Financial Data Analysis by means of Coupled Continuous-Time Random Walk in Rachev-Rűschendorf Model

• Authors: A. Jurlewicz , A. Wyłomańska , P. Żebrowski
• Languages of publication: EN

Abstracts

EN

We adapt the continuous-time random walk formalism to describe asset price evolution. We expand the idea proposed by Rachev and Rűschendorf who analyzed the binomial pricing model in the discrete time with randomization of the number of price changes. As a result, in the framework of the proposed model we obtain a mixture of the Gaussian and a generalized arcsine laws as the limiting distribution of log-returns. Moreover, we derive an European-call-option price that is an extension of the Black-Scholes formula. We apply the obtained theoretical results to model actual financial data and try to show that the continuous-time random walk offers alternative tools to deal with several complex issues of financial markets.

Keywords

EN

89.65.Gh; 05.40.Fb

Discipline

• 89.65.Gh: Economics; econophysics, financial markets, business and management(for economic issues regarding production and use of renewable energy, see 88.05.Lg)
• 05.40.Fb: Random walks and Levy flights

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2008
• Volume: 114
• Issue: 3
• Pages: 629-635

Dates

published

2008-09

received

2007-11-22

Contributors

author

A. Jurlewicz

• Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland

author

A. Wyłomańska

• Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland

author

P. Żebrowski

• Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-348 Wrocław, Poland

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Identifiers

DOI

10.12693/APhysPolA.114.629