Estimation of the Characteristics of the Jumps of a General Poisson-Diffusion Model

We consider a filtered probability space with a standard Brownian motion W, a simple Poisson process N with constant intensity ƒÉ>0, and we consider the process Y such that Y0¸R and dYt=atdt+ƒÐtdWt+ƒÁtdNt,t>0, where a, ƒÐ are predictable bounded stochastic processes, and ƒÁ is a predictable process which is bounded away from zero. A discrete record of n+1 observations {Y0, Yt1, c, Ytn−1, Ytn} is available, with ti=ih. Using such observations, we construct estimators of Nti, i=1, c, n, ƒÉ and ƒÁƒÑj, where ƒÑj are the instants of jump within [0, nh]. They are consistent and asymptotically controlled when the number of observations increases and the step h tends to zero. Keywords: Stock Price Model, Quadratic Variation Process, Paths Of a Brownian Stochastic Integral, Simple Poisson Process, Estimators