Deep Quadratic Hedging

TL;DR

This paper introduces a deep learning-based method for quadratic hedging in high-dimensional incomplete markets, effectively overcoming the curse of dimensionality and enabling accurate computation of optimal hedging strategies.

Contribution

It develops a recursive deep BSDE solver for quadratic hedging, extending applicability to high-dimensional models like Heston and multiasset markets.

Findings

Achieves high accuracy in Heston model hedging

Successfully handles multiasset and multifactor models

Overcomes curse of dimensionality in quadratic hedging

Abstract

We propose a novel computational procedure for quadratic hedging in high-dimensional 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.