Alpha-root Processes for Derivatives pricing

Balakrishna, BS (2010): Alpha-root Processes for Derivatives pricing.

Abstract

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: alpha-root process; square-root process; Cox-Ingersoll-Ross; CIR; stable process; Levy process; term-structure model; volatility smile
• Subjects: 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

References

P. Carr, and L. Wu (2004), ``Time-changed 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) 385-408.

D. Duffie, D. Filipovic, and W. Schachermayer (2003), ``Affine processes and applications in finance'', The Annals of Applied Probability 13 (2003), 984–1053.