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

In this present paper we analyze two exponential Levy 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 financi...

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Bibliographic Details
Published in:Journal of applied mathematics and bioinformatics 2020-01, Vol.10 (1), p.11-30
Main Authors: Staures, Megang Nkamga Junile, Aduda, Jane Akinyi, Momeya, Romuald
Format: Article
Language:English
Subjects:
Applied mathematics
Assets
Diffusion
Kurtosis
Model accuracy
Modelling
Securities markets
Stochastic models
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Summary:In this present paper we analyze two exponential Levy 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.
ISSN:1792-6939
1792-6939