基于不规则期权报价的潜在风险中性密度的逆学习
Inverse Learning of Latent Risk-Neutral Densities from Irregular Option Quotes
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中文总结 AI 辅助
该研究针对不规则期权报价，通过两个基准对比不同模型在潜在风险中性密度逆学习中的表现，发现DeepONet和报价变换器各有优势，支持目标依赖的归纳偏置。
中文摘要 AI 辅助
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，我们通过两个互补基准研究这一区别：受控基准会公开模拟器真实密度用于潜在评估，而时间顺序的NIFTY基准仅测试保留的市场价格。双组分对数正态混合模型在合成基准上的总价格、L¹、Wasserstein及固定尾部误差最低，学习到的算子则保留了更窄的优势：DeepONet相比该混合模型将1%分位数误差和方差误差分别降低39.0%和34.6%，而报价变换器在结构误设定的Merton族上将L¹降低16.4%。数值条件分析解释了为何这些排名可能存在差异：在强制执行质量和远期约束后，126个定价方向中有95个在数值上为零，且L¹=0.061分隔的两个密度在覆盖的行权价上产生相同价格。在524个保留的NIFTY看涨期权上，经验证选择的测试时自适应将DeepONet的RMSE降低28.3%，但按到期日划分的混合模型和SVI拟合仍准确得多。该证据支持目标依赖的归纳偏置，而非存在通用最优方法。
英文摘要
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 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.
