Modelling fluctuations of financial time series: From cascade process to stochastic volatility model

European Physical Journal B

Volumn 17, Issue 3, 2000, Pages 537-548

  Muzy, J F ^a   Delour, J ^a   Bacry, E ^b  

^a CENTRE DE RECHERCHE PAUL PASCAL   (France)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

02.50. r Probability theory, stochastic processes, and statistics; 05.40. a Fluctuation phenomena, random processes, noise, and brownian motion; 05.45.Df Fractals

Indexed keywords

EID: 0002127801     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100510070131     Document Type: Article

References (47)

1. J.P. Bouchaud, M. Potters, Theory of financial risk: From statistical physics to risk management (Cambridge University Press, Cambridge, 1999).
2. R. Mantegna, H.E. Stanley, An introduction to econophysics (Cambridge University Press, Cambridge, 2000).
3. J.D. Farmer, Computing in Science & Engineering, Nov.-Dec. (IEEE) 1999, p. 26 and references therein.
4. B.B. Mandelbrot, J. Business 36, 394 (1963).
5. E.F. Fama, J. Business 38, 34 (1965).
6. R.F. Engle, Econometrica 50, 987 (1982).
7. T. Bollersev, R.Y. Chous, K.F. Kroner, J. Econometrics 52, 5 (1992).
8. R.N. Mantegna, H.E. Stanley, Nature 376, 46 (1995).
9. S. Ghashghaie, W. Breymann, J. Peinke, P. Talkner, Y. Dodge, Nature 381, 767 (1996).
10. A. Arneodo, J.F. Muzy, D. Sornette, Eur. Phys. J. B 2, 277 (1998).
11. R.N. Mantegna, H.E. Stanley, Nature 383, 587 (1996).
12. A. Arneodo, J.P. Bouchaud, R. Cont, J.F. Muzy, M. Potters, D. Sornette, Comment on "Turbulent cascades in Foreign exchange markets", preprint cond-mat/9607120 at xxx.lanl.gov.
13. A. Fisher, L. Calvet, B.B. Mandelbrot, Multifractality of the deutschmark/US dollar exchange rate, Cowles Foundation Discussion Paper (1997).
14. N. Vandewalle, M. Ausloos, Int. J. Mod. Phys. C 9, 711 (1998); Eur. Phys. J. B 4, 257 (1998); Physica A 246, 454 (1997).
15. N. Vandewalle, M. Ausloos, Int. J. Mod. Phys. C 9, 711 (1998); Eur. Phys. J. B 4, 257 (1998); Physica A 246, 454 (1997).
16. N. Vandewalle, M. Ausloos, Int. J. Mod. Phys. C 9, 711 (1998); Eur. Phys. J. B 4, 257 (1998); Physica A 246, 454 (1997).
17. B.B. Mandelbrot, Scientific American 280, 70 (1999).
18. K. Ivanova, M. Ausloos, Eur. Phys. J. B 8, 665 (1999).
19. A. Bershadskii, Eur. Phys. J. B 11, 361 (1999).
20. F. Schmitt, D. Schwertzer, S. Levejoy, Multifractal analysis of Foreign Exchange data, preprint (Mc Gill University, Montreal, 1999).
21. H. Markowitz, Portfolio selection: Efficient diversification of investments (John Wiley and Sons, New-York, 1959).
22. E. Bacry, J. Delour, J.F. Muzy, in preparation.
23. E. Bacry, J. Delour, J.F. Muzy, A multifractal random walk, submitted to Phys. Rev. Lett. (April 2000).
24. J.F. Muzy, D. Sornette, J. Delour, A. Arneodo, Multifractal returns and hierarchical portfolio theory, submitted to J. Quantitative Finance (January 2000).
25. G. Bonanno, F. Lillo, R. Mantegna, Dynamics of the number of trades of financial securities, submitted to Physica A, preprint cond-mat 991212006 at xxx.lanl.gov/.
26. U. Frisch, Turbulence (Cambridge University Press, Cambridge, 1995).
27. Y. Meyer, Ondelettes (Hermann, Paris, 1990).
28. I. Daubechies, Ten lectures on wavelet (SIAM, Philadelphia, 1992).
29. S. Mallat, A wavelet tour in signal processing (Academic Press, New-York, 1998).
30. J.F. Muzy, E. Bacry, A. Arneodo, Phys. Rev. Lett. 67, 3515 (1991).
31. E. Bacry, J.F. Muzy, A. Arneodo, J. Stat. Phys. 70, 635 (1993).
32. J.F. Muzy, E. Bacry, A. Arneodo, Int. J. Bifurc. Chaos 4, 245 (1994).
33. A. Arneodo, E. Bacry, J.F. Muzy, Physica A 213, 232 (1994).
34. S. Jaffard, SIAM J. Math. Anal. 28, 944 (1997); SIAM J. Math. Anal. 28, 971 (1997).
35. S. Jaffard, SIAM J. Math. Anal. 28, 944 (1997); SIAM J. Math. Anal. 28, 971 (1997).
36. W. Feller, An introduction to probability theory and its applications, Vol. 2 (John Wiley & Sons, New-York, 1971).
37. B. Castaing, Y. Gagne, E. Hopfinger, Physica D 46, 177 (1990); B. Chabaud, A. Naert, J. Peinke, F. Chillà, B. Castaing, B. Hebral, Phys. Rev. Lett. 73, 3227 (1994).
38. B. Castaing, Y. Gagne, E. Hopfinger, Physica D 46, 177 (1990); B. Chabaud, A. Naert, J. Peinke, F. Chillà, B. Castaing, B. Hebral, Phys. Rev. Lett. 73, 3227 (1994).
39. A. Arneodo, S. Roux, J.F. Muzy, J. Phys. II France 7, 363 (1997).
40. A. Arneodo, E. Bacry, J.F. Muzy, J. Math. Phys. 39, 4163 (1998).
41. A. Arneodo, E. Bacry, S. Manneville, J.F. Muzy, Phys. Rev. Lett. 80, 708 (1998).
42. M.B. Weissman, Rev. Mod. Phys. 60, 537 (1992) and references therein.
43. B.B. Mandelbrot, H.M. Taylor, Op. Res. 15, 1057 (1967).
44. Z. Ding, C.W.J. Granger, J. Econom. 73, 185 (1996).
45. J.P. Bouchaud, M. Potters, M. Meyer, Eur. Phys. J. B 13, 595 (2000).
46. A. Arneodo, S. Manneville, J.F. Muzy, Eur. Phys. J. B 1, 129 (1998).
47. LastWave software freely available at http://wave.cmap.polytechnique.fr/soft/LastWave.