A new algorithm computes Fourier coefficients for a specified range efficiently.
problem Inefficiency in FFT due to fixed output size for all applications.
method Fast Partial Fourier Transform (PFT) that allows specifying the range of Fourier coefficients to compute.
result PFT achieves significant speedup over state-of-the-art FFT algorithms for small output sizes.
Enhances Fourier estimator performance for asynchronous event-data.
problem Improving correlation and covariance estimation on event-data.
method Implement and test NUFFT methods with different averaging kernels.
result Demonstrates improved performance and relationship between averaging scales.
Efficient trainable front-end for neural speech enhancement.
problem Inefficient STFT front-ends in neural speech enhancement models.
method Butterfly mechanism for Fast Fourier Transform, trainable STFT window.
result Accuracy and efficiency improvements for low-compute systems.
A new NUFFT method speeds up option pricing for various strikes.
problem Efficiently pricing many options of the same maturity but different strikes.
method Non-uniform fast Fourier transform (NUFFT) applied to the COS method.
result Significantly faster computation of option prices.
The paper calculates option prices for assets with stochastic volatility using FFT.
problem Calculating option prices for assets with stochastic volatility.
method Assumed normal asset dynamics with stochastic volatility following CIR process. Used FFT for evaluation and compared with Monte Carlo simulation.
result Comparison of FFT and Monte Carlo results for option pricing.
Analytical pricing formulas and Greeks are obtained for European and American basket put options using Mellin transforms. We assume assets are driven by geometric Brownian motion which exhibit correlation and pay a continuous dividend rate. A novel approach to numerical Mellin inversion is achieved via the fast Fourier…
Efficiently approximates eigenspaces for symmetric and general matrices.
problem Fast computation of eigenspaces for large matrices.
method Factor eigenspaces into fundamental components using transformations, solve minimization problems, and iteratively update.
result Improved computational efficiency for eigenspace approximation.
New method for calculating forex options using LRM for Lévy models.
problem Calculating local risk minimization for forex options in Lévy models.
method Transformed representation of LRM into fast Fourier transform form.
result Validated the method on Merton jump-diffusion and variance gamma models.
New algorithm for 2D SWDFT reduces redundant calculations.
problem Redundant calculations in overlapping windows for 2D SWDFT.
method Tree data structure based on Cooley-Tukey FFT for efficient computation.
result Our algorithm reduces operations to O(N0N1n0n1). Scalable kernel methods for large datasets using Fourier representations and NUFFT.
problem Cubic complexity in kernel methods limits their use on large-scale datasets.
method Fourier representation of kernels combined with NUFFT for O(n log n) complexity.
result Achieves minimax convergence rates and processes up to tens of billions of samples.
GWNN uses graph wavelets for efficient graph CNNs.
problem Spectral graph CNNs' high computational cost and lack of interpretability.
method Graph wavelet transform for efficient graph convolution.
result GWNN significantly outperforms spectral graph CNNs.
A hybrid framework uses machine learning to price options faster and more accurately.
problem Rapid recalibration of option pricing models in dynamic markets.
method Integrates smooth offset algorithm with supervised machine learning models.
result Surrogate pricing operators achieve up to 1000x speedup over direct SOA evaluation.
We propose a new method for the numerical solution of backward stochastic differential equations (BSDEs) which finds its roots in Fourier analysis. The method consists of an Euler time discretization of the BSDE with certain conditional expectations expressed in terms of Fourier transforms and computed using the fast F…
This work improves Fourier pricing for multi-asset options using RQMC with domain transformation.
problem Efficiently pricing multi-asset options in high dimensions with Fourier methods.
method Randomized quasi-Monte Carlo (RQMC) with domain transformation to handle singularities.
result RQMC with domain transformation provides accurate and scalable Fourier pricing for multi-asset options.
Improved numerical solution for BSDEs with reduced boundary errors.
problem Boundary errors in numerical solution of BSDEs.
method Modified damping and shifting schemes to transform target function into a bounded periodic function, applying Fourier transforms.
result Significant reduction in boundary errors with improved accuracy and convergence.
Deep networks struggle to learn efficient representations of simple functions.
problem Can deep learning methods find efficient representations of simple functions?
method Trained deep neural networks on the parity function and fast Fourier transform, using gradient-based optimization.
result Deep networks require initialization close to exact solutions to learn efficient representations of simple functions.
A method for pricing Bermudan options in a defaultable asset model.
problem Pricing Bermudan options in a model with local volatility, default intensity, and locally dependent Lévy measure.
method Analytical approximation of the characteristic function combined with the COS method, Fast Fourier Transform-based algorithm.
result Fast and accurate calculation of option prices with almost no additional computational cost for Greeks.
