Fast Deep Hedging with Second-Order Optimization
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912095442829312 |
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| author | Mueller, Konrad Akkari, Amira Gonon, Lukas Wood, Ben |
| author_facet | Mueller, Konrad Akkari, Amira Gonon, Lukas Wood, Ben |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22568 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fast Deep Hedging with Second-Order Optimization Mueller, Konrad Akkari, Amira Gonon, Lukas Wood, Ben Risk Management Machine Learning Computational Finance 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. |
| title | Fast Deep Hedging with Second-Order Optimization |
| topic | Risk Management Machine Learning Computational Finance |
| url | https://arxiv.org/abs/2410.22568 |