, and co-rotational derivatives. We realize that parametrizing rotation tensor using the Gibbs vector is effective in deriving a closed form formula to obtain any order derivative of the curvature tensor as …

Schwarzian derivative connects to Euler-Lagrange equations in variational calculus.

Paper develops formulas for shape derivatives in wave scattering.

A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of multivector and multiform fields is presented using algebraic and analytical tools developed in previous papers.

Study compares Indian derivatives markets and finds NSE outperforming BSE.

Former physicists share insights on derivatives in interviews.

Introduces Darboux-Lie derivative for fiber bundles.

New derivations on diffeological spaces are not smooth, expanding tangent space definitions.

Develops derived differential geometry theory.

Derives spacetime regularity under specific curvature conditions.

In this article, we combine replication pricing with expectation pricing for derivative trades that are partially collateralized by cash. The derivatives are replicated by underlying assets and cash, using repurchasing agreement (repo) and margining, which incur funding costs. We derive a partial differential equation …

Approximates derivative pricing under fractional stochastic volatility.

We introduce and study a construction of higher derived brackets generated by a (not necessarily inner) derivation of a Lie superalgebra. Higher derived brackets generated by an element of a Lie superalgebra were introduced in our earlier work. Examples of higher derived brackets naturally appear in geometry and mathem…

We characterize the Lie derivative of spinor fields from a variational point of view by resorting to the theory of the Lie derivative of sections of gauge-natural bundles. Noether identities from the gauge-natural invariance of the first variational derivative of the Einstein(--Cartan)--Dirac Lagrangian provide restric…

We calculate the higher derivatives of length functions on Teichmuller space along earthquake deformations. This generalizes the cosine formula for the first derivative by Kerckhoff and Wolpert and the sine formula for second derivative by Wolpert.

Develops a new approach to study nonlinear PDEs and their singularities.

Derives derivatives of risk measures for various types of portfolio losses.

Optimizes material distribution on surfaces using topological derivatives.

Derives a formula for the k-th covariant derivative of tensor fields.

We present a unified derivation of covariant time derivatives, which transform as tensors under a time-dependent coordinate change. Such derivatives are essential for formulating physical laws in a frame-independent manner. Three specific derivatives are described: convective, corotational, and directional. The covaria…

Invariant covariant derivatives on homogeneous spaces are characterized.

Derives derivatives and geometric framework for functions with non-independent variables.

We explain how to translate several recent results in derived algebraic geometry to derived differential geometry. These concern shifted Poisson structures on NQ-manifolds, Lie groupoids, smooth stacks and derived generalisations, and include existence and classification of various deformation quantisations.

The problem of quantile hedging for basket derivatives in the Black-Scholes model with correlation is considered. Explicit formulas for the probability maximizing function and the cost reduction function are derived. Applicability of the results for the widely traded derivatives as digital, quantos, outperformance and …

In the spirit of Arrow-Debreu, we introduce a family of financial derivatives that act as primitive securities in that exotic derivatives can be approximated by their linear combinations. We call these financial derivatives signature payoffs. We show that signature payoffs can be used to nonparametrically price and hed…

Establishes equivalence between models of derived stacks.

New estimator for estimating derivatives in nonparametric regression.

We characterise the link of derivatives in measure, which are introduced in [AKR,Card,ORS] respectively by different means, for functions on the space $\mathbb M$ of finite measures over a Riemannian manifold $M$. For a reasonable class of functions $f$, the extrinsic derivative $D^Ef$ coincides with the linear functio…

Estimates cross-impact on derivatives markets using E-Mini futures and options.

Let $(M,g)$ be a pseudo-Riemannian manifold. We propose a new approach for defining the conformal Schwarzian derivatives. These derivatives are 1-cocycles on the group of diffeomorphisms of $M$ related to the modules of linear differential operators. As operators, these derivatives do not depend on the rescaling of the…

Homotopy equivalence between formalities with different covariant derivatives.