IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2301.09241.html
   My bibliography  Save this paper

Quantum Monte Carlo algorithm for solving Black-Scholes PDEs for high-dimensional option pricing in finance and its complexity analysis

Author

Listed:
  • Jianjun Chen
  • Yongming Li
  • Ariel Neufeld

Abstract

In this paper we provide a quantum Monte Carlo algorithm to solve high-dimensional Black-Scholes PDEs with correlation for high-dimensional option pricing. The payoff function of the option is of general form and is only required to be continuous and piece-wise affine (CPWA), which covers most of the relevant payoff functions used in finance. We provide a rigorous error analysis and complexity analysis of our algorithm. In particular, we prove that the computational complexity of our algorithm is bounded polynomially in the space dimension $d$ of the PDE and the reciprocal of the prescribed accuracy $\varepsilon$. Moreover, we show that for payoff functions which are bounded, our algorithm indeed has a speed-up compared to classical Monte Carlo methods. Furthermore, we provide numerical simulations in one and two dimensions using our developed package within the Qiskit framework tailored to price CPWA options with respect to the Black-Scholes model, as well as discuss the potential extension of the numerical simulations to arbitrary space dimension.

Suggested Citation

  • Jianjun Chen & Yongming Li & Ariel Neufeld, 2023. "Quantum Monte Carlo algorithm for solving Black-Scholes PDEs for high-dimensional option pricing in finance and its complexity analysis," Papers 2301.09241, arXiv.org, revised Apr 2024.
    • Handle: RePEc:arx:papers:2301.09241
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2301.09241
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Shouvanik Chakrabarti & Rajiv Krishnakumar & Guglielmo Mazzola & Nikitas Stamatopoulos & Stefan Woerner & William J. Zeng, 2020. "A Threshold for Quantum Advantage in Derivative Pricing," Papers 2012.03819, arXiv.org, revised May 2021.
    2. Dong An & Noah Linden & Jin-Peng Liu & Ashley Montanaro & Changpeng Shao & Jiasu Wang, 2020. "Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance," Papers 2012.06283, arXiv.org, revised Jun 2021.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ariel Neufeld & Julian Sester, 2023. "Neural networks can detect model-free static arbitrage strategies," Papers 2306.16422, arXiv.org, revised Aug 2024.
    2. Antoine Jacquier & Oleksiy Kondratyev & Gordon Lee & Mugad Oumgari, 2023. "Quantum Computing for Financial Mathematics," Papers 2311.06621, arXiv.org.
    3. Raj G. Patel & Tomas Dominguez & Mohammad Dib & Samuel Palmer & Andrea Cadarso & Fernando De Lope Contreras & Abdelkader Ratnani & Francisco Gomez Casanova & Senaida Hern'andez-Santana & 'Alvaro D'iaz, 2023. "Application of Tensor Neural Networks to Pricing Bermudan Swaptions," Papers 2304.09750, arXiv.org, revised Mar 2024.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yen-Jui Chang & Wei-Ting Wang & Hao-Yuan Chen & Shih-Wei Liao & Ching-Ray Chang, 2023. "Preparing random state for quantum financing with quantum walks," Papers 2302.12500, arXiv.org, revised Mar 2023.
    2. Abha Naik & Esra Yeniaras & Gerhard Hellstern & Grishma Prasad & Sanjay Kumar Lalta Prasad Vishwakarma, 2023. "From Portfolio Optimization to Quantum Blockchain and Security: A Systematic Review of Quantum Computing in Finance," Papers 2307.01155, arXiv.org.
    3. Koichi Miyamoto & Kenji Kubo, 2021. "Pricing multi-asset derivatives by finite difference method on a quantum computer," Papers 2109.12896, arXiv.org.
    4. Mark-Oliver Wolf & Tom Ewen & Ivica Turkalj, 2023. "Quantum Architecture Search for Quantum Monte Carlo Integration via Conditional Parameterized Circuits with Application to Finance," Papers 2304.08793, arXiv.org, revised Sep 2023.
    5. Roman Rietsche & Christian Dremel & Samuel Bosch & Léa Steinacker & Miriam Meckel & Jan-Marco Leimeister, 2022. "Quantum computing," Electronic Markets, Springer;IIM University of St. Gallen, vol. 32(4), pages 2525-2536, December.
    6. Yen-Jui Chang & Wei-Ting Wang & Hao-Yuan Chen & Shih-Wei Liao & Ching-Ray Chang, 2023. "A novel approach for quantum financial simulation and quantum state preparation," Papers 2308.01844, arXiv.org, revised Apr 2024.
    7. Francesca Cibrario & Or Samimi Golan & Giacomo Ranieri & Emanuele Dri & Mattia Ippoliti & Ron Cohen & Christian Mattia & Bartolomeo Montrucchio & Amir Naveh & Davide Corbelletto, 2024. "Quantum Amplitude Loading for Rainbow Options Pricing," Papers 2402.05574, arXiv.org, revised Oct 2024.
    8. Dylan Herman & Cody Googin & Xiaoyuan Liu & Alexey Galda & Ilya Safro & Yue Sun & Marco Pistoia & Yuri Alexeev, 2022. "A Survey of Quantum Computing for Finance," Papers 2201.02773, arXiv.org, revised Jun 2022.
    9. Jo~ao F. Doriguello & Alessandro Luongo & Jinge Bao & Patrick Rebentrost & Miklos Santha, 2021. "Quantum algorithm for stochastic optimal stopping problems with applications in finance," Papers 2111.15332, arXiv.org, revised Jul 2023.
    10. Skavysh, Vladimir & Priazhkina, Sofia & Guala, Diego & Bromley, Thomas R., 2023. "Quantum monte carlo for economics: Stress testing and macroeconomic deep learning," Journal of Economic Dynamics and Control, Elsevier, vol. 153(C).
    11. Vladimir Skavysh & Sofia Priazhkina & Diego Guala & Thomas Bromley, 2022. "Quantum Monte Carlo for Economics: Stress Testing and Macroeconomic Deep Learning," Staff Working Papers 22-29, Bank of Canada.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2301.09241. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.