Boosting Binomial Exotic Option Pricing with Tensor Networks

• URL: http://arxiv.org/abs/2505.17033v1
• Date: Wed, 07 May 2025 18:01:13 GMT
• Title: Boosting Binomial Exotic Option Pricing with Tensor Networks
• Authors: Maarten van Damme, Rishi Sreedhar, Martin Ganahl,
• Abstract summary: Pricing of exotic financial derivatives, such as Asian and multi-asset American basket options, poses significant challenges.<n>This work combines the binomial pricing method for options with tensor network techniques, specifically Matrix Product States (MPS)<n>Our proposed methods scale linearly with the parameters of interest and significantly reduce the computational complexity of pricing exotics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Pricing of exotic financial derivatives, such as Asian and multi-asset American basket options, poses significant challenges for standard numerical methods such as binomial trees or Monte Carlo methods. While the former often scales exponentially with the parameters of interest, the latter often requires expensive simulations to obtain sufficient statistical convergence. This work combines the binomial pricing method for options with tensor network techniques, specifically Matrix Product States (MPS), to overcome these challenges. Our proposed methods scale linearly with the parameters of interest and significantly reduce the computational complexity of pricing exotics compared to conventional methods. For Asian options, we present two methods: a tensor train cross approximation-based method for pricing, and a variational pricing method using MPS, which provides a stringent lower bound on option prices. For multi-asset American basket options, we combine the decoupled trees technique with the tensor train cross approximation to efficiently handle baskets of up to $m = 8$ correlated assets. All approaches scale linearly in the number of discretization steps $N$ for Asian options, and the number of assets $m$ for multi-asset options. Our numerical experiments underscore the high potential of tensor network methods as highly efficient simulation and optimization tools for financial engineering.

Related papers

• MaskPro: Linear-Space Probabilistic Learning for Strict (N:M)-Sparsity on Large Language Models [53.36415620647177]
  Semi-structured sparsity offers a promising solution by strategically retaining $N$ elements out of every $M$ weights.<n>Existing (N:M)-compatible approaches typically fall into two categories: rule-based layerwise greedy search, which suffers from considerable errors, and gradient-driven learning, which incurs prohibitive training costs.<n>We propose a novel linear-space probabilistic framework named MaskPro, which aims to learn a prior categorical distribution for every $M$ consecutive weights and subsequently leverages this distribution to generate the (N:M)-sparsity throughout an $N$-way sampling
  arXiv  Detail & Related papers  (2025-06-15T15:02:59Z)
• Stacey: Promoting Stochastic Steepest Descent via Accelerated $\ell_p$-Smooth Nonconvex Optimization [15.179519413549086]
  We introduce a new accelerated $ell_p$ steepest descent algorithm, called Stacey, to handle non-Euclidean smooth optimization tasks.<n>In addition to providing theoretical guarantees for the foundations of our algorithm, we empirically compare our approach against popular methods.
  arXiv  Detail & Related papers  (2025-06-07T00:47:07Z)
• Monte-Carlo Option Pricing in Quantum Parallel [2.6892244525119184]
  We develop an effective method for simulating many potential asset paths in quantum parallel, leading to a highly accurate final distribution of stock prices.<n>We demonstrate how this algorithm can be extended to price more complex options and analyze risk within derivative portfolios.
  arXiv  Detail & Related papers  (2025-05-14T15:10:27Z)
• Achieving $\widetilde{\mathcal{O}}(\sqrt{T})$ Regret in Average-Reward POMDPs with Known Observation Models [56.92178753201331]
  We tackle average-reward infinite-horizon POMDPs with an unknown transition model.<n>We present a novel and simple estimator that overcomes this barrier.
  arXiv  Detail & Related papers  (2025-01-30T22:29:41Z)
• $f$-PO: Generalizing Preference Optimization with $f$-divergence Minimization [54.94545757220999]
  $f$-PO is a novel framework that generalizes and extends existing approaches.<n>We conduct experiments on state-of-the-art language models using benchmark datasets.
  arXiv  Detail & Related papers  (2024-10-29T02:11:45Z)
• 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)
• A Specialized Semismooth Newton Method for Kernel-Based Optimal Transport [92.96250725599958]
  Kernel-based optimal transport (OT) estimators offer an alternative, functional estimation procedure to address OT problems from samples. We show that our SSN method achieves a global convergence rate of $O (1/sqrtk)$, and a local quadratic convergence rate under standard regularity conditions.
  arXiv  Detail & Related papers  (2023-10-21T18:48:45Z)
• Integrated Variational Fourier Features for Fast Spatial Modelling with Gaussian Processes [7.5991638205413325]
  For $N$ training points, exact inference has $O(N3)$ cost; with $M ll N$ features, state of the art sparse variational methods have $O(NM2)$ cost. Recently, methods have been proposed using more sophisticated features; these promise $O(M3)$ cost, with good performance in low dimensional tasks such as spatial modelling, but they only work with a very limited class of kernels, excluding some of the most commonly used. In this work, we propose integrated Fourier features, which extends these performance benefits to a very broad class of stationary co
  arXiv  Detail & Related papers  (2023-08-27T15:44:28Z)
• Symmetric Tensor Networks for Generative Modeling and Constrained Combinatorial Optimization [72.41480594026815]
  Constrained optimization problems abound in industry, from portfolio optimization to logistics. One of the major roadblocks in solving these problems is the presence of non-trivial hard constraints which limit the valid search space. In this work, we encode arbitrary integer-valued equality constraints of the form Ax=b, directly into U(1) symmetric networks (TNs) and leverage their applicability as quantum-inspired generative models.
  arXiv  Detail & Related papers  (2022-11-16T18:59:54Z)
• Asymmetric Scalable Cross-modal Hashing [51.309905690367835]
  Cross-modal hashing is a successful method to solve large-scale multimedia retrieval issue. We propose a novel Asymmetric Scalable Cross-Modal Hashing (ASCMH) to address these issues. Our ASCMH outperforms the state-of-the-art cross-modal hashing methods in terms of accuracy and efficiency.
  arXiv  Detail & Related papers  (2022-07-26T04:38:47Z)
• Statistical Inference of Constrained Stochastic Optimization via Sketched Sequential Quadratic Programming [53.63469275932989]
  We consider online statistical inference of constrained nonlinear optimization problems.<n>We apply the Sequential Quadratic Programming (StoSQP) method to solve these problems.
  arXiv  Detail & Related papers  (2022-05-27T00:34:03Z)
• Random Manifold Sampling and Joint Sparse Regularization for Multi-label Feature Selection [0.0]
  The model proposed in this paper can obtain the most relevant few features by solving the joint constrained optimization problems of $ell_2,1$ and $ell_F$ regularization. Comparative experiments on real-world data sets show that the proposed method outperforms other methods.
  arXiv  Detail & Related papers  (2022-04-13T15:06:12Z)

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.