Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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EMPIRICAL REALITIES FOR A MINIMAL DESCRIPTION RISKY ASSET MODEL. THE NEED FOR FRACTAL FEATURES

  • Christopher C.Heyde (Center for Applied Probability, Columbia University) ;
  • Liu, S. (School of Mathematical Sciences, Australian National University)
  • Published : 2001.09.01
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Abstract

The classical Geometric Brownian motion (GBM) model for the price of a risky asset, from which the huge financial derivatives industry has developed, stipulates that the log returns are iid Gaussian. however, typical log returns data show a distribution with much higher peaks and heavier tails than the Gaussian as well as evidence of strong and persistent dependence. In this paper we describe a simple replacement for GBM, a fractal activity time Geometric Brownian motion (FATGBM) model based on fractal activity time which readily explains these observed features in the data. Consequences of the model are explained, and examples are given to illustrate how the self-similar scaling properties of the activity time check out in practice.

Keywords

References

  1. Self-Similar Network Traffic Analysis and Performance Evaluation Wavelets for the analysis,estimation and synthesis of scaling data P.Abry;P.Flandrin;M.S.Taqqu;D.Veitch;Park K.;Willinger W.(Ed.)
  2. Statistics for Long-Memory Processes J.Beran
  3. J.Political Econom. v.81 The pricing of options and corporate liabilities F.Black;M.Scholes
  4. J.Econometrics v.73 Modeling volatility persistence of speculative returns: A new approach Z.Ding;C.W.J.Granger
  5. J.Econometrics v.73 Varieties of long memory models C.W.J.Granger;Z.Ding
  6. Operations Research v.27 The effect of long-term dependence on risk-return models of common stocks M.T.Greene;B.D.Fielitz
  7. Quantitative Finance Research Group Research Modelling the stochastic dynamics of volatility for equity indices D.Heath;S.Hurst;E.Platen
  8. J.Appl.Probab. v.36 A risky asset model with strong dependence through fractal activity time C.C.Heyde
  9. Fractals and contingent claims C.C.Heyde;R.Gay
  10. Manuscript in preparation Market activity and fractal scaling C.C.Heyde;S.Liu
  11. J.Appl.Probab. v.34 On defining long-range dependence C.C.Heyde;Y.Yang
  12. L₁-Statistical Procedures and Related Topics;IMS Lecture Notes Monogr.Ser. v.31 The marginal distribution of returns and volatility S.R.Hurst;E.Platen;Dodge Y.(Ed.)
  13. Fing.Eng.Japanese Markets v.4 Subordinated Markov models: a comparison S.R.Hurst;E.Platen;S.T.Rachev
  14. Oper.Res. v.15 On the distribution of stock price differences B.Mandelbrot;H.Taylor
  15. Bell.J.Econom.Manag.Sci. v.4 The theory of rational option pricing R.C.Merton
  16. J.Business v.45 The distribution of share price changes P.Praetz
  17. Facts;Modles;Theory Essentials of Stochastic Finance A.M.Shiryaev
  18. Special issue on Multiscale Statistical Signal Analysis and its Applications v.45 A wavelet-based joint estimator of the parameters of long-range dependence D.Veitch;P.Abry