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Original Articles

Levy models and long correlations applied to the study of exchange traded funds

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Pages 1040-1053 | Received 26 Aug 2008, Published online: 01 Jun 2009

References

  • Amster , P. , Averbuj , C. , Mariani , M. C. and Rial , D. 2005 . A Black—Scholes option pricing model with transaction costs . J. Math. Anal. Appl. , 303 : 688 – 695 .
  • Ausloos , M. and Ivanova , K. 2000 . Introducing false EUR and false EUR exchange rates . Physica A , 286 : 353 – 366 .
  • Ausloos , M. , Vandewalle , N. , Boveroux , Ph. , Minguet , A. and Ivanova , K. 1999 . Applications of statistical physics to economic and financial topics . Physica A , 274 : 229 – 240 .
  • Beben , M. and Orlowski , A. 2001 . Correlations in financial time series: Established versus emerging markets . Eur. Phys. J. B , 20 : 527 – 530 .
  • Bouchaud , J.-Ph. and Potters , M. 1997 . Théorie des riques financiers , Paris : Alea-Saclay/Eyrolles .
  • Buldyrev , S. V. , Goldberger , A. L. , Havlin , S. , Mantegna , R. N. , Matsa , M. E. , Peng , C. K. , Simons , M. and Stanley , H. E. 1995 . Long-range correlation properties of coding and noncoding DNA sequences: GenBank analysis . Phys. Rev. E , 51 : 5084 – 5091 .
  • Cizeau , P. , Liu , Y. H. , Meyer , M. , Peng , C. K. and Stanley , H. E. 1997 . Volatility distribution in the S&P500 stock index . Physica A , 245 : 441 – 445 .
  • Figueroa , M. G. , Mariani , M. C. and Ferraro , M. 2003 . The effects of the Asian crisis of 1997 on emergent markets through a critical phenomena model . Int. J. Theoret. Appl. Finance , 6 : 605 – 612 .
  • Hurst , H. E. 1950 . Long term storage of reservoirs . Trans. Am. Soc. Civil Eng. , 116 : 770 – 808 .
  • Ivanova , K. and Ausloos , M. 1999 . Application of the detrended fluctuation analysis (DFA) method for describing cloud breaking . Physica A , 274 : 349 – 354 .
  • Jaroszewicz , S. , Mariani , M. C. and Ferraro , M. 2005 . Long correlations and truncated Levy walks applied to the study of Latin-American market indices . Physica A , 355 : 461 – 474 .
  • Kantelhardt , J. W. , Berkovits , R. , Havlin , S. and Bunde , A. 1999 . Are the phases in the Anderson model long-range correlated? . Physica A , 266 : 461 – 464 .
  • Khintchine , A. Ya. and Levy , P. 1936 . Sur les lois stables . C. R. Acad. Sci. Paris , 202 : 374 – 376 .
  • Koponen , I. 1995 . Analytic approach to the problem of convergence of truncated Levy flights towards the Gaussian stochastic process . Phys. Rev. E , 52 : 1197 – 1199 .
  • Koscienly-Bunde , E. , Roman , H. E. , Bunde , A. , Havlin , S. and Schellnhuber , H. J. 1998 . Long-range power-law correlations in local daily temperature fluctuations . Phil. Mag. B , 77 : 1331 – 1339 .
  • Koscienly-Bunde , E. , Bunde , A. , Havlin , S. , Roman , H. E. , Goldreich , Y. and Schellnhuber , H. J. 1998 . Indication of universal persistence law governing atmospheric variability . Phys. Rev. Lett. , 81 : 729 – 732 .
  • Levy , P. 1925 . Calcul des probabilités , Paris : Gauthier-Villars .
  • Levy , P. 1937 . Théorie de l'Addition des Variables Aléatoires , Paris : Gauthier-Villars .
  • Liu , Y. H. , Cizeau , P. , Meyer , M. , Peng , C. K. and Stanley , H. E. 1997 . Quantification of correlations in economic time series . Physica A , 245 : 437 – 440 .
  • Mandelbrot , B. B. 1963 . The variation of certain speculative prices . J. Business , 36 : 394 – 419 .
  • Mandelbrot , B. B. 1982 . The Fractal Geometry of Nature , New York : Freeman and Co .
