Finance-Informed Operator Learning for Option Pricing with Quantum-Compatible Realizations
Abstract
Pricing European options under local volatility requires repeatedly solving a PDE whose coefficients change with recalibration, while practitioners need both prices and sensitivities across spot-time surfaces. Neural surrogates can amortize these solves, but near expiry the solution loses regularity, making curvature difficult to learn and allowing violations of no-arbitrage bounds. We propose a finance-informed Deep Operator Network (FI-DeepONet) that decomposes the pricing operator into an input-dependent Black-Scholes carrier and a learned correction. The carrier uses strike-line integrated variance, capturing the leading near-expiry curvature singularity, while a smooth monotone Financial Admissibility Layer enforces pointwise price bounds. We derive a short-maturity estimate and differentiated asymptotics for the exact correction, together with identities linking correction error to price, sensitivity, and PDE-residual errors. On in-distribution tests, FI-DeepONet reduces global relative price error by nearly an order of magnitude versus vanilla and physics-informed DeepONet baselines. On parameter-shift OOD tests within the same local-volatility family, generalization is moderate. On index-option data, the frozen model remains accurate without market-specific retraining, though it does not outperform the same-input analytic formula. We also give a quantum-compatible realization in which selected linear maps are exactly compiled or approximated by a restricted diagonal-orthogonal family before supervised adaptation.
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BibTeX
@misc{feng2026financeinformed,
title = {{Finance-Informed Operator Learning for Option Pricing with Quantum-Compatible Realizations}},
author = {Jiarui Feng and Bingyang Hu and Yu Jiang and Changhong Mou and Yeyu Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.33213},
eprint = {2609.33213},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33213},
}
RIS
TY - UNPB
TI - Finance-Informed Operator Learning for Option Pricing with Quantum-Compatible Realizations
AU - Jiarui Feng
AU - Bingyang Hu
AU - Yu Jiang
AU - Changhong Mou
AU - Yeyu Zhang
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2609.33213
UR - https://arxiv.org/abs/2609.33213
AB - Pricing European options under local volatility requires repeatedly solving a PDE whose coefficients change with recalibration, while practitioners need both prices and sensitivities across spot-time surfaces. Neural surrogates can amortize these solves, but near expiry the solution loses regularity, making curvature difficult to learn and allowing violations of no-arbitrage bounds. We propose a finance-informed Deep Operator Network (FI-DeepONet) that decomposes the pricing operator into an input-dependent Black-Scholes carrier and a learned correction. The carrier uses strike-line integrated variance, capturing the leading near-expiry curvature singularity, while a smooth monotone Financial Admissibility Layer enforces pointwise price bounds. We derive a short-maturity estimate and differentiated asymptotics for the exact correction, together with identities linking correction error to price, sensitivity, and PDE-residual errors. On in-distribution tests, FI-DeepONet reduces global relative price error by nearly an order of magnitude versus vanilla and physics-informed DeepONet baselines. On parameter-shift OOD tests within the same local-volatility family, generalization is moderate. On index-option data, the frozen model remains accurate without market-specific retraining, though it does not outperform the same-input analytic formula. We also give a quantum-compatible realization in which selected linear maps are exactly compiled or approximated by a restricted diagonal-orthogonal family before supervised adaptation.
ER -