simu-ai/garch_densities

GARCH Densities Dataset

GJR-GARCH simulations with Hansen skewed-t innovations, for option pricing and risk modeling. Each row pairs a parameter set Θ with inverse-CDF quantiles of terminal returns at a given maturity step.

Dataset Description

Each example is a tuple (Θ, ti, x) where:

• Θ = (alpha, gamma, beta, var0, eta, lam)
• ti = maturity step index (integer steps)
• x = vector of Q=512 quantiles at probabilities
  p = linspace(0.001, 0.999, 512)

Parameters are sampled by Sobol low-discrepancy sequences under the persistence constraint ( \alpha + \gamma + \beta < 0.95 ).

Features

• alpha (float32) — persistence term
• gamma (float32) — effective leverage term (GJR component)
• beta (float32) — persistence term
• var0 (float32) — initial variance ( \sigma_0^2 ), log-uniform in [1/30, 30]
• eta (float32) — skewed-t degrees of freedom ( \nu ), log-uniform in [4, 100]
• lam (float32) — skewed-t skew ( \lambda ) in [-0.98, 0.98]
• ti (float32) — maturity step index [1, 1000]
• x (list[512]) — quantiles of normalized terminal return ( R_T ) at p above

All numeric columns are float32 for I/O efficiency.

Parameter Sampling

• (alpha, gamma, beta) with ( \alpha + \gamma + \beta < 0.95 )
• ( \nu \in [4, 100] ) (log-uniform), ( \lambda \in [-0.98, 0.98] ) (uniform)
• ( \sigma_0^2 \in [1/30, 30] ) (log-uniform)

Dataset Statistics

• Train: 110 shards, ~145 MB each
• Test: 29 shards, ~145 MB each
• Row groups: zstd compression, ~64–128 MiB target (streaming-friendly)

Usage

Recommended loading

from datasets import load_dataset
ds = load_dataset("sitmo/garch_densities", token=False)  # -> DatasetDict(train/test/sample)
train, test = ds["train"], ds["test"]
print(train)
print(train.features)

PyTorch formatting

import torch
from torch.utils.data import DataLoader

param_cols = ["alpha","gamma","beta","var0","eta","lam","ti"]
cols = param_cols + ["x"]
train = train.with_format("torch", columns=cols)

loader = DataLoader(train, batch_size=256, shuffle=True, num_workers=4, pin_memory=torch.cuda.is_available())
batch = next(iter(loader))

params  = torch.stack([batch[c] for c in param_cols], dim=1)  # [B,7]
targets = batch["x"]                                          # [B,512]
print(params.shape, targets.shape)

Inspect a sample

ex = train[0]
len(ex["x"])  # 512

Methodology

1. Sobol sampling of Θ in 6D under ( \alpha+\gamma+\beta<0.95 )
2. Monte Carlo: GJR-GARCH with Hansen skewed-t innovations
3. Quantiles: empirical quantiles of terminal returns on p = linspace(0.001, 0.999, 512)
4. Performance: inverse-CDF accelerations for skewed-t sampling

Train/Test Split

• Train: 10,000,000 paths per case
• Test: 10,000,000 paths per case
• Independent parameter cases; split preserves Sobol low-discrepancy structure.

Applications

• Option pricing across strikes (quantile-based)
• VaR / CVaR risk metrics
• Learning ( \Theta \mapsto ) return distribution (NNs)
• Validation/benchmarking of GARCH implementations

Limitations

• Restricted to GJR-GARCH with Hansen skewed-t
• Fixed parameter ranges
• Finite MC precision and finite quantile grid resolution (512 points)

Provenance

• Synthetic data from our simulator (GJR-GARCH + Hansen skewed-t)
• Parquet: zstd, row groups ~64–128 MiB, shards ~145 MB

Citation

@dataset{garch_densities_2025,
  title   = {GARCH Densities Dataset},
  author  = {Thijs van den Berg, Paul Wilmott},
  year    = {2025},
  url     = {https://huggingface.co/datasets/sitmo/garch-densities}
}