DeepHedging

Deep hedging research framework. Neural hedging policies are trained by stochastic gradient descent on convex risk measures of terminal PnL over simulated market paths under realistic frictions, with custom CUDA path kernels, whole-episode graph capture, a noise-regenerative backward, and a deep BSDE solver for high-dimensional semilinear pricing PDEs.

Overview

Classical delta hedging assumes frictionless complete markets and derives the hedge analytically. This framework drops both assumptions. Transaction costs, discrete rebalancing, stochastic volatility, jumps, and barrier liabilities enter the simulator, and the optimiser finds the policy the simulated market rewards. Paths are generated on the fly each batch from addressable noise streams, so data is unbounded, nothing overfits a stored dataset, and each batch replays exactly.

Main.ipynb is the executable walkthrough. The experiments/ directory holds the full studies. Every run appends a JSON line with the commit, library versions, device, seeds, and loss history. Each table below regenerates from its committed store.

Results

All numbers are repo artifacts produced on an RTX 5080 from the committed experiment stores and the test suite.

Hedging an at-the-money call daily over thirty days against the Black-Scholes delta baseline, expected shortfall at the ninety-fifth percentile on two hundred thousand common evaluation paths, five seeds:

Proportional cost	Delta hedge	Deep CVaR policy	Improvement
frictionless	0.83	0.85	parity, recovers the model hedge
10 bp	1.13	1.08	5%
20 bp	1.45	1.29	11%
40 bp	2.08	1.65	21%

At forty basis points the deep policy also hedges at a 32% lower mean cost. The stored inventory probes show the learned no-trade band widening with cost at a fitted exponent of 0.28 to 0.33 at the median objective, consistent with the Whalley-Wilmott cube-root law; at higher tail aversion the fitted slope decreases, the expected direction once the objective weights rare deviations rather than local variance.

Further studies in experiments/ cover a barrier option with no analytic hedge where the deep policy cuts the delta baseline's tail by 20-26%, a tradable variance swap removing a further 11-12% of tail risk that the spot cannot span, parameter-matched architecture and risk-objective ablations, and deep BSDE pricing of a geometric basket call within 1.3% of its closed form up to fifty dimensions.

Systems results are pinned by tests and benchmarks. Fused CUDA Philox kernels reach several billion GBM paths per second and roughly two hundred times the eager Heston rate with bitwise replay; whole-iteration graph capture, with the backward and a capturable fused Adam step inside the graph, collapses the dispatch-bound training iteration into one replay, and bfloat16 autocast under capture cuts that iteration by a further third; the noise-regenerative backward cuts peak training memory 12.7x at a quarter-million paths and lifts the feasible batch from a quarter million to beyond two million paths on a sixteen-gigabyte device. The performance review records the profiles, the literature and the before and after measurements behind each optimisation.

Layout

src/deephedging/
|-- market/       GBM (pseudo-random, or scrambled Sobol through a Brownian
|                 bridge), Heston, Merton jumps, rough Bergomi, correlated
|                 multi-asset, local vol, tilted, variance swap; fused CUDA
|                 samplers
|-- instruments/  European, barrier, basket payoffs and adapters
|-- frictions/    Proportional and per-asset transaction cost models
|-- risk/         Rockafellar-Uryasev CVaR, entropic, spectral, mean-variance;
|                 several risk levels trained by one policy
|-- policies/     Feedforward, recurrent, no-transaction-band networks
|-- features.py   Observation construction, including a risk-level code
|-- training/     Episode engine, training loop, graph capture,
|                 regenerative backward
|-- calibration/  Heston characteristic function, COS pricing, surface fit,
|                 Let's Be Rational implied volatility
|-- evaluation/   Closed forms through the normalised Black function,
|                 American exercise, baselines, metrics
|-- bsde/         Deep BSDE solver and the deep backward scheme, reflected
|                 for American claims
|-- pricing.py    Closed-form and Monte Carlo pricers
`-- experiment.py Append-only provenance records
csrc/             Fused Philox path kernels (CUDA)
experiments/      Seven studies with committed result stores
tests/            Unit suite, golden tests, design invariants, benchmarks,
                  ghostwritten equivalence and fuzz tests
docs/             Roadmap and the profiling-driven performance review
Main.ipynb        End-to-end walkthrough

Getting started

Requires Python 3.12+ and uv. A CUDA device is used automatically when available, and everything also runs on CPU. The fused kernels compile on first use, which needs a CUDA toolchain and, on Windows, an MSVC host compiler.

git clone https://github.com/ZacKienzle2/DeepHedging.git
cd DeepHedging
uv sync                      # the package and the dev dependency group
uv sync --extra notebook     # additionally, for Main.ipynb

Reproduce a study:

uv run python experiments/hedging_frontier.py --smoke   # minutes, CPU
uv run python experiments/hedging_frontier.py           # full grid, GPU
uv run python experiments/band_scaling.py               # fit from the store

Quality gates

The sessions in noxfile.py run the same tools CI runs.

nox                                  # lint and tests
uv run pytest --benchmark-only       # pytest-benchmark throughput suite
uv run pytest -m gpu                 # kernel and capture parity

Tests pin statistical relationships and closed-form references rather than bitwise values, plus design invariants. Antithetic pairing measured harmful at convergence, additive control variates measured gradient-inert, and regenerated paths measured loss-identical to stored ones.

Design notes

Each module docstring explains the decisions made there and the failure modes they prevent. Examples include log-space path evolution, the learned CVaR threshold with quantile warm start, addressable noise streams mapped onto Philox subsequences, the whole-episode capture unit, the seed requirement on the regenerative backward, and the semilinear scope fence on the BSDE solver. Main.ipynb closes with a summary.

License

Proprietary. All rights reserved. See LICENSE.