Fast Deep Hedging with Second-Order Optimization

TL;DR

This paper introduces a second-order optimization method for deep hedging that significantly accelerates training convergence, especially for complex options with long maturities, by efficiently approximating the curvature matrix.

Contribution

We develop a second-order optimization scheme leveraging pathwise differentiability and Kronecker-factored approximations to improve deep hedging training efficiency.

Findings

Reduces training steps to one-quarter of standard methods

Effectively hedges a complex cliquet option with stochastic volatility

Demonstrates faster convergence in realistic market simulations

Abstract

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.