In this present paper we analyze two exponential L´evy models, the Black-Scholes model and the Merton Jump-Diffusion model from the perspective of the investigation of the skewness and excess kurtosis present in underlying assets log-returns distribution. Calibrating both models on real-world financial data and investigating their various moments and mean square error, we obtain results which show how the Merton jump-diffusion model performs better than the Black-Scholes model for modeling log-returns. This conclusion was also confirmed by using the Diebold-Mariano test to compare the forecast accuracy of the two models.
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