Initial Release

LICENSE

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+cc-by-4.0

README.md

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+---
+license: cc-by-4.0
+task_categories:
+- other
+language:
+- en
+tags:
+- garch
+- finance
+- density-estimation
+- time-series
+size_categories:
+- 10M<n<100M
+---
+
+# GARCH Densities Dataset
+
+A comprehensive dataset of GJR-GARCH model simulations with Hansen skewed-t innovations, designed for option pricing and financial risk modeling applications.
+
+## Dataset Description
+
+This dataset contains Monte Carlo simulation results from the GJR-GARCH model with Hansen skewed-t distributed innovations. Each entry corresponds to a parameter set Θ, together with empirical quantiles of terminal returns R_T at selected maturities T. Storing quantiles instead of raw paths provides a compact representation that is directly relevant for option pricing across strikes.
+
+### Model Parameters
+
+The dataset consists of tuples (Θ, T, {x_q}), where {x_q} are quantiles of the normalized return distribution. Parameters are drawn using Sobol low-discrepancy sequences to ensure uniform coverage of the parameter space:
+
+- **alpha** (α): GARCH persistence parameter, uniform on simplex constraint
+- **gamma** (γ_eff): GJR-GARCH leverage effect parameter, uniform on simplex constraint  
+- **beta** (β): GARCH persistence parameter, uniform on simplex constraint
+- **var0** (σ₀²): Initial variance, logarithmic in [1/30, 30]
+- **eta** (ν): Degrees of freedom for Hansen skewed-t distribution, logarithmic in [4, 100]
+- **lam** (λ): Skew parameter for Hansen skewed-t distribution, uniform in [-0.98, 0.98]
+- **num_sim_paths**: Number of Monte Carlo simulation paths (10⁶ for train, 10⁷ for test)
+- **job_row**: Parameter case identifier
+- **ti**: Time index/maturity
+- **p**: Uniform [0,1] random number for splitting while preserving low-discrepancy
+- **x**: Quantile values array (inverse CDF values)
+
+## Dataset Statistics
+
+### Computational Scale
+- **Training set**: 135,000 parameter cases, each with 10,000,000 paths and 1,000 timesteps
+- **Test set**: 32,000 independent cases, same paths
+- **Total dataset size**: ~18GB (14GB train, 3.7GB test)
+- **Sharding**: 139 total shards (~65k rows each) for efficient loading
+
+### Parameter Space Coverage
+Parameters are sampled using Sobol low-discrepancy sequences to ensure uniform coverage:
+- **Persistence terms** (α, γ_eff, β): Uniform sampled on simplex with α + γ_eff + β < 0.95
+- **Degrees of freedom** ν: Logarithmic in [4, 100] 
+- **Skew parameter** λ: Uniform in [-0.98, 0.98]
+- **Initial variance** σ₀²: Logarithmic in [1/30, 30]
+
+![Parameter Distributions](parameter_distributions.png)
+
+![Parameter Correlations](parameter_correlations.png)
+
+## Usage
+
+### Basic Loading
+```python
+from datasets import load_dataset
+
+# Load the dataset
+dataset = load_dataset("sitmo/garch-densities")
+
+# Access train and test splits
+train_data = dataset["train"]
+test_data = dataset["test"]
+
+print(f"Training samples: {len(train_data):,}")
+print(f"Test samples: {len(test_data):,}")
+```
+
+### Exploring Parameter Distributions
+```python
+import numpy as np
+import matplotlib.pyplot as plt
+
+# Access a sample
+sample = train_data[0]
+print(f"GARCH parameters: α={sample['alpha']:.3f}, γ={sample['gamma']:.3f}, β={sample['beta']:.3f}")
+print(f"Skewed-t parameters: ν={sample['eta']:.3f}, λ={sample['lam']:.3f}")
+print(f"Quantile array length: {len(sample['x'])}")
+
+# Plot quantile distribution
+plt.figure(figsize=(10, 6))
+plt.plot(sample['x'])
+plt.xlabel('Quantile Index')
+plt.ylabel('Quantile Value')
+plt.title('Sample Quantile Distribution')
+plt.grid(True)
+plt.show()
+```
+
+![Quantile Samples](quantile_samples.png)
+
+### Training Neural Networks
+```python
+from torch.utils.data import DataLoader
+import torch
+
+# Create data loader for training
+train_loader = DataLoader(train_data, batch_size=32, shuffle=True)
+
+# Example training loop
+for batch in train_loader:
+    # Extract features (GARCH parameters)
+    features = torch.stack([
+        batch['alpha'], batch['gamma'], batch['beta'], 
+        batch['var0'], batch['eta'], batch['lam']
+    ]).T
+    
+    # Extract targets (quantile values)
+    targets = batch['x']  # List of arrays
+    
+    # Your model training code here
+    break
+```
+
+## Methodology
+
+### Simulation Process
+1. **Parameter Sampling**: Sobol sequences ensure uniform coverage of the 6D parameter space
+2. **Monte Carlo Simulation**: GJR-GARCH model with Hansen skewed-t innovations
+3. **Quantile Computation**: Empirical quantiles computed from terminal return distributions
+4. **Optimization**: Precomputed inverse CDF lookup tables for efficient skewed-t sampling
+
+### Train/Test Split
+- **Training set**: Broad parameter coverage with 10⁶ paths per case
+- **Test set**: Independent parameter cases with 10⁷ paths for high-precision evaluation
+- **Split method**: Preserves low-discrepancy properties of Sobol sampling
+
+## Applications
+
+This dataset is designed for:
+- **Option Pricing**: Direct quantile access enables efficient option pricing across strikes
+- **Risk Management**: VaR and CVaR calculations using quantile distributions
+- **Neural Network Training**: Learn mappings from GARCH parameters to return distributions
+- **Model Validation**: Benchmark GARCH implementations against high-precision simulations
+- **Financial Research**: Study the relationship between GARCH parameters and return distributions
+
+## Limitations
+
+- **Model Scope**: Limited to GJR-GARCH with Hansen skewed-t innovations
+- **Parameter Ranges**: Fixed ranges may not cover all market conditions
+- **Computational Constraints**: Generated under practical compute limits (50 GPU servers)
+- **Quantile Resolution**: Limited by Monte Carlo precision and quantile grid size
+
+## Related Work
+
+This dataset supports research in:
+- GARCH model estimation and validation
+- Option pricing with stochastic volatility
+- Neural network applications in quantitative finance
+- Monte Carlo methods for financial modeling
+
+## Citation
+
+If you use this dataset, please cite:
+
+```bibtex
+@dataset{garch_densities_2025,
+  title={GARCH Densities Dataset},
+  author={Thijs van den Berg},
+  year={2025},
+  url={https://huggingface.co/datasets/sitmo/garch-densities}
+}
+```

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