Scaling of Lévy-Student processes

Physica A: Statistical Mechanics and its Applications

Volumn 389, Issue 7, 2010, Pages 1455-1463

  Grothe, Oliver ^a   Schmidt, Rafael ^a  

^a UNIVERSITY OF COLOGNE   (Germany)

Author keywords

Convolutions; High frequency asset returns; L vy processes; Student's t distributions

Indexed keywords

CONVOLUTION; NORMAL DISTRIBUTION; SCALING LAWS;

ANALYTICAL SCALING; DIFFUSION PROCESS; HEAVY-TAILED; HIGH FREQUENCY HF; MARGINAL DISTRIBUTION; PRICE RETURNS; SCALING BEHAVIOR; STUDENT'S T DISTRIBUTION;

STUDENTS;

EID: 73449110966     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2009.11.039     Document Type: Article

References (30)

1. Cont R. Empirical properties of asset returns: Stylized facts and statistical issues. Quantitative Finance 1 2 (2001) 223-236
2. Gopikrishnan P., Plerou V., Amaral L.A.N., Meyer M., and Eugene Stanley H. Scaling of the distributions of fluctuations of financial market indices. Physical Review E 60 5 (1999) 5305-5316
3. Plerou V., Gopikrishnan P., Amaral L.A.N., Meyer M., and Eugene Stanley H. Scaling of the distribution of price fluctuations of individual companies. Physical Review E 60 6 (1999) 6519-6529
4. Mandelbrot B. The variation of certain speculative prices. The Journal of Business 36 4 (1963) 394-419
5. Eberlein E., and Keller U. Hyperbolic distributions in finance. Bernoulli 1 3 (1995) 281-299
6. Praetz P.D. The distribution of share price changes. The Journal of Business 45 1 (1972) 49-55
7. Blattberg R.C., and Gonedes N.J. A comparison of the stable and Student distributions as statistical models for stock prices. The Journal of Business 47 2 (1974) 244-280
8. Kon S.J. Models of stock returns-A comparison. The Journal of Finance 39 1 (1984) 147-165
9. Barndorff-Nielsen O.E. Normal inverse Gaussian distributions and stochastic volatility modelling. Scandinavian Journal of Statistics 24 1 (1997) 1-13
10. Mantegna R.N., and Eugene Stanley H. Stochastic processes with ultraslow convergence to a Gaussian: The truncated Lévy flight. Physical Review Letters 73 22 (1994) 2946-2949
11. Mantegna R.N., and Eugene Stanley H. Scaling behaviour in the dynamics of an economic index. Nature 376 6535 (1995) 46-49
12. Podobnik B., Ivanov P.Ch., Lee Y., and Eugene Stanley H. Scale-invariant truncated Lévy process. Europhysics Letters 52 5 (2000) 491-497
13. Hurst S.R., Platen E., and Rachev S.T. Subordinated market index models: A comparison. Asia-Pacific Financial Markets 4 2 (1997) 97-124
14. Heyde C.C. A risky asset model with strong dependence through fractal activity time. Journal of Applied Probability 36 4 (1999) 1234-1239
15. Bingham N.H., and Kiesel R. Semi-parametric modelling in finance: Theoretical foundations. Quantitative Finance 2 4 (2002) 241-250
16. Schoutens W. Lévy Processes in Finance: Pricing Financial Derivatives (2003), Wiley, New York
17. Grosswald E. The Student t-distribution of any degree of freedom is infinitely divisible. Probability Theory and Related Fields 36 2 (1976) 103-109
18. Jurek Y.J. Remarks on the self-decomposability and new examples. Demonstratio Mathematica XXXIV 2 (2001) 241-250
19. Nadarajah S., and Dey D.K. Convolutions of the t-distribution. Computers & Mathematics with Applications 49 (2005) 715-721
20. Cufaro Petroni N. Mixtures in nonstable Lévy processes. Journal of Physics A: Mathematical and Theoretical 40 (2007) 2227-2250
21. Barndorff-Nielsen O.E., and Shephard N. Financial Volatility: Stochastic Volatility and Lévy Based Models (2004), Cambridge University Press, Cambridge
22. Oliveira F.A., Mello B.A., and Xavier I.M. Scaling transformation of random walk distributions in a lattice. Physical Review E 61 6 (2000) 7200-7203
23. Heyde C.C., and Leonenko N.N. Student processes. Advances in Applied Probability 37 2 (2005) 342-365
24. Berg C., and Vignat C. On some results of Cufaro Petroni about Student t-processes. Journal of Physics A: Mathematical and Theoretical 41 26 (2008) 265004
25. Berg C., and Vignat C. Linearization coefficients of Bessel polynomials and properties of Student t-distributions. Constructive Approximation 27 1 (2008) 15-32
26. C. Vignat, A. Plastino, Elliptical invariance of distributions of the power type: The stability and extensitivity issues, 2006. arXiv:cond-mat/0602018
27. C. Berg, C. Vignat, On the density of the sum of two independent Student t-random vectors, 2009. arXiv:0906.3037v1[math.PR]
28. Silverman B.W. Density Estimation for Statistics and Data Analysis (1986), Chapman and Hall, London
29. Cont R., and Tankov P. Financial Modelling with Jump Processes (2004), Chapman and Hall, Boca Raton, FL
30. Bouchaud J.-P., and Potters M. Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management. 2nd ed. (2004), Cambridge University Press