# Fast Deep Hedging with Second-Order Optimization

arXiv: https://arxiv.org/abs/2410.22568 · HTML: https://mlsanity.com/paper/2410.22568/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 43 references that are in the map.
- First posted on arXiv 29 Oct 2024.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [What Matters In On-Policy Reinforcement Learning? A Large-Scale Empirical Study](https://mlsanity.com/paper/2006.05990/) (2020)
- [Fast Approximate Natural Gradient Descent in a Kronecker-factored Eigenbasis](https://mlsanity.com/paper/1806.03884/) (2018)
- [Scalable trust-region method for deep reinforcement learning using Kronecker-factored approximation](https://mlsanity.com/paper/1708.05144/) (2017)
- [Recent Advances in Reinforcement Learning in Finance](https://mlsanity.com/paper/2112.04553/) (2021)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [Adaptive Gradient Methods at the Edge of Stability](https://mlsanity.com/paper/2207.14484/) (2022)
- [Natural Neural Networks](https://mlsanity.com/paper/1507.00210/) (2015)
- [Neural networks for option pricing and hedging: a literature review](https://mlsanity.com/paper/1911.05620/) (2019)
- [The Geometry of Neural Nets' Parameter Spaces Under Reparametrization](https://mlsanity.com/paper/2302.07384/) (2023)
- [Deep Hedging: Continuous Reinforcement Learning for Hedging of General Portfolios across Multiple Risk Aversions](https://mlsanity.com/paper/2207.07467/) (2022)
- [Deep Hedging under Rough Volatility](https://mlsanity.com/paper/2102.01962/) (2021)

## Built on by (most cited first, 6 of 6)

- [Distributional Adversarial Attacks and Training in Deep Hedging](https://mlsanity.com/paper/2508.14757/) (2025)
- [A New Way: Kronecker-Factored Approximate Curvature Deep Hedging and its Benefits](https://mlsanity.com/paper/2411.15002/) (2024)
- [Generating Financial Time Series by Matching Random Convolutional Features](https://mlsanity.com/paper/2606.05138/) (2026)
- [A Topological Approach to Parameterizing Deep Hedging Networks](https://mlsanity.com/paper/2510.16938/) (2025)
- [Robust Control under Stationary Ambiguity](https://mlsanity.com/paper/2608.04832/) (2026)
- [Taming the Greeks: Option Portfolios with Inductive Biases](https://mlsanity.com/paper/2609.33767/) (2026)

## Abstract (arXiv)

Hedging exotic options in presence of market frictions is an important risk management task. Deep hedging can solve such hedging problems by training neural network policies in realistic simulated markets. Training these neural networks may be delicate and suffer from slow convergence, particularly for options with long maturities and complex sensitivities to market parameters. To address this, we propose a second-order optimization scheme for deep hedging. We leverage pathwise differentiability to construct a curvature matrix, which we approximate as block-diagonal and Kronecker-factored to efficiently precondition gradients. We evaluate our method on a challenging and practically important problem: hedging a cliquet option on a stock with stochastic volatility by trading in the spot and vanilla options. We find that our second-order scheme can optimize the policy in 1/4 of the number of steps that standard adaptive moment-based optimization takes.