Affine Diffusion Processes: Theory and Applications

Details Affine Diffusion Processes: Theory and Applications Affine Diffusion Processes: Theory and Applications

2009-01-26

arxiv.org/abs/0901.4003v3

Radon Series Comp. Appl. Math 8, 1-40, 2009

Mathematics

Probability

29 pages, 1 figure

Scientific paper

We revisit affine diffusion processes on general and on the canonical state space in particular. A detailed study of theoretic and applied aspects of this class of Markov processes is given. In particular, we derive admissibility conditions and provide a full proof of existence and uniqueness through stochastic invariance of the canonical state space. Existence of exponential moments and the full range of validity of the affine transform formula are established. This is applied to the pricing of bond and stock options, which is illustrated for the Vasicek, Cox-Ingersoll-Ross and Heston models.

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