Local Volatility Surface for SPX Options

End-to-end Dupire local-volatility modeling pipeline on an SPX option chain snapshot. Starts from raw quotes, infers the forward/discount curve from put-call parity, fits an arbitrage-aware SVI implied-variance surface, derives the Dupire local volatility, prices vanillas under the local-vol model with both Monte Carlo and a Crank–Nicolson PDE, and validates the PDE Greeks against Black–Scholes.

Project layout

Local_Volatility/
├── data/
│   └── data.csv              # SPX option chain snapshot (one or more quote dates)
├── src/local_vol/            # Library code (importable as `local_vol`)
│   ├── config.py             # Calibration knobs and Dupire safety floors
│   ├── data_loader.py        # Load + clean the option chain
│   ├── black_scholes.py      # BS pricer, vega, delta, full greeks
│   ├── forward_curve.py      # Parity-implied F(T), D(T), r_eff, q_eff (+ diagnostics)
│   ├── implied_vol.py        # Solve implied vols from mid/bid/ask prices
│   ├── smile.py              # Build OTM smile (best-side selection)
│   ├── svi.py                # Quasi-explicit SVI calibration with arbitrage penalties
│   ├── local_volatility.py   # Dupire local vol from SVI + LV interpolator
│   ├── pricing.py            # MC + Crank–Nicolson PDE pricers under LV
│   ├── greeks.py             # PDE finite-difference greeks
│   ├── evaluation.py         # Pricing-error diagnostics vs market
│   ├── validation.py         # PDE-recovers-BS unit tests
│   └── plotting.py           # Smile / surface / 3D plots
├── notebooks/
│   ├── 01_data_exploration.ipynb
│   ├── 02_forward_and_iv.ipynb
│   ├── 03_svi_calibration.ipynb
│   ├── 04_local_vol_surface.ipynb
│   ├── 05_pde_pricing.ipynb
│   └── 06_greeks_validation.ipynb
├── scripts/
│   └── run_full_pipeline.py  # End-to-end command-line entry point
├── requirements.txt
└── README.md

Quick start

python -m venv .venv
source .venv/bin/activate
pip install -r requirements.txt

# Run the full pipeline on the snapshot in data/data.csv
python scripts/run_full_pipeline.py --data data/data.csv

Or open the notebooks under notebooks/ and step through the analysis.

Pipeline overview

1. Preprocess the option chain: filter crossed quotes, compute mids, spreads, log-moneyness, and time-to-maturity.
2. Infer F(T), D(T) for each maturity by fitting C-P ≈ pv * (F - K) on near-ATM strikes (put-call parity).
3. Recompute implied vols from mid / bid / ask prices using the inferred forward and discount, providing per-quote IV bid/ask spreads used as calibration weights.
4. Build the OTM smile: for each (T, K), keep the OTM side; near ATM pick the side with the tighter bid/ask spread.
5. Calibrate SVI in the quasi-explicit (a, p, q, m, η) form per maturity, with penalties for:
   • Negative risk-neutral density (Gatheral butterfly),
   • Roger-Lee wing slopes b(1 ± ρ) > 2,
   • Calendar crossedness against the previous slice.
6. Compute Dupire local vol via numerical derivatives of total variance w(T, y); enforce calendar arbitrage-freeness via isotonic regression in T per y-column.
7. Price under local vol using either a log-Euler Monte Carlo or a Crank–Nicolson PDE in x = ln(S/S0).
8. Validate the PDE against Black–Scholes for constant sigma (recovers prices and the four major greeks).

Data

data/data.csv is an SPX option chain snapshot with bid/ask/IV/greek columns per (QUOTE_DATE, EXPIRE_DATE, K). The loader cleans bracketed column names (e.g. [C_IV]) and converts IV percent values to decimals automatically.