面向期权定价的金融信息算子学习及其量子兼容实现
Finance-Informed Operator Learning for Option Pricing with Quantum-Compatible Realizations
- Shanghai University of Finance and Economics（上海财经大学）
- Auburn University（奥本大学）
- Utah State University（犹他州立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出金融信息深度算子网络（FI-DeepONet），通过Black-Scholes载体和修正项分解定价算子，结合金融可接受性层，在局部波动率下高效定价欧式期权，显著降低误差并支持量子兼容实现。
AI中文摘要：
在局部波动率模型下对欧式期权定价需要反复求解偏微分方程（PDE），其系数会随重新校准而变化，而实践者需要跨现货-时间曲面的价格和敏感性。神经替代模型可以摊销这些求解，但在临近到期时解失去正则性，使得曲率难以学习，并可能导致无套利界限被违反。我们提出了一种金融信息深度算子网络（FI-DeepONet），将定价算子分解为依赖于输入的Black-Scholes载体和一个学习的修正项。载体使用行权价线积分方差，捕捉临近到期的主导曲率奇异性，而一个平滑单调的金融可接受性层强制实施逐点价格界限。我们推导了精确修正的短期估计和微分渐近，以及将修正误差与价格、敏感性和PDE残差误差联系起来的恒等式。在分布内测试中，FI-DeepONet相比普通和物理信息DeepONet基线，将全局相对价格误差减少了近一个数量级。在相同局部波动率族内的参数偏移分布外（OOD）测试中，泛化表现适中。在指数期权数据上，冻结模型无需特定市场重新训练即可保持准确，尽管它并未优于同输入解析公式。我们还提供了一种量子兼容实现，其中选定的线性映射在监督适应之前被精确编译或由受限的对角-正交族近似。
英文摘要：
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.
