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Quantum advantage for multi-option portfolio pricing and valuation adjustments

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  • Jeong Yu Han
  • Patrick Rebentrost

Abstract

A critical problem in the financial world deals with the management of risk, from regulatory risk to portfolio risk. Many such problems involve the analysis of securities modelled by complex dynamics that cannot be captured analytically, and hence rely on numerical techniques that simulate the stochastic nature of the underlying variables. These techniques may be computationally difficult or demanding. Hence, improving these methods offers a variety of opportunities for quantum algorithms. In this work, we study the problem of Credit Valuation Adjustments (CVAs) which have significant importance in the valuation of derivative portfolios. We propose quantum algorithms that accelerate statistical sampling processes to approximate the CVA under different measures of dispersion, using known techniques in Quantum Monte Carlo (QMC) and analyse the conditions under which we may employ these techniques.

Suggested Citation

  • Jeong Yu Han & Patrick Rebentrost, 2022. "Quantum advantage for multi-option portfolio pricing and valuation adjustments," Papers 2203.04924, arXiv.org.
    • Handle: RePEc:arx:papers:2203.04924
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    References listed on IDEAS

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    1. Javier Alcazar & Andrea Cadarso & Amara Katabarwa & Marta Mauri & Borja Peropadre & Guoming Wang & Yudong Cao, 2021. "Quantum algorithm for credit valuation adjustments," Papers 2105.12087, arXiv.org.
    2. Adam Bouland & Wim van Dam & Hamed Joorati & Iordanis Kerenidis & Anupam Prakash, 2020. "Prospects and challenges of quantum finance," Papers 2011.06492, arXiv.org.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    5. 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.
    6. Jian-Huang She & Dan Grecu, 2018. "Neural Network for CVA: Learning Future Values," Papers 1811.08726, arXiv.org.
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    Cited by:

    1. 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.
    2. Jinge Bao & Patrick Rebentrost, 2022. "Fundamental theorem for quantum asset pricing," Papers 2212.13815, arXiv.org, revised Apr 2023.

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