Inverse Learning of Latent Risk-Neutral Densities from Irregular Option Quotes
2026-07-29 • Machine Learning
Machine Learning
AI summaryⓘ
The authors show that even if option prices are accurate, it doesn't mean we can perfectly find the hidden risk-neutral density that generated them. They compare different methods using both a synthetic benchmark with known
option pricingrisk-neutral densitylognormal mixtureDeepONetNIFTY indexWasserstein errorMerton modelnumerical conditioningprice fittingRMSE
Authors
Lennon J. Shikhman, Michael Galarnyk, Aadi Dash, Nicholas A. Welsh
Abstract
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.