implied-vol-surface-lab-cpp

A mini quant research lab for building and stress-testing implied volatility surfaces: from Black–Scholes pricing and IV inversion to smile fitting (Polynomial vs SVI), no-arbitrage health checks, and parameter time-series stability.

Run a demo with sample quotes

./iv_lab ../data/sample_quotes.csv 100 0.5 0.02 put

Plot results with Python

python3 plot_smile.py python3 plot_term_structure.py python3 svi_fit.py --S 100 --T 0.5 python3 rolling_stability.py --S 100 --T 0.5 --r 0.02 --n 30 python3 rolling_stability_smoothed.py --S 100 --T 0.5 --r 0.02 --n 30 --alpha 0.2 --rho_step 0.05 python3 rolling_stability_controls.py --S 100 --T 0.5 --r 0.02 --n 30 --alpha 0.35 ...

Mini Term Structure

SVI (single-expiry) demo

Rolling stability (2-min cadence, simulated)

We simulate 30 time steps with mild wing/ATM perturbations and re-fit SVI each step. Outputs:

• results/svi_params_timeseries.png
• data/svi_params_timeseries_example.csv (example)

Key takeaways in our demo:

• ATM IV is highly stable (CV < 1%).
• b, σ are reasonably stable; ρ is the jumpiest (wing asymmetry + parameter coupling).
• Discrete butterfly QC on reconstructed call prices passes (no violations).

Rolling stability — smoothed controls

We add EMA smoothing (α=0.2) and a per-step rate limit on ρ (±0.05). Result: substantial CV reduction across parameters while ATM stays stable. Artifacts:

• results/svi_params_timeseries_smoothed.png
• data/svi_params_timeseries_smoothed_example.csv

Controls tuning (single-expiry)

• Multi-parameter rate-limits + fallback-to-last-good dropped fallbacks to 5/30.
• CVs stay low; ρ remains the most volatile parameter → expected due to skew sensitivity.
• Artifact: results/svi_params_timeseries_controls.png, CSV: data/svi_params_timeseries_controls_example.csv.

Stability Tuning

In practice, raw SVI parameter updates can be noisy, especially for skew (ρ) and shift (m).
We introduced two stabilization techniques:

1. Regularization: a stronger prior on ρ (and a light anchor on m) to prevent erratic jumps.
2. Fallback logic: only revert to the last good state when both loss and violation conditions are triggered.

Results:

• Raw → EMA coefficient of variation (CV) dropped significantly (e.g. ρ: 2.15 → 0.0148 in the controlled run).
• Fallbacks remained moderate (~5 out of 30 steps).
• Skew volatility was markedly reduced, while other parameters (a, b, σ) stayed stable.

This tuning mimics production-style calibration, where stability is as important as fit quality.

Stability Tuning: CV Comparison

Parameter	Raw CV	EMA CV
a	0.64	0.246
b	0.212	0.0421
ρ (rho)	2.15	0.0148
m	0.608	0.114
σ (sigma)	0.226	0.0716

• ρ jitter 2.15 → 0.0148 (biggest improvement).
• Other parameters smoother while preserving fit accuracy.
• Fallbacks limited to ~5/30 → calibration robust without over-correction.

Note: The fallback count (≈5/30) indicates that only a handful of calibration steps required rolling back to the last good parameter set. This mimics production-style workflows where stability is as critical as fit accuracy: too few fallbacks → risk of unstable fits slipping through; too many fallbacks → model becomes over-constrained. Around 5/30 is a healthy balance.

What we learned

• How to invert market option prices into implied volatilities.
• How to fit Polynomial vs SVI smiles and check arbitrage constraints.
• How to evaluate parameter stability across a rolling time series.
• Why stability tuning (priors, EMA smoothing, fallbacks) is critical in practice.
• Practical skills in C++ model prototyping and Python visualization for quant research.

Next steps

• Extend from single-expiry to a full term structure (SVI / SABR).
• Add real market option data ingestion.
• Explore production-style calibration pipelines with robust monitoring.
• Stress-test under extreme skew / jump scenarios.