  In this paper, enlightened by the asymptotic expansion methodology developed
by Li(2013b) and Li and Chen (2016), we propose a Taylor-type approximation for
the transition densities of the stochastic differential equations (SDEs) driven
by the gamma processes, a special type of Levy processes. After representing
the transition density as a conditional expectation of Dirac delta function
acting on the solution of the related SDE, the key technical method for
calculating the expectation of multiple stochastic integrals conditional on the
gamma process is presented. To numerically test the efficiency of our method,
we examine the pure jump Ornstein--Uhlenbeck (OU) model and its extensions to
two jump-diffusion models. For each model, the maximum relative error between
our approximated transition density and the benchmark density obtained by the
inverse Fourier transform of the characteristic function is sufficiently small,
which shows the efficiency of our approximated method.
