Deep Quadratic Hedging

• 成果类型: Article; Early Access
• 署名作者: Gnoatto, Alessandro; Lavagnini, Silvia; Picarelli, Athena
• 署名单位: University of Verona; BI Norwegian Business School
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2023.0213
• 发表日期: 2024
• 关键词: partial-differential-equations; stochastic volatility; Optimal investment; options; schemes; MODEL

摘要

We propose a novel computational procedure for quadratic hedging in highdimensional incomplete markets, covering mean-variance hedging and local risk minimization. Starting from the observation that both quadratic approaches can be treated from the point of view of backward stochastic differential equations (BSDEs), we (recursively) apply a deep learning-based BSDE solver to compute the entire optimal hedging strategies paths. This allows us to overcome the curse of dimensionality, extending the scope of applicability of quadratic hedging in high dimension. We test our approach with a classic Heston model and with a multiasset and multifactor generalization thereof, showing that this leads to high levels of accuracy.