Balakrishna, B S (2010): Alpha-root Processes for Derivatives pricing.
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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|
|Keywords:||alpha-root process; square-root process; Cox-Ingersoll-Ross; CIR; stable process; Levy process; affine process; term-structure model; volatility smile|
|Subjects:||C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C16 - Specific Distributions
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
|Depositing User:||S Balakrishna|
|Date Deposited:||16. Mar 2010 01:19|
|Last Modified:||19. Feb 2013 18:43|
S. Asmussen and J. Rosinski (2001), ``Approximations of small jumps of Levy processes with a view towards simulation'', Journal of Applied Probability 38, 482-493.
J. Bertoin (2000), ``Subordinators, Levy Processes with no negative jumps and branching processes'', MaPhySto Lecture Notes, Series 8.
D. Brigo and A. Alfonsi (2005), ``Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model '', Finance and Stochastics 9, 29-42.
P. Carr and L. Wu (2004), ``Time-changed Levy processes and option pricing'', Journal of Financial Economics 71, 113-141.
D. Duffie, D. Filipovic and W. Schachermayer (2003), ``Affine processes and applications in finance'', The Annals of Applied Probability 13, 984-1053.
P. Tankov (2009), ``Pricing and hedging in exponential Levy models: review of recent results'', Lecture notes, available from http://people.math.jussieu.fr/~tankov/.
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Alpha-root Processes for Derivatives pricing. (deposited 11. Jan 2010 17:32)
Alpha-root Processes for Derivatives pricing. (deposited 17. Jan 2010 18:43)
Alpha-root Processes for Derivatives pricing. (deposited 16. Feb 2010 22:38)
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- Alpha-root Processes for Derivatives pricing. (deposited 17. Jan 2010 18:43)