Cross-Cube Vega Hedging: A Swaption Market-Making Lab
Single-tenor vega is a mirage - a swaption cube moves in factors, and naive hedges leak P&L.
Terminal P&L across 1,000 market-making paths. Factor-neutral hedging compresses dispersion at the cost of upside; delta-only earns the most edge but carries the widest left tail.
- SABR cube construction, per-slice vs joint no-arbitrage calibration, and arb-violation accounting on a simulated cube with observation noise.
- PCA recovery of latent level/slope/curvature factors with cosine-similarity validation against the data-generating loadings.
- A market-maker Monte Carlo with Poisson client flow, four hedging policies (delta-only, single-tenor vega-flat, bucketed vega-flat, factor-neutral QP), and reconciled P&L attribution into edge, theta, delta, first-order vega, cross-vega, and hedge cost.
- An Avellaneda-Stoikov-style quoting overlay adapted to factor inventory in vol space, with the heuristic nature of the adaptation stated honestly.
A market-maker can flatten reported node vega and still carry a large exposure to cube factors: ATM level, expiry slope, curvature, and skew. This repo simulates that problem end to end with a SABR swaption cube, a client-flow market-maker, four hedging rules, and reconciled P&L attribution. In the baseline run, delta-only earns the most spread but has the widest left tail; factor-neutral hedging gives up some edge and pays hedge cost, but cuts dispersion sharply and pulls the 5% tail close to flat.
cross-cube-vega/
|-- configs/ # deterministic model and scenario YAML
|-- src/cxvega/ # simulator, SABR, hedging, market-maker, reporting
|-- scripts/ # CLI pipeline entry points
|-- tests/ # fast unit tests, no Monte Carlo dependence
|-- notebooks/ # walkthrough notebooks
|-- docs/report/ # report sources, figures, and PDF
|-- docs/site/ # static HTML mini-site
`-- outputs/ # regenerated artefacts
make install
make allExpected runtime is under 10 minutes on a modern laptop. On this machine the full baseline Monte Carlo and report rebuild runs in roughly a few minutes after packages are cached.
Determinism: master seed in configs/default.yaml, separate RNG streams for simulation and observation noise, make clean && make all rebuilds every figure, table, the static site, and the PDF from scratch.
Stack: Python 3.11, numpy/scipy/pandas, matplotlib + plotly, scikit-learn for PCA, mypy strict and ruff clean.
PDF renderer: WeasyPrint is preferred; the build falls back to headless Chromium via Playwright when system Pango/GObject libraries are unavailable, and to a matplotlib emergency renderer behind an explicit flag. See BUILD.md.
The cube spans seven expiries and four swap tenors. ATM log-vol follows three correlated OU factors with smooth level, slope, and curvature loadings. SABR beta is fixed, rho is bounded, log-nu mean reverts, and skew/wing dynamics are correlated with the level factor. Details and limitations are in the PDF report.
Baseline terminal P&L across 1000 paths and 252 trading days:
| Strategy | Mean ($mm) | Std ($mm) | 5% VaR ($mm) | Sharpe |
|---|---|---|---|---|
| Delta-only | 30.66 | 70.57 | -77.49 | 0.43 |
| Single-tenor vega-flat | 15.73 | 37.53 | -46.12 | 0.42 |
| Bucketed vega-flat | 10.50 | 22.32 | -25.00 | 0.47 |
| Factor-neutral | 9.69 | 6.37 | -0.46 | 1.52 |
No real market data are used. The lab assumes single-curve discounting, fixed beta, perfectly observed mids, no jumps, no funding asymmetry, and a simplified client-crossing model. See section 13 of the PDF for the full list.
Natural extensions include a real-data overlay, rough-vol factor dynamics, multi-curve pricing, joint cap-swaption calibration, Bermudan exposure via LSM, strategic broker quoting, and an RL policy layer. See section 14 of the PDF.
Andersen and Piterbarg (2010); Hagan, Kumar, Lesniewski, and Woodward (2002); Rebonato (2002); Bergomi (2016); Bartlett (2006); Avellaneda and Stoikov (2008); Gatheral (2006).
Imran Hakim — independent research, May 2026
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