SigMA: Path Signatures and Multi-head Attention for Learning Parameters in fBm-driven SDEs

Battle Count: 69

Highly relevant to quantitative trading through rough volatility modeling. The paper directly addresses calibration of the Hurst exponent in rough volatility models (rHeston), which is critical for option pricing, risk management, and trading strategy development. The empirical application to equity-index realized volatility demonstrates practical utility. Accurate joint estimation of H, kappa1, kappa2, and theta parameters is essential for pricing and hedging under rough volatility. However, the paper focuses on parameter estimation rather than direct trading strategy development.

Moderate complexity. Requires understanding of rough path theory and signature transforms (iisignature library), multi-head attention mechanisms, and convolutional preprocessing. The architecture itself is relatively compact (87,226 parameters). Key implementation challenges include: correct signature computation with time augmentation, lifting procedure with appropriate stride, multi-head attention aligned with signature levels, and proper handling of irregularly sampled data. The code is available on GitHub, reducing implementation burden. Training uses standard PyTorch with Adam optimizer.

Code publicly available on GitHub. Detailed implementation specs provided: PyTorch 2.8.0, Python 3.10.12, CUDA 12.8, Adam optimizer, batch size 60, 150 epochs, learning rate 1e-4. Synthetic data generation scripts included. Specific parameter distributions, path simulation methods (Cholesky for fBm, fast algorithm for rHeston), and all baseline architectures documented in appendix. Results averaged over 3-10 training runs.