Daksh Kumar.
All projects
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
Implied vol % · simulated
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%