Fast Deep Hedging with Second-Order Optimization

ArXiv ID: 2410.22568 “View on arXiv”

Authors: Unknown

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.

Keywords: deep hedging, second-order optimization, neural networks, stochastic volatility, cliquet options, Equity Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper presents advanced mathematical concepts like pathwise differentiability, curvature matrix approximation, and Kronecker-factored preconditioning (KFAC), placing it firmly in high math complexity. It demonstrates empirical rigor by testing the proposed optimization scheme on a realistic hedging problem (cliquet option with stochastic volatility) and reporting specific performance improvements (1/4 reduction in steps) compared to standard methods like Adam.

  flowchart TD
    A["Research Goal: Fast Deep Hedging in Realistic Markets"] --> B["Data Inputs: Simulated Market<br/>Stochastic Volatility Model"]
    B --> C["Methodology: Second-Order Optimization<br/>Pathwise Differentiability & Kronecker Approx"]
    C --> D["Computational Process:<br/>Block-Diagonal Curvature Matrix Construction"]
    D --> E["Outcome: 4x Faster Convergence<br/>vs. First-Order Optimizers"]