What Does Deep Hedging Actually Learn? Delta Corrections, Regime Fragility, and Symbolic Distillation

TL;DR

This paper investigates what deep hedging models learn for S&P 500 options, revealing systematic delta corrections, regime fragility, and the potential for symbolic distillation to produce interpretable, yet fragile, hedging formulas.

Contribution

It analyzes the learned hedge behaviors, explains delta corrections, and introduces symbolic regression to distill neural policies into interpretable formulas.

Findings

Deep hedging agents learn systematic delta haircuts relative to Black-Scholes.

Delta corrections often improve reward and reduce downside variance.

Distilled formulas retain much of the neural policies' performance but are also regime fragile.

Abstract

This paper studies empirical deep hedging for S&P 500 index options under a local downside-shortfall reward. It moves beyond performance comparison by asking what the learned hedge does, when it fails, and whether it can be made auditable. TD3 agents are compared with a daily-updated Black-Scholes delta hedge on the same option episodes. In walk-forward tests from 2015 to 2023, the agents usually learn a systematic delta haircut relative to Black-Scholes. The correction is explained by spot-implied-volatility co-movement and often improves accumulated reward and terminal downside variance, but it is regime-fragile: 2022 exposes losses in adverse daily states, while 2023 shows that underhedging can raise ordinary variance when option P&L is spot-dominated and the volatility channel is unusually weak. Symbolic regression distills the neural policies into compact formulas that can be traded out of sample; these formulas preserve much of the reward, downside-variance, and CVaR advantage over Black-Scholes, and sometimes sharpen it, but inherit the same fragility in difficult regimes.