SABR + Copula Multi-Asset Pricing

A practical pricing toolkit that calibrates SABR smiles per asset and couples them via a t-Copula to simulate joint terminals/paths, price basket options, range accrual, and snowball structures.

• SABR calibration with robust loss, vega weighting, curvature regularization, 3-fold CV. (see sabr.py)
• Copula fitting & model selection among Gaussian / t / Clayton / Frank / Gumbel with MLE and AIC/BIC comparison. (see copula.py)
• Pricing & Greeks using SABR-ATM marginals + t-Copula for joint terminal and GBM path simulation (basket call, range accrual, snowball). (see pricing.py)

Environment

python -m venv .venv
# Windows PowerShell:
.venv\Scripts\Activate.ps1
pip install -r requirements.txt

1) SABR calibration

Prepare your option dataset under ./data. Run:

python sabr.py --input ./data/your_option_file.xlsx --outdir ./sabr_final

Output: ./sabr_final/sabr_params.csv with columns: symbol, T, F, alpha, beta, rho, nu (per maturity)

Highlights: robust Huber loss, vega weighting, curvature penalty, 3-fold CV, adaptive beta grid.

2) Copula fitting & comparison (two modes)

A) Online data (default, AkShare)

Fetch CN indices/ETF, compute returns, PIT transform, then MLE-fit multiple copulas with AIC/BIC comparison:

python copula.py

Output under ./copula_out/:

• copula_compare_aic.csv
• If t-copula is selected, saves t_copula_params.npz (R, nu) and tail-dependence text.

B) Local CSV mode (no network)

If you can't use AkShare, provide your own return CSVs and run:

python copula_local.py --files ./data/returns_510500.csv ./data/returns_000852.csv ./data/returns_000300.csv --names 510500 000852 000300 --outdir ./copula_out

Each CSV should contain a single column named ret with daily returns.

3) Pricing with SABR marginals + t-Copula

Given sabr_final/sabr_params.csv and copula_out/, run:

python pricing.py ^
  --sabr_csv ./sabr_final/sabr_params.csv ^
  --copula_dir ./copula_out ^
  --symbols 510500 000852 000300 ^
  --outdir ./pricing_out ^
  --allow_ko_after_ki ^
  --N_terminal 120000 --N_paths 60000

What it does:

• Build ATM marginal distributions via Hagan ATM approximation and interpolation.
• Load t-Copula params (R, nu) from copula_out or fallback defaults.
• Joint terminal sampling and path GBM simulation under t-Copula.
• Price basket call (ATM strike), compute Greeks (Delta/Gamma/Rho vs basket), price Range Accrual (monthly), and Snowball (worst-of) with daily KI / monthly KO.

Key flags:

• --ko_level --ki_level --coupon_pa --ko_freq {monthly,daily} --months
• --range_lower --range_upper --range_coupon_pa
• --copula_R_default --copula_nu_default as safe fallback.

Outputs: CSVs & charts under ./pricing_out.

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Notes

• No GPU required.
• If AkShare fails (network/proxy), use copula_local.py with your own CSV returns.
• Directory placeholders .keep files are included so Git tracks empty folders.