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
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.