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2008 | 114 | 3 | 629-635
Article title

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

Content
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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
Year
Volume
114
Issue
3
Pages
629-635
Physical description
Dates
published
2008-09
received
2007-11-22
References
  • 1. R. Merton, Continuous Time Finance, Blackwell, Oxford, U.K. 1993
  • 2. F. Black, M. Scholes, J. Political Economy 81, 637 (1973)
  • 3. J.C. Cox, S.A. Ross, M. Rubinstein, J. Finance Econ. 7, 229 (1979)
  • 4. A.N. Shiryaev, Essentials of Stochastic Finance: Facts, Models, Theory, World Sci., Singapore 1999
  • 5. A. Rejman, A. Weron, R. Weron, Stochastic Models 13, 867 (1997)
  • 6. J. Laurent, D. Leisen, in: Quantitative Analysis in Financial Markets, Ed. M. Avellaneda, World Sci., New York 2000, p. 216
  • 7. S. Rachev, S. Mittnik, Stable Paretian Models in Finance, Wiley, New York 2000
  • 8. D. Bertsimas, I. Popescu, Operations Res. 50, 358 (2002)
  • 9. R. Weron, Probabil. Math. Statist. 22, 417 (2002)
  • 10. J.C. Hull, Options, Futures and Other Derivatives, 6th ed., Prentice Hall, London 2005
  • 11. M. Bellalah, M. Lavielle, Multinational Finance J. 6, 99 (2002)
  • 12. M.M. Meerschaert, E. Scalas, Physica A 370, 114 (2006)
  • 13. S. Rachev, L. Rűschendorf, Theory Probab. Appl. 39, 120 (1994)
  • 14. L. Rűschendorf, Tr. Mian. 237, 143 (2002)
  • 15. R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000)
  • 16. I.M. Sokolov, Phys. Rev. E 63, 011104 (2000);Phys. Rev. E 66, 041101 (2002)
  • 17. E. Gudowska-Nowak, K. Weron, Phys. Rev. E 65, 011103 (2001)
  • 18. A.A. Stanislavsky, Theor. Math. Phys. 138, 418 (2004)
  • 19. E. Gudowska-Nowak, K. Bochenek, A. Jurlewicz, K. Weron, Phys. Rev. E 72, 061101 (2005)
  • 20. A. Piryatinska, A.I. Saichev, W.A. Woyczynski, Physica A 349, 375 (2005)
  • 21. K. Weron, A. Jurlewicz, Def. Diff. Forum 237-240, 1093 (2005)
  • 22. K. Weron, A. Jurlewicz, M. Magdziarz, Acta Phys. Pol. B 36, 1855 (2005)
  • 23. M. Magdziarz, K. Weron, Acta Phys. Pol. B 37, 1617 (2006)
  • 24. M. Magdziarz, A. Weron, K. Weron, Phys. Rev. E 75, 016708 (2007)
  • 25. M. Magdziarz, A. Weron, Phys. Rev. E 75, 056702 (2007);76, 066708 (2007)
  • 26. E. Scalas, Physica A 362, 225 (2006)
  • 27. M. Magdziarz, P. Miśta, A. Weron, Acta Phys. Pol. B 38, 1647 (2007)
  • 28. M.M. Meerschaert, H.-P. Scheffler, J. Appl. Probab. 41, 623 (2004)
  • 29. A. Jurlewicz, Diss. Math. 4311, 05
  • (2030). W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 2, Wiley, New York 1966
  • 31. A. Gut, Stopped Random Walks. Limit Theorems and Applications, Springer, New York 1988
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.bwnjournal-article-appv114n319kz
Identifiers
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