Analytical Representations for the Basic Affine Jump Diffusion

The Basic Affine Jump Diffusion (BAJD) process is widely used in financial modeling. In this paper, we develop an exact analytical representation for its transition density in terms of a series expansion that is uniformly-absolutely convergent on compacts. Computationally, our formula complements existing approaches based on numerical inversion and analytical approximation. Furthermore, it can be easily generalized to give an analytical expression for the transition density of the subordinate BAJD process which is more realistic than the BAJD process, while existing approaches cannot