Option pricing under stochastic volatility on a quantum computer

Guoming Wang; Angus Kan

doi:10.22331/q-2024-10-23-1504

Option pricing under stochastic volatility on a quantum computer

ORCA Computing

Published:	2024-10-23, volume 8, page 1504
Eprint:	arXiv:2312.15871v3
Doi:	https://doi.org/10.22331/q-2024-10-23-1504
Citation:	Quantum 8, 1504 (2024).

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Abstract

We develop quantum algorithms for pricing Asian and barrier options under the Heston model, a popular stochastic volatility model, and estimate their costs, in terms of T-count, T-depth and number of logical qubits, on instances under typical market conditions. These algorithms are based on combining well-established numerical methods for stochastic differential equations and quantum amplitude estimation technique. In particular, we empirically show that, despite its simplicity, weak Euler method achieves the same level of accuracy as the better-known strong Euler method in this task. Furthermore, by eliminating the expensive procedure of preparing Gaussian states, the quantum algorithm based on weak Euler scheme achieves drastically better efficiency than the one based on strong Euler scheme. Our resource analysis suggests that option pricing under stochastic volatility is a promising application of quantum computers, and that our algorithms render the hardware requirement for reaching practical quantum advantage in financial applications less stringent than prior art.

► BibTeX data

@article{Wang2024optionpricingunder,
  doi = {10.22331/q-2024-10-23-1504},
  url = {https://doi.org/10.22331/q-2024-10-23-1504},
  title = {Option pricing under stochastic volatility on a quantum computer},
  author = {Wang, Guoming and Kan, Angus},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1504},
  month = oct,
  year = {2024}
}

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