Alpha-root Processes for Derivatives pricing

A class of mean reverting positive stochastic processes driven by alpha-stable distributions, 1<=alpha<2, are discussed. They are referred to as alpha-root processes in analogy to the square root process or the Cox-Ingersoll-Ross process derived from the Brownian motion. They are affine models in the same sense as the square root process, providing semi-analytical results for the implied term structures as well as for the characteristic exponents for their associated distributions. Though likely that they have caught the attention of researchers in the field, their use has not been appreciated perhaps due to lack of an efficient numerical algorithm to supplement their semi-analytical results. The present article introduces a formulation that admits an efficient simulation algorithm to enable an extensive investigation of their properties.