Pricing Lookback Options on a Quantum Computer

Florence Paquette, Tania Belabbas, Emmanuel Hamel and Anne MacKay

Papers from arXiv.org

Abstract: We develop a quantum algorithm to price discretely monitored lookback options in the Black-Scholes framework using imaginary time evolution. By rewriting the pricing PDE as a Schrodinger-type equation, the problem becomes the imaginary time evolution of a quantum state under a non-Hermitian Hamiltonian. This evolution is approximated with the Variational Quantum imaginary time evolution (VarQITE) method, which replaces the exact non-unitary dynamics with a parameterized, hardware-efficient quantum circuit. A central challenge arises from jump conditions caused by the discrete updating of the running maximum. This feature is not present in standard quantum treatments of European or Asian options. To address this, we propose two quantum-compatible formulations: (i) a sequential approach that models jumps via dedicated jump Hamiltonians applied at monitoring dates, and (ii) a simultaneous multi-function evolution that removes explicit jumps at the expense of an increased number of dimensions. We compare both approaches in terms of qubit resources, circuit complexity and numerical accuracy, and benchmark them against Monte Carlo simulations. Our results show that discretely monitored, path-dependent options with jump conditions can be handled within a variational quantum framework, paving the way toward the quantum pricing of more complex derivatives with non-smooth dynamics.

Date: 2026-03
New Economics Papers: this item is included in nep-cmp
References: Add references at CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2604.00389 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2604.00389

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().