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,[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. References
|