  • Mandelbrot , B. B. and Van Ness , J. W. 1968 . Fractional Brownian motions, fractional noises and applications . SIAM Rev , 10 ( 4 ) : 422 – 437 .
  • Mantegna , R. N. and Stanley , H. E. 1994 . Stochastic process with ultra-slow convergence to a Gaussian: The truncated Levy flight . Phys. Rev. Lett. , 73 : 2946 – 2949 .
  • Mantegna , R. N. and Stanley , H. E. 1999 . An Introduction to Econophysics: Correlations and Complexity in Finance , Cambridge : Cambridge University Press .
  • Mantegna , R. N. and Stanley , H. E. 1995 . Scaling behaviour in the dynamics of an economic index . Nature , 376 : 46 – 49 .
  • Mariani , M. C. , Martin , K. , Dombrowski , D. W. and Martinez , D. 2007 . Normalized truncated Levy models applied to the study of financial markets . Aust. J. Math. Anal. Appl. , 4 ( 2, 13 ) : 1 – 9 .
  • Mariani , M. C. and Liu , Y. 2006 . A new analysis of intermittence, scale invariance and characteristic scales applied to the behaviour of financial indices near a crash . Physica A , 367 : 345 – 352 .
  • Mariani , M. C. and Liu , Y. 2007 . Normalized truncated Levy walks applied to the study of financial indices . Physica A , 377 : 590 – 598 .
  • Mariani , M. C. , Libbin , J. D. , Beccar Varela , M. P. , Kumar Mani , V. , Erickson , C. A. and Valles-Rosales , D. J. 2008 . Long correlations and normalized truncated Levy models applied to the study of Indian market indices in comparison with other emerging markets . Physica A , 387 ( 5 ) : 1273 – 1282 .
  • Matia , K. , Pal , M. , Salunkay , H. and Stanley , H. E. 2004 . Scale-dependent price fluctuations for the Indian stock market . Europhys. Lett , 66 ( 6 ) : 909 – 914 .
  • Peng , C. K. , Mietus , J. , Hausdorff , J. M. , Havlin , S. , Stanley , H. E. and Goldberger , A. L. 1993 . Long-range anticorrelations and non-Gaussian behaviour of the heartbeat . Phys. Rev. Lett. , 70 : 1343 – 1346 .
  • Peng , C. K. , Buldyrev , S. V. , Havlin , S. , Simons , M. , Stanley , H. E. and Goldberger , A. L. 1994 . Mosaic organization of DNA nucleotides . Phys. Rev. E , 49 : 1685 – 1689 .
  • Peng , C. K. , Buldyrev , S. V. , Goldberger , A. L. , Mantegna , R. N. , Simons , M. and Stanley , H. E. 1995 . Statistical properties of DNA sequences . Physica A , 221 : 180 – 192 . [Proc. Int'l IUPAP Conf. on Statistical Physics, Taipei]
  • Peng , C. K. , Havlin , S. , Stanley , H. E. and Goldberger , A. L. 1995 . Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series . Chaos , 5 : 82 – 87 . [Proc. NATO Dynamical Disease conference]
  • Podobnik , B. , Horvatic , D. , Pammolli , F. , Wang , F. , Stanley , H. E. and Grosse , I. 2008 . Size-dependent standard deviation for growth rates: Empirical results and theoretical modelling . Phys. Rev. E , 77 : 056102
  • Razdan , A. 2002 . Scaling in the Bombay stock exchange index . PRAMANA , 58 ( 3 ) : 537 – 544 .
  • Stanley , H. E. , Amaral , L. A.N. , Canning , D. , Gopikrishnan , P. , Lee , Y. and Liu , Y. 1999 . Econophysics: Can physicists contribute to the science of economics? . Physica A , 269 : 156 – 169 . [Proc. 1998 Econophysics Workshop]
  • Vandewalle , N. , Ausloos , M. , Houssa , M. , Mertens , P. W. and Heyns , M. M. 1999 . Non-Gaussian behaviour and anticorrelations in ultrathin gate oxides after soft breakdown . Appl. Phys. Lett. , 74 : 1579 – 1581 .
  • Weron , R. 2001 . Levy-stable distributions revisited: tail index >2 does not exclude the Levy-stable regime . Int. J. Mod. Phys. C , 12 : 209 – 223 .
  • Willmott , P. , Dewynne , J. N. and Howison , S. D. 1993 . Option Pricing: Mathematical Models and Computation , Oxford : Oxford Financial Press .

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