End-to-End PDE-Based Quantum Algorithms for Multi-Asset Option Pricing under Local and Stochastic Volatility
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Quantum Physics arXiv:2605.26610 (quant-ph) [Submitted on 26 May 2026] Title:End-to-End PDE-Based Quantum Algorithms for Multi-Asset Option Pricing under Local and Stochastic Volatility Authors:Nikita Guseynov, Nana Liu, Chi Seng Pun, Tushar Vaidya View a PDF of the paper titled End-to-End PDE-Based Quantum Algorithms for Multi-Asset Option Pricing under Local and Stochastic Volatility, by Nikita Guseynov and 3 other authors View PDF HTML (experimental) Abstract:Multi-asset option pricing under local- and stochastic-volatility models leads naturally to high-dimensional parabolic PDEs. We develop an end-to-end quantum PDE framework for European option pricing under local-volatility Black--Scholes and Heston models. The framework takes classical contract and model data as input and returns classical estimates of selected option values. We solve the pricing PDEs after finite-difference discretization on spatial grids. For $N=2^n$ grid points per spatial direction and $d$ assets, the end-to-end gate complexity for single-point recovery, counted in elementary CNOT gates and one-qubit Pauli-axis rotations, has leading grid-size dependence $\widetilde{O}(d^2 N^{2+d/2})$ for local-volatility Black--Scholes and $\widetilde{O}(d^2 N^{d+2})$ for Heston. Relative to grid-based finite-difference baselines, these scalings correspond to polynomial improvement factors $N^{d/2}$ and $N^d$, respectively. These estimates translate to Clifford+T resources via standard compilation. We complement the complexity analysis with numerical benchmarks against standard classical methods. In the Heston setting, the framework recovers option prices across strikes together with the associated implied-volatility smile/skew. Overall, this work provides a complete end-to-end quantum pricing pipeline with explicit resource accounting and theoretical performance guarantees. Comments: Subjects: Quantum Physics (quant-ph); Computational Finance (q-fin.CP) Cite as: arXiv:2605.26610 [quant-ph] (or arXiv:2605.26610v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.26610 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Nikita Guseynov [view email] [v1] Tue, 26 May 2026 06:46:40 UTC (5,263 KB) Full-text links: Access Paper: View a PDF of the paper titled End-to-End PDE-Based Quantum Algorithms for Multi-Asset Option Pricing under Local and Stochastic Volatility, by Nikita Guseynov and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: q-fin q-fin.CP References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)