arXiv research

The square root of Fredholm determinants causes numerical instabilities in option pricing models.

We compare the CPU effort and pricing biases of seven Fourier-based implementations. Our analyses show that truncation and discretization errors significantly increase as we move away from the Black-Scholes-Merton framework. We rank the speed and accuracy of the competing choices, showing which methods require smaller …

Sinh-acceleration speeds up B-spline option pricing.

Introduces a new Lévy process for modeling illiquid markets.

New Fourier metrics equivalent to Wasserstein distances in image processing.

Paper provides a method to price electricity storage contracts using COS technique.

A new FFT method for Heston model option pricing with explicit error bounds.

The article prices exchange options using variance gamma-like models.

Study pricing options on forward contracts using infinite-dimensional affine models.

Tensor trains speed up option pricing for multi-asset options.

Various valuation adjustments, or XVAs, can be written in terms of non-linear PIDEs equivalent to FBSDEs. In this paper we develop a Fourier-based method for solving FBSDEs in order to efficiently and accurately price Bermudan derivatives, including options and swaptions, with XVA under the flexible dynamics of a local…

A machine learning method for short-maturity options with jumps and stochastic volatility.

The stochastic leverage effect, defined as the standardized covariation between the returns and their related volatility, is analyzed in a stochastic volatility model set-up. A novel estimator of the effect is defined using a pre-estimation of the Fourier coefficients of the return and the volatility processes. The con…

Quantum methods improve option pricing accuracy.

iCOS method estimates risk-neutral densities and option prices without model assumptions.

Proposes a new jump-diffusion model for option pricing.

Hybrid LSMC-PDE method for Bermudan options under GDMR model.

A new method computes Greeks for multi-asset options using tensor trains and Fourier transforms.

We develop a multi-factor stochastic volatility Libor model with displacement, where each individual forward Libor is driven by its own square-root stochastic volatility process. The main advantage of this approach is that, maturity-wise, each square-root process can be calibrated to the corresponding cap(let)vola-stri…

A new method optimizes Fourier pricing for multi-asset options using adaptive quadrature.

New algorithms learn sparse set functions in non-orthogonal Fourier bases.

We propose a numerical algorithm for backward stochastic differential equations based on time discretization and trigonometric wavelets. This method combines the effectiveness of Fourier-based methods and the simplicity of a wavelet-based formula, resulting in an algorithm that is both accurate and easy to implement. F…

Scalable methods integrate multiview data for clinical outcomes.

The paper develops adaptive confidence intervals for Efron's Gaussian two-groups model with unknown contamination.

New method uses neural networks for better financial hedging.

New model explains visual illusions using sub-Riemannian geometry.

We propose a Fourier-based learning algorithm for highly nonlinear multiclass classification. The algorithm is based on a smoothing technique to calculate the probability distribution of all classes. To obtain the probability distribution, the density distribution of each class is smoothed by a low-pass filter separate…

We propose a Fourier-based approach for optimization of several clustering algorithms. Mathematically, clusters data can be described by a density function represented by the Dirac mixture distribution. The density function can be smoothed by applying the Fourier transform and a Gaussian filter. The determination of th…

The Immersed Boundary (IB) method is a widely-used numerical methodology for the simulation of fluid-structure interaction problems. The IB method utilizes an Eulerian discretization for the fluid equations of motion while maintaining a Lagrangian representation of structural objects. Operators are defined for transmit…

This paper optimizes Gaussian mixture model learning with optimal sampling complexity.

Although neural networks are routinely and successfully trained in practice using simple gradient-based methods, most existing theoretical results are negative, showing that learning such networks is difficult, in a worst-case sense over all data distributions. In this paper, we take a more nuanced view, and consider w…

Let $Φ\in\mathbb{R}^{m\times n}$ be a sparse Johnson-Lindenstrauss transform [KN14] with $s$ non-zeroes per column. For a subset $T$ of the unit sphere, $\varepsilon\in(0,1/2)$ given, we study settings for $m,s$ required to ensure $\mathop{\mathbb{E}}_Φ\sup_{x\in T} \left|\|Φx\|_2^2 - 1 \right| < \varepsilon ,$ i.e…

In this paper we propose a scalable version of a state-of-the-art deterministic time-invariant feature extraction approach based on consecutive changes of basis and nonlinearities, namely, the scattering network. The first focus of the paper is to extend the scattering network to allow the use of higher order nonlinear…

We provide a computationally and statistically efficient method for estimating the parameters of a stochastic covariance model observed on a regular spatial grid in any number of dimensions. Our proposed method, which we call the Debiased Spatial Whittle likelihood, makes important corrections to the well-known Whittle…

Calibrates historical and implied correlations in energy markets.

New Fourier-based diffusion model improves high-frequency generation quality.

Bayesian calibration for BCP self-assembly models using image data and measure transport.

The paper sets sample complexity bounds for learning high-dimensional simplices in noisy data.

Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear regression setting, there is no clear concept of an effect size for regression coeffici…

Improved bounds for neural network approximations of functions.

Paper finds sample complexity for learning high-dimensional simplices from noisy data.

A new method integrates Fourier basis expansion and mapping for improved time series forecasting.

The paper uncovers the impact of price and payoff autocorrelations in multi-period asset pricing models.

Paper proves L2 regression can learn k-juntas without distributional assumptions.

Paper introduces benchmark-neutral pricing for long-term contracts.

We explore nature of price formation in financial markets and develop a theory of bid and ask price dynamics in which the two prices form due to quantum-chaotic interaction between buy and sell orders. In this model bid and ask prices are represented by eigenvalues of a 2x2 price operator corresponding to 'bid' and 'as…

New pricing algorithm learns demand curves and optimizes prices in dynamic markets.

In this paper we study dynamic pricing mechanisms of financial derivatives. A typical model of such pricing mechanism is the so-called g--expectation defined by solutions of a backward stochastic differential equation with g as its generating function. Black-Scholes pricing model is a special linear case of this pricin…