Fast Deep Hedging with Second-Order Optimization
This addresses a practical risk management problem for financial institutions dealing with complex options, though it appears incremental as it improves training efficiency rather than introducing a new paradigm.
The paper tackles the slow convergence problem in deep hedging for exotic options by proposing a second-order optimization scheme that uses pathwise differentiability to construct an efficiently approximated curvature matrix, achieving optimization in 1/4 the steps compared to standard methods.
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.