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Abstract

A class of mean reverting positive stochastic processes driven by alpha-stable distributions, referred to here as alpha-root processes in analogy to the square root process Cox-Ingersoll-Ross process, is a subclass of affine processes, in particular continuous state branching processes with immigration CBI processes. Being affine, they provide semi-analytical results for the implied term structures as well as for the characteristic exponents for their associated distributions. Their use has not been appreciated in the field perhaps due to lack of an efficient numerical algorithm to supplement their semi-analytical results. The present article introduces a convenient formulation of such processes, CBI processes in general, in the form of pure-jump processes of infinite activity. The formulation admits an efficient simulation algorithm that enables an extensive investigation of their properties.



Item Type: MPRA Paper -

Original Title: Alpha-root Processes for Derivatives pricing-

Language: English-

Keywords: alpha-root process; square-root process; Cox-Ingersoll-Ross; CIR; stable process; Levy process; affine process; term-structure model; volatility smile-

Subjects: ?? C16 ??C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C46 - Specific Distributions ; Specific StatisticsC - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: GeneralG - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing-





Autor: Balakrishna, BS

Fuente: https://mpra.ub.uni-muenchen.de/20720/







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