KANHedge: 用基于Kolmogorov-Arnold网络的BSDE求解器高效对冲高维期权
KANHedge: Efficient Hedging of High-Dimensional Options Using Kolmogorov-Arnold Network-Based BSDE Solver
AI总结：
KANHedge通过基于Kolmogorov-Arnold网络的BSDE求解器提升高维期权对冲性能。
摘要：
高维期权定价和对冲在量化金融中带来了重大挑战，其中传统基于PDE的方法因维度诅咒而显得力不从心。BSDE框架为PDE方法提供了一个计算效率更高的替代方案，而近期提出的一种深度BSDE求解器通常利用传统多层感知机（MLP）来在此基础上提供一种可扩展的替代方案。在本研究中，我们表明尽管基于MLP的深度BSDE在期权定价方面表现有希望，但在对冲性能方面仍有改进空间。为了解决这一问题，我们引入了KANHedge，一种基于BSDE的新型对冲器，它在BSDE框架中利用Kolmogorov-Arnold网络（KANs）。与传统MLP方法使用固定激活函数不同，KANs采用可学习的B-样条激活函数，为连续导数提供了更强的函数逼近能力。我们全面评估了KANHedge在欧式和美式篮子期权上多个维度和市场条件下的表现。我们的实验结果表明，虽然KANHedge和MLP在定价准确性上相当，但KANHedge在对冲性能上有所提升。具体而言，KANHedge在对冲成本指标上实现了显著的减少，展示了更强的风险控制能力。
英文摘要：
High-dimensional option pricing and hedging present significant challenges in quantitative finance, where traditional PDE-based methods struggle with the curse of dimensionality. The BSDE framework offers a computationally efficient alternative to PDE-based methods, and recently proposed deep BSDE solvers, generally utilizing conventional Multi-Layer Perceptrons (MLPs), build upon this framework to provide a scalable alternative to numerical BSDE solvers. In this research, we show that although such MLP-based deep BSDEs demonstrate promising results in option pricing, there remains room for improvement regarding hedging performance. To address this issue, we introduce KANHedge, a novel BSDE-based hedger that leverages Kolmogorov-Arnold Networks (KANs) within the BSDE framework. Unlike conventional MLP approaches that use fixed activation functions, KANs employ learnable B-spline activation functions that provide enhanced function approximation capabilities for continuous derivatives. We comprehensively evaluate KANHedge on both European and American basket options across multiple dimensions and market conditions. Our experimental results demonstrate that while KANHedge and MLP achieve comparable pricing accuracy, KANHedge provides improved hedging performance. Specifically, KANHedge achieves considerable reductions in hedging cost metrics, demonstrating enhanced risk control capabilities.
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