Volume 95, Number 2, July 2011
|Number of page(s)||5|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||04 July 2011|
Exact probability distribution function for multifractal random walk models of stocks
Institute of Physics, Academia Sinica - Nankang, Taipei 11529, Taiwan
2 Yerevan Physics Institute - 2 Alikhanian Brothers St., Yerevan 375036, Armenia
3 Physics Division, National Center for Theoretical Sciences, National Taiwan University Taipei 106, Taiwan
4 Yerevan State University - Alex Manoogian 1, Yerevan 375025, Armenia
5 Graduate School of Education, The University of Tokyo - Bunkyo-ku, Tokyo 113-0033, Japan
Accepted: 2 June 2011
We investigate the multifractal random walk (MRW) model, popular in the modelling of stock fluctuations in the financial market. The exact probability distribution function (PDF) is derived by employing methods proposed in the derivation of correlation functions in string theory, including the analytical extension of Selberg integrals. We show that the recent results by Y. V. Fyodorov, P. Le Doussal and A. Rosso obtained with the logarithmic Random Energy Model (REM) model are sufficient to derive exact formulas for the PDF of the log returns in the MRW model.
PACS: 89.65.Gh – Economics; econophysics, financial markets, business and management / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EPLA, 2011
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