Calibration of the subdiffusive arithmetic Brownian motion with tempered stable waiting-times
In the classical analysis many models used to real data description are based on the standard Brownian diffusion-type processes. However, some real data exhibit characteristic periods of constant values. In such cases the popular systems seem not to be applicable. Therefore we propose an alternative approach, based on the combination of the popular arithmetic Brownian motion and tempered stable subordinator. The probability density function of the proposed model can be described by a Fokker-Planck type equation and therefore it has many similar properties as the popular arithmetic Brownian motion. In this paper we propose the estimation procedure for the considered tempered stable subdiffusive arithmetic Brownian motion and calibrate the analyzed process to the real financial data.
|Date of creation:||2010|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Janczura, Joanna & Wyłomańska, Agnieszka, 2009. "Subdynamics of financial data from fractional Fokker-Planck equation," MPRA Paper 30649, University Library of Munich, Germany.
- Marcin Magdziarz & Sebastian Orzel & Aleksander Weron, 2011. "Option pricing in subdiffusive Bachelier model," HSC Research Reports HSC/11/05, Hugo Steinhaus Center, Wroclaw University of Technology.
- Rosinski, Jan, 2007. "Tempering stable processes," Stochastic Processes and their Applications, Elsevier, vol. 117(6), pages 677-707, June.
- Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501, July.
- Sebastian Orzel & Aleksander Weron, 2009. "Calibration of the subdiffusive Black–Scholes model," HSC Research Reports HSC/09/02, Hugo Steinhaus Center, Wroclaw University of Technology.
- Szymon Borak & Wolfgang Härdle & Rafal Weron, 2005. "Stable Distributions," SFB 649 Discussion Papers SFB649DP2005-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Sokolov, I.M & Chechkin, A.V & Klafter, J, 2004. "Fractional diffusion equation for a power-law-truncated Lévy process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 245-251.
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:28593. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter)
If references are entirely missing, you can add them using this form.