Robust Multi-Layer Calibration of the Heston Stochastic Volatility Model: The Balanced Premium Calibration Method

Abstract

This thesis presents the balanced premium calibration method (BPCM), a three-layer framework for robustly fitting the Heston stochastic volatility model to large option datasets. The BPCM method involves three layers. Layer 1 ensures market consistency by filtering and structurally repairing raw quotes via put-call parity and bid-ask bounds, separating stable observations from noise. Layer 2 performs daily least-squares calibration of the Heston parameters using closed-form characteristic function pricing and derived analytic gradients and Hessians, thereby achieving rapid convergence without finite-difference approximations. Layer 3 redistributes errors and allows for controlled adjustments to model inputs and outputs, absorbing residual pricing errors and restoring arbitrage-free consistency. Working with 1.5 million call and put quotes on a major equity from 2018 to 2024, BPCM ensured that model prices closely adhere to market bid-ask spreads (91.58% adherence) for stable regimes while maintaining realistic spot price behaviour. The calibrated model achieves high consistency with observed prices and reconstructs the underlying spot price trajectory with minimal deviation even during market crises. In addition to BPCM, this thesis derives explicit closed-form expressions for the Heston model's Hessians.