arXiv research

Study examines USD exchange rate dynamics using Kramers-Moyal expansion.

Neural networks solve SPDEs using Wiener chaos expansion.

We propose an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps. The method is based on the eigenfunction expansion of the pricing operator. Given the set of call and pu…

We develop an expansion approach for the pricing of European quanto options written on LIBOR rates (of a foreign currency). We derive the dynamics of the system of foreign LIBOR rates under the domestic forward measure and then consider the price of the quanto option. In order to take the skew/smile effect observed in …

Some expansion methods have been proposed for approximately pricing options which has no exact closed formula. Benhamou et al. (2010) presents the smart expansion method that directly expands the expectation value of payoff function with respect to the volatility of volatility, then uses it to price options in the stoc…

In this paper we are interested in term structure models for pricing zero coupon bonds under rapidly oscillating stochastic volatility. We analyze solutions to the generalized Cox-Ingersoll-Ross two factors model describing clustering of interest rate volatilities. The main goal is to derive an asymptotic expansion of …

The paper characterizes probability and entropy of exponentially growing sample spaces.

We consider a non-trapping $n$-dimensional Lorentzian manifold endowed with an end structure modeled on the radial compactification of Minkowski space. We find a full asymptotic expansion for tempered forward solutions of the wave equation in all asymptotic regimes. The rates of decay seen in the asymptotic expansion a…

We obtain expressions for the shear and the vorticity tensors of perfect-fluid spacetimes, in terms of the divergence of the Weyl tensor. For such spacetimes, we prove that if the gradient of the energy density is parallel to the velocity, then either the expansion rate is zero, or the vorticity vanishes. This statemen…

Proposes a new model for negative interest rates that fits market data closely.

This study provides an explicit expansion of KL divergence's gradient flow in Fisher-Rao geometry.

We consider the wave equation on a product cone and find a joint asymptotic expansion for solutions near null and future infinities. The rates of decay seen in the expansion at future infinity are the resonances of a hyperbolic cone and were computed by the authors in a previous paper. The expansion treats an asymptoti…

Bayesian optimisation algorithm for unknown search spaces with sub-linear regret.

New models for short rates show longer periods at higher rates.

A new Lagrangian formulation of the Raychaudhuri equation in non-Riemannian geometry.

This paper examines the risk-adjusted performance and differential fund flows for socially responsible mutual funds (SRMF). The results show that SRMF rated high on ESG, perform better than lower rated ESG funds during the period of economic crisis. The findings also show that low ESG rated SRMF had higher differential…

The Wiener chaos approach to interest rate modelling arises from the observation that the pricing kernel admits a representation in terms of the conditional variance of a square-integrable random variable, which in turn admits a chaos expansion. When the expansion coefficients factorise into multiple copies of a single…

Recommender System research suffers currently from a disconnect between the size of academic data sets and the scale of industrial production systems. In order to bridge that gap we propose to generate more massive user/item interaction data sets by expanding pre-existing public data sets. User/item incidence matrices …

New analysis of stochastic approximation with non-expansive mappings.

New Hermite approximations accelerate convergence with adaptive coordinate transformations.

Study on DiTs' rates of approximation and estimation under various data assumptions.

We characterize geometrically the Lyapunov exponents of a cocycle (of arbitrary rank) with respect to a harmonic current defined on a hyperbolic Riemann surface lamination. Our characterizations are formulated in terms of the expansion rates of the cocycle along geodesic rays.

We give a survey of the approaches to classifying foliations, starting with the Haefliger classifying spaces and the various results and examples about the secondary classes of foliations. Various dynamical properties of foliations are introduced and discussed, including expansion rate, local entropy, and orbit growth …

Asymptotic expansions for call prices and implied volatilities in exponential Lévy models.

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

Derives a series expansion for Asian option pricing with polynomial jump-diffusion moments.

We demonstrate that the use of asymptotic expansion as prior knowledge in the "deep BSDE solver", which is a deep learning method for high dimensional BSDEs proposed by Weinan E, Han & Jentzen (2017), drastically reduces the loss function and accelerates the speed of convergence. We illustrate the technique and its imp…

We study the problem of nonparametric dependence detection. Many existing methods may suffer severe power loss due to non-uniform consistency, which we illustrate with a paradox. To avoid such power loss, we approach the nonparametric test of independence through the new framework of binary expansion statistics (BEStat…

In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $Δt$, and a series expansion of the deviation of its logarithm from that of a Gaussian distribution…

This paper presents a new method for estimating high dimensional covariance matrices. The method, permuted rank-penalized least-squares (PRLS), is based on a Kronecker product series expansion of the true covariance matrix. Assuming an i.i.d. Gaussian random sample, we establish high dimensional rates of convergence to…

The study optimizes Gaussian process approximations for finite-rank models.

We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable $X$ lead to consistent estimators of the mean embedding of $f(X)$. For Matérn ke…

We deal with the interest rate model proposed by Schaefer and Schwartz, which models the long rate and the spread, defined as the difference between the short and the long rates. The approximate analytical formula for the bond prices suggested by the authors requires a computation of a certain constant, defined via a n…

Large deviation principle for deep neural networks with ReLU activation.

We construct geometric realization for non-exceptional mutation-finite cluster algebras by extending the theory of Fomin and Thurston to skew-symmetrizable case. Cluster variables for these algebras are renormalized lambda lengths on certain hyperbolic orbifolds. We also compute growth rate of these cluster algebras, p…

We derive semi-analytic approximation formulae for bond and swaption prices in a Black-Karasiński interest rate model. Approximations are obtained using a novel technique based on the Karhunen-Loève expansion. Formulas are easily computable and prove to be very accurate in numerical tests. This makes them useful for nu…

ML models predict stock prices poorly during recessions.

We consider a general one-factor short rate model, in which the instantaneous interest rate is driven by a univariate diffusion with time independent drift and volatility. We construct recursive formula for the coefficients of the Taylor expansion of the bond price and its logarithm around $τ=0$, where $τ$ is time to m…

Enhances swaption modeling with rough stochastic volatility.

Improved volatility models for option pricing with weak error rates.

Rescaling expansiveness proven for k*-expansive vector fields.

EigenVI uses orthogonal function expansions for efficient variational inference.

A new method approximates option pricing in stochastic interest rate markets.

The paper derives expansions for Green's operators and resolvents using Hadamard methods.

In high dimensions, the mean and geometric median are nearly identical.

Given for instance a finite volume negatively curved Riemannian manifold $M$, we give a precise relation between the logarithmic growth rates of the excursions into cusps neighborhoods of the strong unstable leaves of negatively recurrent unit vectors of $M$ and their linear divergence rates under the geodesic flow. As…

The SABR model is a benchmark stochastic volatility model in interest rate markets, which has received much attention in the past decade. Its popularity arose from a tractable asymptotic expansion for implied volatility, derived by heat kernel methods. As markets moved to historically low rates, this expansion appeared…

The asymptotic concentration of the Fr{é}chet mean of IID random variables on a Rieman-nian manifold was established with a central limit theorem by Bhattacharya \& Patrangenaru (BP-CLT) [6]. This asymptotic result shows that the Fr{é}chet mean behaves almost as the usual Euclidean case for sufficiently concentrated di…