Stable distributions

Statistical Tools for Finance and Insurance

Volumn , Issue , 2005, Pages 21-44

  Borak, Szymon ^a   Härdle, Wolfgang ^a   Weron, Rafał ^b  

^a HUMBOLDT UNIVERSITY   (Germany)

^b WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84889995352     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/3-540-27395-6_1     Document Type: Chapter

References (36)

1. Bouchaud, J.-P. and Potters, M. (2000). Theory of Financial Risk, Cambridge University Press, Cambridge.
2. Carr, P., Geman, H., Madan, D. B., and Yor, M. (2002). The fine structure of asset returns: an empirical investigation, Journal of Business 75:305-332.
3. Chambers, J. M., Mallows, C. L., and Stuck, B. W. (1976). A method for simulating stable random variables, Journal of the American Statistical Association 71:340-344.
4. D'Agostino, R. B. and Stephens, M. A. (1986). Goodness-of-Fit Techniques, Marcel Dekker, New York.
5. Embrechts, P., Kluppelberg, C., and Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance, Springer.
6. Fama, E. F. (1965). The behavior of stock market prices, Journal of Business 38:34-105.
7. Fama, E. F. and Roll, R. (1971). Parameter estimates for symmetric stable distributions, Journal of the American Statistical Association 66:331-338.
8. Gopikrishnan, P., Plerou, V., Amaral, L. A. N., Meyer, M. and Stanley, H. E. (1999). Scaling of the distribution of fluctuations of financial market indices, Physical Review E 60(5):5305-5316.
9. Guillaume, D. M., Dacorogna, M. M., Dave, R. R., Müller, U. A., Olsen, R. B., and Pictet, O. V. (1997). From the birds eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets, Finance & Stochastics 1:95-129.
10. Härdle, W., Klinke, S., and Müller, M. (2000). XploRe Learning Guide, Springer.
11. Hill, B. M. (1975). A simple general approach to inference about the tail of a distribution, Annals of Statistics 3:1163-1174.
12. Janicki, A. and Weron, A. (1994). Simulation and Chaotic Behavior of a-Stable Stochastic Processes, Marcel Dekker.
13. Kanter, M. (1975). Stable densities under change of scale and total variation inequalities, Annals of Probability 3:697-707.
14. Koutrouvelis, I. A. (1980). Regression-type estimation of the parameters of stable laws, Journal of the American Statistical Association 75:918-928.
15. Kogon, S. M. and Williams, D. B. (1998). Characteristic function based estimation of stable parameters, in R. Adler, R. Feldman, M. Taqqu (eds.), A Practical Guide to Heavy Tails, Birkhauser, pp. 311-335.
16. Levy, P. (1925). Calcul des Probabilites, Gauthier Villars.
17. Mandelbrot, B. B. (1963). The variation of certain speculative prices, Journal of Business 36:394-419.
18. Mantegna, R. N. and Stanley, H. E. (1995). Scaling behavior in the dynamics of an economic index, Nature 376:46-49.
19. McCulloch, J. H. (1986). Simple consistent estimators of stable distribution parameters, Communications in Statistics - Simulations 15:1109-1136.
20. McCulloch, J. H. (1996). Financial applications of stable distributions, in G. S. Maddala, C. R. Rao (eds.), Handbook of Statistics, Vol. 14, Elsevier, pp. 393-425.
21. McCulloch, J. H. (1997). Measuring tail thickness to estimate the stable index α: A critique, Journal of Business & Economic Statistics 15:74-81.
22. Mittnik, S., Doganoglu, T., and Chenyao, D. (1999). Computing the probability density function of the stable Paretian distribution, Mathematical and Computer Modelling 29:235-240.
23. Mittnik, S., Rachev, S. T., Doganoglu, T. and Chenyao, D. (1999). Maximum likelihood estimation of stable Paretian models, Mathematical and Computer Modelling 29:275-293.
24. Nolan, J. P. (1997). Numerical calculation of stable densities and distribution functions, Communications in Statistics - Stochastic Models 13:759-774.
25. Nolan, J. P. (1999). An algorithm for evaluating stable densities in Zolotarev's (M) parametrization, Mathematical and Computer Modelling 29:229-233.
26. Nolan, J. P. (2001). Maximum likelihood estimation and diagnostics for stable distributions, in O. E. Barndorff-Nielsen, T. Mikosch, S. Resnick (eds.), L ́evy Processes, Brikḧauser, Boston.
27. Press, S. J. (1972). Estimation in univariate and multivariate stable distribution, Journal of the American Statistical Association 67:842-846.
28. Rachev, S., ed. (2003). Handbook of Heavy-tailed Distributions in Finance, North Holland.
29. Rachev, S. and Mittnik, S. (2000). Stable Paretian Models in Finance, Wiley.
30. Samorodnitsky, G. and Taqqu, M. S. (1994). Stable Non-Gaussian Random Processes, Chapman & Hall.
31. Stoyanov, S. and Racheva-Iotova, B. (2004). Univariate stable laws in the field of finance - parameter estimation, Journal of Concrete and Applicable Mathematics 2(4), in print.
32. Weron, R. (1996). On the Chambers-Mallows-Stuck method for simulating skewed stable random variables, Statistics and Probability Letters 28:165-171.
33. See also R. Weron, Correction to: On the Chambers-Mallows-Stuck method for simulating skewed stable random variables, Research Report HSC/96/1, Wroclaw University of Technology, 1996, http://www.im.pwr.wroc.pl/~hugo/Publications. html.
34. Weron, R. (2001). Levy-stable distributions revisited: Tail index > 2 does not exclude the Levy-stable regime, International Journal of Modern Physics C 12:209-223.
35. Weron, R. (2004). Computationally intensive Value at Risk calculations, in J. E. Gentle, W. Hardle, Y. Mori (eds.) Handbook of Computational Statistics, Springer, Berlin, 911-950.
36. Zolotarev, V. M. (1986). One-Dimensional Stable Distributions, American Mathematical Society.