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

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Jurlewicz A., Wyłomańska A., Żebrowski P.
Acta Physica Polonica A
|
2008
|
vol. 114
|
issue 3
629-635
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.
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