Tensor train representations of Greeks for Fourier-based pricing of multi-asset options

• URL: http://arxiv.org/abs/2507.08482v1
• Date: Fri, 11 Jul 2025 10:51:17 GMT
• Title: Tensor train representations of Greeks for Fourier-based pricing of multi-asset options
• Abstract summary: Efficient computation of Greeks for multi-asset options remains a key challenge in quantitative finance.<n>We propose a framework to compute Greeks in a single evaluation of a tensor train (TT)<n> Numerical experiments on a five-asset min-call option in the Black-Sholes model show significant speed-ups of up to about $105 times$ over Monte Carlo simulation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Efficient computation of Greeks for multi-asset options remains a key challenge in quantitative finance. While Monte Carlo (MC) simulation is widely used, it suffers from the large sample complexity for high accuracy. We propose a framework to compute Greeks in a single evaluation of a tensor train (TT), which is obtained by compressing the Fourier transform (FT)-based pricing function via TT learning using tensor cross interpolation. Based on this TT representation, we introduce two approaches to compute Greeks: a numerical differentiation (ND) approach that applies a numerical differential operator to one tensor core and an analytical (AN) approach that constructs the TT of closed-form differentiation expressions of FT-based pricing. Numerical experiments on a five-asset min-call option in the Black-Sholes model show significant speed-ups of up to about $10^{5} \times$ over MC while maintaining comparable accuracy. The ND approach matches or exceeds the accuracy of the AN approach and requires lower computational complexity for constructing the TT representation, making it the preferred choice.

