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Quantum-inspired variational algorithms for partial differential equations: Application to financial derivative pricing

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Listed:
  • Tianchen Zhao
  • Chuhao Sun
  • Asaf Cohen
  • James Stokes
  • Shravan Veerapaneni

Abstract

Variational quantum Monte Carlo (VMC) combined with neural-network quantum states offers a novel angle of attack on the curse-of-dimensionality encountered in a particular class of partial differential equations (PDEs); namely, the real- and imaginary time-dependent Schr\"odinger equation. In this paper, we present a simple generalization of VMC applicable to arbitrary time-dependent PDEs, showcasing the technique in the multi-asset Black-Scholes PDE for pricing European options contingent on many correlated underlying assets.

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  • Tianchen Zhao & Chuhao Sun & Asaf Cohen & James Stokes & Shravan Veerapaneni, 2022. "Quantum-inspired variational algorithms for partial differential equations: Application to financial derivative pricing," Papers 2207.10838, arXiv.org.
    • Handle: RePEc:arx:papers:2207.10838
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    References listed on IDEAS

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    1. Tristan Guillaume, 2019. "On the multidimensional Black–Scholes partial differential equation," Annals of Operations Research, Springer, vol. 281(1), pages 229-251, October.
    2. Filipe Fontanela & Antoine Jacquier & Mugad Oumgari, 2019. "A Quantum algorithm for linear PDEs arising in Finance," Papers 1912.02753, arXiv.org, revised Feb 2021.
    3. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
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