Basic affine jump diffusion
In probability theory, a basic affine jump diffusion is a stochastic process Z of the form
where is a standard Brownian motion, and is an independent compound Poisson process with constant jump intensity and independent exponentially distributed jumps with mean. For the process to be well defined, it is necessary that and. A basic AJD is a special case of an affine process and of a jump diffusion. On the other hand, the Cox–Ingersoll–Ross process is a special case of a basic AJD.
Basic AJDs are attractive for modeling default times in credit risk applications, since both the moment generating function
and the characteristic function
are known in closed form.
The characteristic function allows one to calculate the density of an integrated basic AJD
by Fourier inversion, which can be done efficiently using the FFT.
