![]() | This article may be too technical for most readers to understand.(January 2022) |
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, [1] [2] [3] [4] since both the moment generating function
and the characteristic function
are known in closed form. [3]
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.
{{
cite journal}}
: Cite journal requires |journal=
(
help)
Preprint
![]() | This article may be too technical for most readers to understand.(January 2022) |
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, [1] [2] [3] [4] since both the moment generating function
and the characteristic function
are known in closed form. [3]
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.
{{
cite journal}}
: Cite journal requires |journal=
(
help)
Preprint