Journal of Mathematics and Statistics

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

J. Cesars, S.P. Nuiro and J. Vaillant

DOI : 10.3844/jmssp.2019.196.200

Journal of Mathematics and Statistics

Volume 15, 2019

Pages 196-200


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.


© 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.