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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

Statistical Inference on a Black-Scholes Model with Jumps. Application in Hydrology

J. Cesars1, S.P. Nuiro1 and J. Vaillant1
  • 1 Université des Antilles, Guadeloupe

Abstract

We consider a Stochastic Differential Equation (SDE) driven by a Wiener process and a Poisson measure. This latter measure is associated with a sequence of identically distributed jump amplitudes. Properties of the SDE solution are presented with respect to the associated Wiener and Poisson processes. An algorithm is provided allowing exact numerical simulations of such SDE and implementable within R environment. Statistical inference tools are presented and applied to hydrology data.

Journal of Mathematics and Statistics
Volume 15 No. 1, 2019, 196-200

DOI: https://doi.org/10.3844/jmssp.2019.196.200

Submitted On: 12 June 2019 Published On: 24 July 2019

How to Cite: Cesars, J., Nuiro, S. & Vaillant, J. (2019). Statistical Inference on a Black-Scholes Model with Jumps. Application in Hydrology. Journal of Mathematics and Statistics, 15(1), 196-200. https://doi.org/10.3844/jmssp.2019.196.200

Open AccessCopyright: © 2019 J. Cesars, S.P. Nuiro and J. Vaillant. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Stochastic Differential Equation
  • Wiener Process
  • Poisson Process
  • Likelihood Technique