In-Sample Fit or Out-of-sample Robustness? a Comparison between the Black–Scholes and Merton Jump-Diffusion Models

Financial markets are subject to sudden changes in volatility, which can challenge standard option pricing models such as Black–Scholes. While the Black–Scholes model remains a widely used benchmark, its assumptions of constant volatility and continuous price movements may limit its performance during turbulent market conditions. This thesis examines whether the Merton jump–diffusion model provides more reliable option pricing results when evaluated out-of-sample (OOS). The analysis uses European S&P 500 index call options from two periods representing different volatility regimes. The models are calibrated and evaluated based on root mean squared error (RMSE) in both in-sample (IS) and OOS tests. The results show that although the Black–Scholes model fits the calibration data well, its pricing accuracy deteriorates OOS, particularly during high-volatility periods. The Merton model exhibits higher pricing errors in absolute terms but delivers more stable performance across market regimes. Overall, the findings suggest that the main advantage of the Merton jump–diffusion model lies in its greater robustness to changing market conditions rather than consistently lower pricing errors.