ETD

• Black-Scholes
• calibration
• Heston model
• option pricing
• SABR model
• volatility models
• volatility smile

This thesis presents a comparative calibration study of three volatility modeling approaches for equity option pricing: the Black-Scholes model as a constant-volatility benchmark, the SABR model as a parsimonious smile parameterization, and the Heston model as a stochastic volatility specification.

The empirical analysis is conducted on a snapshot of the SPY option surface, covering five expiries with maturities under three months. A preprocessed implied volatility surface is constructed from market data, applying quality filters to ensure data consistency and employing a per-expiry train/test split strategy to assess both in-sample fit and out-of-sample generalization. Black-Scholes is calibrated as a global constant volatility. SABR is calibrated separately for each expiry using Hagan's closed-form implied volatility approximation. Heston is calibrated globally across all maturities via Fourier-based characteristic function methods.

Model performance is evaluated through multiple criteria: root mean squared error on implied volatility for both training and test sets, calibrated parameter stability and economic interpretability, convergence diagnostics, computational efficiency, and qualitative assessment of static arbitrage-free conditions. The comparative framework identifies trade-offs between model complexity, calibration speed, fit quality, and out-of-sample robustness, providing practical guidance for model selection in different operational contexts.