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

A. Jurlewicz a, A. Wyłomańska a and P. Żebrowski b a Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland b Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-348 Wrocław, Poland

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Received: 22 11 2007;

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.

DOI: 10.12693/APhysPolA.114.629 PACS numbers: 89.65.Gh, 05.40.Fb