Solving 2D Black Scholes Equation via Hermitian Block Embedding and Generalised Quantum Signal Processing
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Quantum Physics arXiv:2606.00458 (quant-ph) [Submitted on 30 May 2026] Title:Solving 2D Black Scholes Equation via Hermitian Block Embedding and Generalised Quantum Signal Processing Authors:James W. Greenwell, Jingbo Wang, Des Hill View a PDF of the paper titled Solving 2D Black Scholes Equation via Hermitian Block Embedding and Generalised Quantum Signal Processing, by James W. Greenwell and 2 other authors View PDF HTML (experimental) Abstract:The Black Scholes equation provides a fundamental model for the no arbitrage pricing of financial derivatives. After finite difference discretisation, the pricing problem can be formulated as a finite dimensional linear algebra problem involving the inverse of a non Hermitian time step matrix. Recent advances in quantum linear algebra algorithms, particularly the generalised quantum signal processing (GQSP)algorithm, enable matrix functions to be implemented through polynomial transformations of a suitable unitary or Hermitian form. In this paper, we develop a Hermitian block embedding method that enables GQSP to be applied to the two dimensional Black Scholes equation. Numerical simulations for two asset European call options are performed to evaluate the proposed approach. GQSP based solutions are benchmarked against the classical polynomial approximation with backward Euler finite difference method, showing close agreement. This indicates that the Hermitian block embedding construction accurately captures the dynamics of the original non Hermitian operator. These results demonstrate the feasibility of combining Hermitian block embeddings with GQSP for multidimensional Black Scholes problems and provide a proof of principle for applying modern quantum linear algebra techniques to option pricing. Subjects: Quantum Physics (quant-ph); Numerical Analysis (math.NA) Cite as: arXiv:2606.00458 [quant-ph] (or arXiv:2606.00458v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.00458 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jingbo Wang [view email] [v1] Sat, 30 May 2026 00:51:52 UTC (6,250 KB) Full-text links: Access Paper: View a PDF of the paper titled Solving 2D Black Scholes Equation via Hermitian Block Embedding and Generalised Quantum Signal Processing, by James W. Greenwell and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cs cs.NA math math.NA 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?)