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Basic affine jump diffusion

Stochastic process From Wikipedia, the free encyclopedia

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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.

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