Journal of Applied Mathematics & Bioinformatics

Modeling Underlying Assets Log-return in Merton Jump-Diffusion Framework

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  • Abstract

    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.

    Keywords: Black-Scholes (BS) model; Merton jump-diffusion (MJD) model; log-returns; skewness; excess kurtosis