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Quantum Monte Carlo simulations for financial risk analytics: scenario generation for equity, rate, and credit risk factors

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  • Titos Matsakos
  • Stuart Nield

Abstract

Monte Carlo (MC) simulations are widely used in financial risk management, from estimating value-at-risk (VaR) to pricing over-the-counter derivatives. However, they come at a significant computational cost due to the number of scenarios required for convergence. If a probability distribution is available, Quantum Amplitude Estimation (QAE) algorithms can provide a quadratic speed-up in measuring its properties as compared to their classical counterparts. Recent studies have explored the calculation of common risk measures and the optimisation of QAE algorithms by initialising the input quantum states with pre-computed probability distributions. If such distributions are not available in closed form, however, they need to be generated numerically, and the associated computational cost may limit the quantum advantage. In this paper, we bypass this challenge by incorporating scenario generation -- i.e. simulation of the risk factor evolution over time to generate probability distributions -- into the quantum computation; we refer to this process as Quantum MC (QMC) simulations. Specifically, we assemble quantum circuits that implement stochastic models for equity (geometric Brownian motion), interest rate (mean-reversion models), and credit (structural, reduced-form, and rating migration credit models) risk factors. We then integrate these models with QAE to provide end-to-end examples for both market and credit risk use cases.

Suggested Citation

  • Titos Matsakos & Stuart Nield, 2023. "Quantum Monte Carlo simulations for financial risk analytics: scenario generation for equity, rate, and credit risk factors," Papers 2303.09682, arXiv.org, revised Mar 2024.
  • Handle: RePEc:arx:papers:2303.09682
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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. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    3. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
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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.

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