North Carolina State University · Jan 2026 – May 2026
Calibration and Hedging of Local, Stochastic, and Hybrid Volatility Models
A unified calibration and hedging framework for Local (Dupire), Stochastic (Heston), and Stochastic-Local Volatility (SLV) models across 5,000+ SPX option contracts.
DupireHestonSVIPDEDelta Hedging
Market IV
SVI model fit
Delta-hedging P&L leakage, indexed to Black-Scholes = 100Lower is better · simulated
Charts are illustrative reconstructions matching the reported metrics; the underlying course project is not public.
Approach & findings
- Developed a unified calibration and hedging framework in Python for Local (Dupire), Stochastic (Heston), and Stochastic-Local Volatility (SLV) models using 5,000+ SPX option contracts.
- Constructed an arbitrage-free volatility surface via SVI parameterization, achieving an overall RMSE of 2.47% and a 94% convergence rate for Black-Scholes inversion using the Secant Method.
- Implemented a finite-difference PDE solver for the Dupire model and calibrated Heston parameters to capture dynamic smile effects, reducing pricing errors by ~15% in deep out-of-the-money strikes.
- Benchmarked Delta-hedging performance against a Black-Scholes baseline, demonstrating a 12% reduction in P&L leakage across a 1-year backtest, and stress-tested model robustness against the 2020 COVID-19 regime, maintaining surface stability with a maximum RMSE of 3.8% during peak VIX periods.
Results
- Surface RMSE
- 2.47%
- BS Inversion Convergence
- 94%
- Deep-OTM Error Reduction
- ~15%
- P&L Leakage Reduction
- 12%