[论文] Inverse Learning of Latent Risk-Neutral Densities from Irregular Optio...

论文概要

研究领域: ML 作者: Lennon J. Shikhman, Michael Galarnyk, Aadi Dash, Nicholas A. Welsh 发布时间: 2026-07-29 arXiv: 2607.27188

中文摘要

准确的期权价格并不意味着能准确恢复潜在的风险中性密度。我们通过两个互补的基准测试来研究这一区别。受控基准暴露模拟器真实密度用于潜在评估，而按时间顺序的NIFTY基准仅测试留出的市场价格。双组分对数正态混合分布在合成基准上具有最低的综合价格、L¹、Wasserstein和固定尾部误差。学习算子保留了更窄的优势：DeepONet相比混合分布将1%分位数误差和方差误差分别降低39.0%和34.6%，而报价transformer在结构误设的Merton族上将L¹降低16.4%。数值条件分析解释了为什么这些排名可能不同：在施加质量和远期约束后，126个定价方向中有95个在数值上为零，两个L¹距离为0.061的密度在覆盖的执行价上产生相同的价格。在524个留出的NIFTY看涨期权上，验证选择的测试时自适应将DeepONet的RMSE降低28.3%，但按到期日的混合分布和SVI拟合仍然准确得多。

原文摘要

Accurate option prices do not imply accurate recovery of the latent risk-neutral density. We study this distinction with two complementary benchmarks. A controlled benchmark exposes simulator-truth densities for latent evaluation, while a chronological NIFTY benchmark tests only held-out market prices. A two-component lognormal mixture has the lowest aggregate price, L^1, Wasserstein, and fixed-tail errors on the synthetic benchmark. Learned operators retain narrower strengths: DeepONet reduces 1% quantile and variance error by 39.0% and 34.6% relative to the mixture, and a quote transformer reduces L^1 by 16.4% on the structurally misspecified Merton family. A numerical conditioning analysis explains why these rankings can differ: after enforcing mass and forward constraints, 95 of 126 pr...

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