FIt-SNE accelerates t-SNE for large datasets.
problem Slow computation of t-SNE for large datasets.
method Interpolation-based t-SNE (FIt-SNE) using FFT and oocPCA.
result Significant acceleration of t-SNE computation for large datasets.
New method for optimizing risk in financial models using Fourier transforms.
problem Optimizing risk in financial models with multi-period mean-CVaR.
method Strictly monotone 2D integration scheme via Fourier-trained transition kernels.
result Established robust and accurate optimization method for financial models.
In this paper we consider Fourier transform techniques to efficiently compute the Value-at-Risk and the Conditional Value-at-Risk of an arbitrary loss random variable, characterized by having a computable generalized characteristic function. We exploit the property of these risk measures of being the solution of an ele…
Spread options are a fundamental class of derivative contract written on multiple assets, and are widely used in a range of financial markets. There is a long history of approximation methods for computing such products, but as yet there is no preferred approach that is accurate, efficient and flexible enough to apply …
New algorithm for estimating multivariate quantiles using stochastic optimal transport.
problem Estimating multivariate quantiles from data.
method Stochastic algorithm for entropic optimal transport in Banach spaces, using Fourier coefficients.
result Almost sure convergence of the stochastic algorithm in infinite-dimensional Banach spaces.
DAFNO learns surrogates for complex systems on irregular geometries.
problem Learning accurate surrogates for complex physical systems on irregular geometries.
method DAFNO incorporates a smoothed characteristic function in the integral layer architecture of FNOs, leveraging FFT for rapid computations.
result DAFNO achieves state-of-the-art accuracy on material modeling and airfoil simulation datasets.
Quantum algorithm for pricing European call options.
problem Accurate valuation of financial derivatives, especially for complex models and options.
method Transforms classical FFT into quantum QFT for pricing European call options.
result Quantum algorithm outperforms classical Monte Carlo simulation in NISQ era.
A fast calibration method for rough volatility models with jumps.
problem Calibrating stochastic volatility models to market data efficiently.
method Structure-preserving approach: split pricing formula, precompute data-independent integrals, and approximate market-dependent remainder with neural networks.
result Calibration achieves high accuracy and speed, and a pure-jump rough volatility model adequately captures VIX dynamics.
Sp(n)-instantons linked to complex Lagrangian graphs via Fourier-Mukai transform.
problem Understanding Sp(n)-instantons on hyperkahler manifolds with conical singularities.
method Relating Sp(n)-instantons to deformed instantons and studying their properties on hyperkahler manifolds.
result Sp(n)-instantons on hyperkahler manifolds correspond to tri-contact instantons on the 3-Sasakian link.
The paper provides VIX option pricing and hedging strategies for two stochastic volatility models.
problem Pricing and hedging of VIX options for specific stochastic volatility models.
method Develops representations of VIX call option prices and locally risk-minimizing strategies for Barndorff-Nielsen and Shephard models.
result Efficient representations and locally risk-minimizing strategies for numerical methods.
New algorithm reduces dictionary learning complexity.
problem Efficiently learning dictionaries from high-dimensional data.
method IcTKM algorithm using dimensionality reduction and fast Fourier transform.
result Locally recovers dictionary with high probability.
New neural network improves MRI reconstruction for non-Cartesian data.
problem Improving MRI reconstruction for non-Cartesian data acquisitions.
method Density-compensated unrolled neural networks.
result Density-compensated unrolled neural networks outperform baselines.
Random Fourier features improve tabular deep learning convergence.
problem Tabular deep learning convergence issues.
method Random Fourier projections as a pre-processing step, projecting inputs into a fixed feature space.
result Random Fourier pre-processing accelerates tabular deep learning convergence.
A robust method for decomposing spectral peaks robust to distortion and interference.
problem Decomposing spectral peaks in the presence of distortion and interference.
method Optimizing a nonparametric approach using pseudo-symmetric functions with nonincreasing behavior.
result Decomposed spectral peaks show pseudo-orthogonal behavior and power preserving equality.
New tensor method for faster, more accurate convolutional dictionary learning.
problem Learning shift-invariant models with additional invariances.
method Developed novel tensor decomposition algorithms based on alternating least squares with efficient projections onto circulant matrices.
result Our method converges faster and more accurately to the dictionary compared to existing methods.
