Basic affine jump diffusion
where B is a standard Brownian motion, and J is an independent compound Poisson process with constant jump intensity l and independent exponentially distributed jumps with mean μ. For the process to be well defined, it is necessary that and . A basic AJD is a special case of an and of a jump diffusion. On the other hand, the Cox–Ingersoll–Ross (CIR) process is a special case of a basic AJD.
and the characteristic function
are known in closed form.
The characteristic function allows one to calculate the density of an integrated basic AJD
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