Bridging Stochastic Control and Deep Hedging: Structural Priors for No-Transaction Band Networks

TL;DR

This paper integrates stochastic control and deep learning to improve hedging strategies for European call options under transaction costs, introducing structural priors for better convergence and generalization.

Contribution

It proposes two deep hedging architectures that incorporate stochastic control insights, enhancing convergence speed and accuracy in modeling no-transaction bands.

Findings

WW-NTBN converges faster than previous methods.

The models closely match stochastic control no-transaction bands.

Both frameworks reveal non-linearity in option prices under transaction costs.

Abstract

This paper studies the problem of hedging and pricing a European call option under proportional transaction costs, from two complementary perspectives. We first derive the optimal hedging strategy under CARA utility, following the stochastic control framework of Davis et al. (1993), characterising the no-transaction band via the Hamilton-Jacobi-Bellman Quasi-Variational Inequality (HJBQVI) and the Whalley-Wilmott asymptotic approximation. We then adopt a deep hedging approach, proposing two architectures that build on the No-Transaction Band Network of Imaki et al. (2023): NTBN-Delta, which makes delta-centring explicit, and WW-NTBN, which incorporates the Whalley-Wilmott formula as a structural prior on the bandwidth and replaces the hard clamp with a differentiable soft clamp. Numerical experiments show that WW-NTBN converges faster, matches the stochastic control no-transaction bands more closely, and generalises well across transaction cost regimes. We further apply both frameworks to the bull call spread, documenting the breakdown of price linearity under transaction costs.