Attribution of SC–Deep Hedging Price Divergence at High Transaction Costs

Determine, through a refined numerical study, the respective contributions of (i) binomial-tree discretization and the ±Δy per-step trade-size restriction in the stochastic control dynamic programming scheme, (ii) finite-sample training and tail-scenario underrepresentation in deep hedging networks, and (iii) differing time discretizations (binomial tree versus Monte Carlo), to the observed divergence between stochastic control and deep hedging writer indifference prices at high proportional transaction cost levels.

Background

In their numerical comparison of pricing under proportional transaction costs, the authors report that writer indifference prices produced by the stochastic control dynamic programming scheme rise more rapidly with the transaction cost level than those obtained from deep hedging models (MLP, NTBN-A, and WW-NTBN), creating a noticeable gap at higher frictions.

They hypothesize several contributing factors: approximation error from the binomial-tree discretization and the ±Δy trade restriction in the stochastic control scheme, finite-batch training and potential underweighting of rare extreme scenarios in deep hedging, and systematic differences arising from the use of different time discretizations (binomial tree for stochastic control versus Monte Carlo paths for deep hedging). The authors explicitly flag separating the impact of these factors as an open question requiring a more refined numerical study.