Inverse Learning of Latent Risk-Neutral Densities from Irregular Option Quotes: Benchmarks and Findings

Forum topic · 小凯 · 2026-07-31

Summary

A paper by Shikhman, Galarnyk, Dash, and Welsh (arXiv:2607.27188) studies whether accurate option pricing implies accurate recovery of the latent risk-neutral density. Using two complementary benchmarks—a controlled simulator benchmark with known truth densities and a chronological NIFTY benchmark testing only held-out market prices—the authors evaluate learned operators against classical methods. A two-component lognormal mixture achieves the lowest aggregate price, L^1, Wasserstein, and fixed-tail errors on synthetic data. Learned operators retain narrower strengths: DeepONet cuts 1% quantile and variance errors by 39.0% and 34.6% versus the mixture, while a quote transformer reduces L^1 by 16.4% on the misspecified Merton family. A conditioning analysis shows 95 of 126 pricing directions are numerically zero after mass and forward constraints, explaining divergent rankings. On 524 held-out NIFTY calls, test-time adaptation reduces DeepONet RMSE by 28.3%, though mixture and SVI fits by maturity remain far more accurate.

Paper Overview

Field: Machine Learning Authors: Lennon J. Shikhman, Michael Galarnyk, Aadi Dash, Nicholas A. Welsh arXiv: 2607.27188

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 zero, and two densities with L^1 distance 0.061 produce identical prices over covered strikes. On 524 held-out NIFTY calls, validation-selected test-time adaptation reduces DeepONet RMSE by 28.3%, but mixture and SVI fits by maturity remain substantially more accurate.

Key Findings

Prices ≠ density recovery: accurate option pricing does not guarantee accurate recovery of the underlying risk-neutral density.
Synthetic benchmark: the two-component lognormal mixture wins on aggregate price, L^1, Wasserstein, and fixed-tail errors.
Learned operators: DeepONet improves tail (1% quantile) error by 39.0% and variance error by 34.6% over the mixture; the quote transformer cuts L^1 error by 16.4% on the misspecified Merton family.
Ill-conditioning: after enforcing mass and forward constraints, 95 of 126 pricing directions are numerically zero; two densities with L^1 distance 0.061 are price-identical over covered strikes—explaining divergent rankings.
Market test: on 524 held-out NIFTY calls, test-time adaptation lowers DeepONet RMSE by 28.3%, but mixture and SVI fits per maturity remain much more accurate.