Volatility Arbitrage Research System

A modular C++20 research framework for studying equity options volatility dynamics and model-implied mispricing. Implements a Black-Scholes-Merton pricing engine, a hybrid Newton-Raphson/bisection implied volatility solver, and a Levenberg-Marquardt SVI (Stochastic Volatility Inspired) surface fitter, with an automated synthetic validation harness.

What this is (and isn't)

This is a pricing and surface-analytics engine, validated end-to-end against synthetic data with known ground truth — not a backtested trading strategy. Every accuracy number below comes from generating option chains with known parameters, running them through the real pipeline, and measuring recovery error against those known values. No live or historical market data was used to evaluate profitability. See Validation for exactly what was and wasn't tested.

Provider abstraction: IMarketData is a single interface with hot-swappable backends — synthetic data for research/CI, a cached wrapper for any provider, and a live IBKR paper/live trading path. Everything above the data layer (pricer, solver, surface fitter) is provider-agnostic.

Pipeline

Option chain (IMarketData)
    ↓
IV solve per quote          (iv_solver.hpp: Newton-Raphson → bisection)
    ↓
Raw volatility surface       (svi_surface.hpp: build_raw_surface)
    ↓
SVI fit per expiry slice     (svi_surface.hpp: fit — Levenberg-Marquardt)
    ↓
Mispricing signals           (svi_surface.hpp: find_mispricing —
                               market IV vs. model IV)

Build & run

mkdir -p build && cd build
cmake ..
cmake --build . --target bs_pricer         # live pipeline (synthetic by default)
cmake --build . --target validate_synthetic # validation harness
./bs_pricer
./validate_synthetic

bs_pricer runs against SyntheticProvider by default (no external dependency, no API key). Set VOL_PROVIDER=ibkr_paper or ibkr_live to use the IBKR path once it's implemented.

Validation

validate_synthetic generates option chains from known SVI parameters, runs them through the real pipeline (not a separate test-only code path), and measures recovery error against ground truth. Five stages:

1. IV solver recovery — solved IV vs. true IV per contract, exercised through the production build_raw_surface call path.
2. SVI fit recovery — fitted {a, b, ρ, m, σ} vs. the true parameters used to generate the chain, across 4 distinct surface shapes (flat/calm, steep skew, high curvature, low-vol regime) and 4 expiry slices each.
3. Zero-noise signal check — confirms find_mispricing stays quiet when market IV equals model IV by construction.
4. Degenerate-case handling — deep ITM/OTM and short-tenor contracts, where price-based IV inversion is fundamentally ill-conditioned near zero vega.
5. Injected mispricing sweep — deliberately shifts known contracts by a known IV offset and measures true-positive/false-positive detection across offset magnitudes.

Results

Metric	Result
SVI parameter recovery (zero noise)	within 0.006 across all 4 regimes
Non-convergent fits	0 / 8 scenarios
Mispricing detection	100% detected, 0 false positives, at ≥3 vol-point offsets
Detection threshold	consistent under both clean and realistic bid-ask noise

Full per-scenario output (including known solver limitations at near-zero vega) is reproducible by running validate_synthetic directly.

Roadmap

• IBKR live/paper data provider (currently stubbed)
• True-positive/false-positive testing under smooth (non-outlier) background noise, where the current detector under-detects
• Historical backtesting once a real market data source is integrated

Disclaimer

Research and educational code. Not investment advice. Pricing and surface analytics have been validated against synthetic ground truth only — no claims are made about performance on live or historical market data.