Abstract. In the present paper we perform a comparison between the standard Black and Scholes model and the Merton jump-diffusion one, from the point of view of the study of the leptokurtic feature of log-returns and also concerning the volatility smile fitting. Provided results are obtained by calibrating on market data and by mean of numerical simulations which clearly show how the jump-diffusion model outperforms the classical geometric Brownian motion approach.

Received: August 3, 2016

Revised: September 16, 2016

Published: October 1, 2016

AMS Subject Classification: 60H15, 60H35, 91B60, 91G20, 91G60

Key Words and Phrases: Black and Scholes model, Merton model, stochastic differential equations, log-returns, volatility smile
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DOI: 10.12732/ijpam.v109i3.19 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 3
Pages: 719 - 736

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This work is licensed under the Creative Commons Attribution International License (CC BY).

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