Subordinated alpha-stable Ornstein-Uhlenbeck process as a tool for financial data description
AbstractThe classical financial models are based on the standard Brownian diffusion-type processes. However, in exhibition of some real market data (like interest or exchange rates) we observe characteristic periods of constant values. Moreover, in the case of financial data, the assumption of normality is often unsatisfied. In such cases the popular Vasicek model, that is a mathematical system describing the evolution of interest rates based on the Ornstein-Uhlenbeck process, seems not to be applicable. Therefore we propose an alternative approach based on a combination of the popular Ornstein-Uhlenbeck process with a stable distribution and subdiffusion systems that demonstrate such characteristic behavior. The probability density function of the proposed process can be described by a Fokker-Planck type equation and therefore it can be examined as an extension of the basic Ornstein-Uhlenbeck model. In this paper we propose the parameters' estimation method and calibrate the subordinated Vasicek model to the interest rate data.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Hugo Steinhaus Center, Wroclaw University of Technology in its series HSC Research Reports with number HSC/11/03.
Length: 13 pages
Date of creation: 2011
Date of revision:
Publication status: Published in Physica A 390 (2011) 4379–4387.
Vasicek model; Ornstein-Uhlenbeck process; Alpha-stable distribution; Subdiffusion; Estimation; Calibration; Interest rates;
Find related papers by JEL classification:
- C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
- E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
- E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-10-09 (All new papers)
- NEP-ECM-2011-10-09 (Econometrics)
- NEP-ETS-2011-10-09 (Econometric Time Series)
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.:
- Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
- Borak, Szymon & Misiorek, Adam & Weron, Rafal, 2010.
"Models for Heavy-tailed Asset Returns,"
25494, University Library of Munich, Germany.
- Szymon Borak & Adam Misiorek & Rafal Weron, 2010. "Models for Heavy-tailed Asset Returns," HSC Research Reports HSC/10/01, Hugo Steinhaus Center, Wroclaw University of Technology.
- Szymon Borak & Adam Misiorek & Rafał Weron, 2010. "Models for Heavy-tailed Asset Returns," SFB 649 Discussion Papers SFB649DP2010-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Burnecki, Krzysztof & Janczura, Joanna & Weron, Rafal, 2010.
"Building Loss Models,"
25492, University Library of Munich, Germany.
- Young Kim & Svetlozar Rachev & Michele Bianchi & Frank Fabozzi, 2009. "Computing VAR and AVaR in Infinitely Divisible Distributions," Yale School of Management Working Papers amz2569, Yale School of Management.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Rafal Weron).
If references are entirely missing, you can add them using this form.