用二阶优化加速深度对冲，提升长周期复杂期权的训练效率。
Fast Deep Hedging with Second-Order Optimization
- 基于路径可微性构建曲率矩阵，通过分块对角与克罗内克分解高效预处理梯度
- 在随机波动率模型下，对敲式期权对冲任务中仅需1/4步数完成优化
- 适合需要快速训练神经网络对冲策略的研究者与量化从业者
在存在市场摩擦的情况下对冲奇异期权是一项重要的风险管理任务。深度对冲通过在真实模拟市场中训练神经网络策略来解决此类问题。然而，这类神经网络的训练可能十分棘手且收敛缓慢，尤其针对久期较长、对市场参数敏感性复杂的期权。为此，本文提出一种用于深度对冲的二阶优化方案。我们利用路径可微性构造曲率矩阵，并将其近似为分块对角与克罗内克分解形式，以高效地预处理梯度。我们在一个具有挑战性且具实际意义的问题上评估该方法：在随机波动率模型下，通过交易标的资产与平价期权对冲一个敲击式期权。结果表明，与标准自适应动量优化相比，我们的二阶方法可在四分之一的迭代步数内完成策略优化。
原文摘要 · Abstract (English)
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.
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