American Basket Options — Deep RNN-BSDE vs. Longstaff–Schwartz (GBM & Heston)

Research-grade, reproducible code for pricing and hedging high-dimensional American basket options. Baselines include LSMC under correlated GBM and a paper-faithful two-head RNN-BSDE; we extend to correlated Heston with a learned stock driver (α) to improve hedging in incomplete markets.

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Highlights

• Two paradigms, one repo
  • LSMC (Longstaff–Schwartz) for a transparent Monte-Carlo baseline.
  • Deep RNN-BSDE (two heads: price Y, delta Δ) for scalable pricing & greeks along the time grid.
• Correlated Heston extension: adds a third head to learn the stock Brownian driver α and converts it to shares for hedging when delta alone is insufficient.
• Calibration → Training pipeline: helpers to fit per-asset Heston parameters + cross-asset correlation; exported as CSV for training.
• Hedging focus: daily P&L attribution (gamma/theta drift vs realized variance, vega/vanna terms, financing/borrow) and delta-hedge evaluation on simulated paths.
• Reproducible: deterministic seeds, minimal dependencies, CPU-friendly defaults (GPU optional).

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Repository structure

american-basket-option/
├─ data/                         # Model checkpoints & calibrated CSVs (gitignored)
├─ heston_calib/                 # Heston calibration helpers + scripts
├─ results_notebook/             # Result exploration / plotting utilities
├─ heston_calibrator_top30.py    
├─ longstaff_schwartz.py         # LSMC baseline
├─ gbm_rnn_model.py              # GBM RNN-BSDE (price + delta)
├─ heston_rnn_model.py           # Heston RNN-BSDE (price + delta + alpha)
├─ __init__.py
├─ README.md
└─ license

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Install

Tested with Python 3.10+.

# (Recommended) Create an isolated environment
python -m venv .venv
# macOS/Linux
source .venv/bin/activate
# Windows
# .venv\Scripts\activate

# Core scientific stack
pip install numpy pandas matplotlib scikit-learn torch tqdm

Tip: On CPU, start with modest path counts (e.g., n_paths=5_000) for quick runs, then scale.

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Quickstart

1) LSMC baseline (GBM)

python longstaff_schwartz.py

Outputs an American price via polynomial regression on simulated correlated GBM paths.

2) Deep RNN-BSDE (GBM)

python rnn_model.py

• Price head (Y) learns continuation.
• Delta head (Δ) learns the BSDE driver term (paper-style).
• Training tricks: batch-mean look-ahead labels, mild terminal smoothing, optional sequence reversal for stability.

3) Deep RNN-BSDE (Heston, with α-driver)

python heston_rnn_model.py

• Heads: price, delta (aux), and α (stock driver).
• Inputs per step: ([S_n, \sqrt{v_n}, g(S_n)]) with g = signed moneyness feature for the basket payoff.
• α labels: ridge/OLS of discounted continuation increments on standardized stock shocks.
• Hedging: in the continuation region, map learned α → shares; at exercise, use payoff gradient.

Console prints include estimates for (Y_0), average (\Delta_0), average (\alpha_0), and a suggested hedge vector.

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Data & calibration

Place CSVs in data/:

• heston_parameters.csv with columns:

  Ticker,Spot_Price,v0,kappa,theta,sigma,rho
  

• heston_correlation_matrix.csv — a symmetric (d \times d) matrix (ones on diagonal).

If your scripts produce different filenames, adjust the constants/paths in heston_rnn_model.py.

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