Automatically learns efficient algorithms for structured transforms like FFT.
problem Efficient algorithms for structured linear transforms.
method Generic parameterization of divide-and-conquer methods.
result Reproduces Cooley-Tukey FFT algorithm to machine precision.
A new method speeds up financial option pricing.
problem Efficiently pricing financial options.
method Adapting empirical magic point interpolation for Fourier-based parametric pricing.
result Significant efficiency gain in option pricing, even for complex cases.
The paper proposes efficient dictionary learning algorithms that avoid multiplications for sparse representations.
problem Sparse representation with reduced computational complexity.
method Factorizations of the dictionary into binary orthonormal, scaling, and shear transformations with closed-form solutions.
result The proposed methods are effective and can be compared to well-known transforms like FFT and DCT.
A new quasi-Newton method tackles NMF with transform learning on orthogonal manifolds.
problem Efficiently learning transforms for NMF in non-convex optimization on orthogonal manifolds.
method Derives a quasi-Newton method on the orthogonal matrix manifold using sparse approximations of the Hessian.
result Outperforms state-of-the-art methods by orders of magnitude in experiments on synthetic and real audio data.
Spectral filters enhance option pricing methods using Hilbert transforms.
problem Improving convergence rates of option pricing methods.
method Using spectral filters to improve convergence of numerical schemes based on discrete Hilbert transforms.
result Improved convergence rates, especially polynomial convergence, achieved with spectral filtering.
New method improves option pricing for non-smooth functions.
problem Inefficiency of Fourier techniques with non-smooth probability density functions.
method Singular Fourier-Padé (SFP) method
result Restores global spectral convergence rate and fast error convergence.
The computation of Greeks for exponential Lévy models are usually approached by Malliavin Calculus and other methods, as the Likelihood Ratio and the finite difference method. In this paper we obtain exact formulas for Greeks of European options based on the Lewis formula for the option value. Therefore, it is possible…
Paper proves Fourier transform for valuations, simplifying previous work.
problem Existence of isomorphism for translation-invariant smooth valuations.
method Directly describes Alesker's isomorphism in terms of Fourier transform on functions.
result Simple proofs of Alesker's Fourier transform properties, including a previously conjectured result.
Paper proposes a method to numerically approximate differential privacy guarantees using FFT.
problem Computing tight differential privacy guarantees for machine learning algorithms.
method The method uses numerical approximation of an integral formula, discretization, and the fast Fourier transform algorithm.
result Significant improvements in bound tightness and computation time compared to state-of-the-art techniques.
A new SINC method for fast and accurate option pricing.
problem Computing option prices efficiently and accurately.
method SINC approach based on Shannon Sampling Theorem.
result SINC provides the most accurate and fast pricing computation.
The convolution method for the numerical solution of forward-backward stochastic differential equations (FBSDEs), introduced in [21], uses a uniform space grid. In this paper we utilize a tree-like spatial discretization that approximates the BSDE on the tree, so that no spatial interpolation procedure is necessary. In…
The study compares Fourier-based pricing methods, identifying the most efficient and accurate.
problem Comparing CPU effort and pricing biases of Fourier-based implementations.
method Numerical analysis of seven Fourier-based implementations, focusing on truncation and discretization errors.
result The multi-strike version of the COS method is notably faster, and the strike-optimized Carr Madan's formula is both faster and more accurate.
New MCMC method speeds up quantum physics simulations by a factor of 100.
problem Simulating quantum many-body systems with high computational complexity.
method FFT-accelerated MCMC with coupled particle and auxiliary variables.
result Achieves O(NlogN) scaling, significantly faster than traditional O(N3) methods. Simplified Butterfly-Net2 improves CNN efficiency in solving PDEs and signal processing tasks.
problem Improving CNN efficiency in solving PDEs and signal processing tasks.
method Introducing BNet2, a simplified Butterfly-Net, and Fourier transform initialization.
result BNet2 achieves similar accuracy as CNN but with fewer parameters and improves accuracy over randomly initialized CNN.
A new method slices and sums radial kernels faster.
problem Fast computation of large kernel sums in kernel methods.
method Random projections to 1D subspaces and QMC for selecting projections.
result QMC-slicing outperforms existing methods on test datasets.
A new method solves complex financial equations efficiently.
problem Solving worst-case and best-case prices for two-factor uncertain volatility models.
method Decompose and integrate, then optimize; piecewise constant control; closed-form Green's functions; 2D convolution integrals; monotone numerical integration; Fast Fourier Transforms.
result The method efficiently computes the value function and optimal control, converging to the viscosity solution of the HJB equation.