从不规则期权报价中逆向学习隐含风险中性密度，提升定价准确性。
Inverse Learning of Latent Risk-Neutral Densities from Irregular Option Quotes
- 用双基准验证方法：合成数据与真实市场数据并行测试。
- DeepONet 和报价转换器在特定场景下分别降低39%和16.4%误差。
- 结果依赖目标，无通用最优模型，需按任务调整策略。
准确的期权价格并不意味着能准确恢复隐含风险中性密度。本文通过两个互补基准研究这一区别：可控基准使用模拟生成的真实密度进行评估，时间序列基准仅测试未见的市场报价。在合成基准上，双成分对数正态混合模型在总价格、$L^1$、Wasserstein及固定尾部误差上表现最佳。学习型算子表现更优：DeepONet将1%分位数与方差误差分别相对降低39.0%和34.6%，报价转换器在结构误设的Merton族上使$L^1$误差减少16.4%。数值条件分析表明：施加质量与远期约束后，126个定价方向中有95个数值退化为零，且两个密度间$L^1=0.061$的差距在覆盖行权价上产生相同价格。在524个未见的NIFTY看涨期权上，经验证选择的测试时自适应使DeepONet RMSE降低28.3%，但按到期日的混合模型与SVI拟合仍更准确。证据支持目标依赖的归纳偏置，而非通用最优解。
原文摘要 · Abstract (English)
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 pricing directions are numerically null, and two densities separated by $L^1 = 0.061$ produce identical prices on the covered strikes. On 524 held-out NIFTY calls, validation-selected test-time adaptation reduces DeepONet RMSE by 28.3%, but per-expiry mixture and SVI fits remain much more accurate. The evidence supports target-dependent inductive bias, not a universal winner.
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