Related papers

• Classical Tensor Network and Quantum Fourier Transform Approaches for Large-Scale Carr-Madan Option Pricing [1.0742675209112622]
  We reformulate the Carr-Madan pricing framework using tensor networks.<n>We show that the proposed SFFT method maintains pricing accuracy while substantially reducing memory requirements.<n>The accompanying quantum simulations and hardware executions enable a direct comparison between the classical tensor network formulation and its QFT-based quantum counterpart.
  arXiv  Detail & Related papers  (2026-07-30T16:12:44Z)
• Transformers Provably Learn to Internalize Chain-of-Thought [65.41010769606844]
  Implicit Chain-of-Thought (ICoT) trains models to internalize intermediate steps within their hidden states.<n>Log-ICoT removes thinking tokens one at a time, reducing the number of stages from linear in $k$ to logarithmic.<n>Experiments on multi-layer transformers confirm the theory and visualize how reasoning is progressively absorbed into deeper layers.
  arXiv  Detail & Related papers  (2026-05-27T15:17:06Z)
• Recursive Sketched Interpolation: Efficient Hadamard Products of Tensor Trains [3.1007879499686957]
  The Hadamard product of two tensors in the tensor-train (TT) format is a fundamental operation across various applications.<n>We introduce Recursive Sketched Interpolation (RSI), a scale product'' algorithm that computes the Hadamard product of TTs at a computational cost.
  arXiv  Detail & Related papers  (2026-02-20T04:07:37Z)
• Variational Entropic Optimal Transport [67.76725267984578]
  We propose Variational Entropic Optimal Transport (VarEOT) for domain translation problems.<n>VarEOT is based on an exact variational reformulation of the log-partition $log mathbbE[exp(cdot)$ as a tractable generalization over an auxiliary positive normalizer.<n> Experiments on synthetic data and unpaired image-to-image translation demonstrate competitive or improved translation quality.
  arXiv  Detail & Related papers  (2026-02-02T15:48:44Z)
• Laplace Approximation For Tensor Train Kernel Machines In System Identification [6.101839518775971]
  We introduce a Bayesian tensor train kernel machine that applies Laplace approximation to estimate the posterior distribution over a selected TT-core.<n>Experiments show that core selection is largely independent of TT-ranks and feature structure, and that VI replaces cross-validation while offering up to 65x faster training.
  arXiv  Detail & Related papers  (2025-12-02T08:55:59Z)
• FFT-Accelerated Auxiliary Variable MCMC for Fermionic Lattice Models: A Determinant-Free Approach with $O(N\log N)$ Complexity [52.3171766248012]
  We introduce a Markov Chain Monte Carlo (MCMC) algorithm that dramatically accelerates the simulation of quantum many-body systems.<n>We validate our algorithm on benchmark quantum physics problems, accurately reproducing known theoretical results.<n>Our work provides a powerful tool for large-scale probabilistic inference and opens avenues for physics-inspired generative models.
  arXiv  Detail & Related papers  (2025-10-13T07:57:21Z)
• Tensor Decomposition Networks for Fast Machine Learning Interatomic Potential Computations [63.945006006152035]
  tensor decomposition networks (TDNs) achieve competitive performance with dramatic speedup in computations.<n>We evaluate TDNs on PubChemQCR, a newly curated molecular relaxation dataset containing 105 million DFT-calculated snapshots.
  arXiv  Detail & Related papers  (2025-07-01T18:46:27Z)
• Fractured Chain-of-Thought Reasoning [61.647243580650446]
  We introduce Fractured Sampling, a unified inference-time strategy that interpolates between full CoT and solution-only sampling.<n>We show that Fractured Sampling consistently achieves superior accuracy-cost trade-offs, yielding steep log-linear scaling gains in Pass@k versus token budget.
  arXiv  Detail & Related papers  (2025-05-19T11:30:41Z)
• Benefits of Learning Rate Annealing for Tuning-Robustness in Stochastic Optimization [29.174036532175855]
  Learning rate in gradient methods is a critical hyperspecification that is notoriously costly to tune via standard grid search.<n>We identify a theoretical advantage of learning rate annealing schemes that decay the learning rate to zero at a rate, such as the widely-used cosine schedule.
  arXiv  Detail & Related papers  (2025-03-12T14:06:34Z)
• Unveiling the Statistical Foundations of Chain-of-Thought Prompting Methods [59.779795063072655]
  Chain-of-Thought (CoT) prompting and its variants have gained popularity as effective methods for solving multi-step reasoning problems. We analyze CoT prompting from a statistical estimation perspective, providing a comprehensive characterization of its sample complexity.
  arXiv  Detail & Related papers  (2024-08-25T04:07:18Z)
• Learning parameter dependence for Fourier-based option pricing with tensor trains [0.0]
  We propose a pricing method, where, by a tensor train learning algorithm, we build tensor trains that approximate functions appearing in FT-based option pricing.<n>As a benchmark test, we run the proposed method to price a multi-asset option for the various values of volatilities and present asset prices.<n>We show that, in the tested cases involving up to 11 assets, the proposed method outperforms Monte Carlo-based option pricing with $106$ paths in terms of computational complexity.
  arXiv  Detail & Related papers  (2024-04-17T01:57:19Z)
• D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory [79.50644650795012]
  We propose a deep learning approach to solve Kohn-Sham Density Functional Theory (KS-DFT) We prove that such an approach has the same expressivity as the SCF method, yet reduces the computational complexity. In addition, we show that our approach enables us to explore more complex neural-based wave functions.
  arXiv  Detail & Related papers  (2023-03-01T10:38:10Z)
• Stochastic optimal transport in Banach Spaces for regularized estimation of multivariate quantiles [0.0]
  We introduce a new algorithm for solving entropic optimal transport (EOT) between two absolutely continuous probability measures $mu$ and $nu$.<n>We study the almost sure convergence of our algorithm that takes its values in an infinite-dimensional Banach space.
  arXiv  Detail & Related papers  (2023-02-02T10:02:01Z)
• Matching Pursuit Based Scheduling for Over-the-Air Federated Learning [67.59503935237676]
  This paper develops a class of low-complexity device scheduling algorithms for over-the-air learning via the method of federated learning. Compared to the state-of-the-art proposed scheme, the proposed scheme poses a drastically lower efficiency system. The efficiency of the proposed scheme is confirmed via experiments on the CIFAR dataset.
  arXiv  Detail & Related papers  (2022-06-14T08:14:14Z)
• Permutation Compressors for Provably Faster Distributed Nonconvex Optimization [68.8204255655161]
  We show that the MARINA method of Gorbunov et al (2021) can be considered as a state-of-the-art method in terms of theoretical communication complexity. Theory of MARINA to support the theory of potentially em correlated compressors, extends to the method beyond the classical independent compressors setting.
  arXiv  Detail & Related papers  (2021-10-07T09:38:15Z)
• Provable Tensor-Train Format Tensor Completion by Riemannian Optimization [22.166436026482984]
  We provide the first theoretical guarantees of the convergence of RGrad algorithm for TT-format tensor completion. We also propose a novel approach, referred to as the sequential second-order moment method.
  arXiv  Detail & Related papers  (2021-08-27T08:13:58Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.