Basic affine jump diffusion
In mathematics probability theory, a basic affine jump diffusion (basic AJD) 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 (CIR) 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. References

Stochastic processes