Balakrishna, BS (2010): Alpharoot Processes for Derivatives pricing.
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Abstract
A class of mean reverting positive stochastic processes driven by alphastable distributions, 1<=alpha<2, are discussed. They are referred to as alpharoot processes in analogy to the square root process or the CoxIngersollRoss process derived from the Brownian motion. They are affine models in the same sense as the square root process, providing semianalytical 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 semianalytical results. The present article introduces a formulation that admits an efficient simulation algorithm to enable an extensive investigation of their properties.
Item Type:  MPRA Paper 

Original Title:  Alpharoot Processes for Derivatives pricing 
Language:  English 
Keywords:  alpharoot process; squareroot process; CoxIngersollRoss; CIR; stable process; Levy process; termstructure model; volatility smile 
Subjects:  ?? C16 ?? C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C46  Specific Distributions ; Specific Statistics C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General G  Financial Economics > G1  General Financial Markets > G13  Contingent Pricing ; Futures Pricing 
Item ID:  19949 
Depositing User:  S Balakrishna 
Date Deposited:  11. Jan 2010 17:32 
Last Modified:  19. Feb 2013 19:12 
References:  P. Carr, and L. Wu (2004), ``Timechanged Levy processes and option pricing'', Journal of Financial Economics 71 (2004), 113–141. J. C. Cox, J. E. Ingersoll and S. A. Ross (1985), ``A theory of the term structure of interest rates'', Econometrica 53 (1985) 385408. D. Duffie, D. Filipovic, and W. Schachermayer (2003), ``Affine processes and applications in finance'', The Annals of Applied Probability 13 (2003), 984–1053. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/19949 
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