next up previous contents index
Next: 2. Econometrics Up: csahtml Previous: 1.4 Value at Risk,

References

1
Akgiray, V. and Booth, G.G. (1988). The Stable-law Model of Stock Returns, Journal of Business & Economic Statistics 6: 51-57.

2
Artzner, P., Delbaen, F., Eber, J.-M. and Heath, D. (1999). Coherent measures of risk, Mathematical Finance 9: 203-228.

3
Atkinson, A.C. (1982). The simulation of generalized inverse Gaussian and hyperbolic random variables, SIAM Journal of Scientific & Statistical Computing 3: 502-515.

4
Barndorff-Nielsen, O.E. (1977). Exponentially decreasing distributions for the logarithm of particle size, Proceedings of the Royal Society London A 353: 401-419.

5
Barndorff-Nielsen, O.E. (1995). Normal $ \backslash\backslash$Inverse Gaussian Processes and the Modelling of Stock Returns, Research Report 300, Department of Theoretical Statistics, University of Aarhus.

6
Barndorff-Nielsen, O.E. and Blaesild, P. (1981). Hyperbolic distributions and ramifications: Contributions to theory and applications, in C. Taillie, G. Patil, B. Baldessari (eds.) Statistical Distributions in Scientific Work, Volume 4, Reidel, Dordrecht, pp. 19-44.

7
Basle Committee on Banking Supervision (1995). An internal model-based approach to market risk capital requirements, http://www.bis.org.

8
Bergström, H. (1952). On some expansions of stable distributions, Arkiv for Mathematik II: 375-378.

9
Bibby, B.M. and Sørensen, M. (1997). A hyperbolic diffusion model for stock prices, Finance & Stochastics 1: 25-41.

10
Blaesild, P. and Sorensen, M. (1992). HYP - a Computer Program for Analyzing Data by Means of the Hyperbolic Distribution, Research Report 248, Department of Theoretical Statistics, Aarhus University.

11
Blattberg, R.C. and Gonedes, N.J. (1974). A Comparison of the Stable and Student Distributions as Statistical Models of Stock Prices, Journal of Business 47: 244-280.

12
Borak, Sz., Härdle, W. and Weron, R. (2004). Stable Distributions, in P. Cizek, W. Härdle, R. Weron (eds.) Statistical Tools for Finance and Insurance, Springer.

13
Bouchaud, J.-P. and Potters, M. (2000). Theory of Financial Risk, Cambridge University Press, Cambridge.

14
Box, G.E.P. and Muller, M.E. (1958). A note on the generation of random normal deviates, Annals of Mathematical Statistics 29: 610-611.

15
Boyarchenko, S.I. and Levendorskii, S.Z. (2000). Option pricing for truncated Lévy processes, International Journal of Theoretical and Applied Finance 3: 549-552.

16
Bradley, B.O. and Taqqu, M.S. (2003). Financial Risk and Heavy Tails, in S.T. Rachev (ed.) Handbook of Heavy-tailed Distributions in Finance, North Holland.

17
Brorsen, B.W. and Yang, S.R. (1990). Maximum Likelihood Estimates of Symmetric Stable Distribution Parameters, Communications in Statistics - Simulations 19(4): 1459-1464.

18
Burnecki, K., Kukla, G., Misiorek, A. and Weron, R. (2004). Loss distributions, in P. Cizek, W. Härdle, R. Weron (eds.) Statistical Tools for Finance and Insurance, Springer.

19
Campbell, J.B. (1980). A FORTRAN IV subroutine for the modified Bessel functions of the third kind of real order and real argument, Report NRC/ERB-925, National Research Council, Canada.

20
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.

21
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.

22
Cizek, P., Härdle, W. and Weron, R. (2004). Statistical Tools for Finance and Insurance, Springer. See also: http://www.xplore-stat.de/ebooks/ebooks.html.

23
Cont, R., Potters, M. and Bouchaud, J.-P. (1997). Scaling in stock market data: Stable laws and beyond, in B. Dubrulle, F. Graner, D. Sornette (eds.) Scale Invariance and Beyond, Proceedings of the CNRS Workshop on Scale Invariance, Springer, Berlin.

24
D'Agostino, R.B. and Stephens, M.A. (1986). Goodness-of-Fit Techniques, Marcel Dekker, New York.

25
Dagpunar, J.S. (1989). An Easily Implemented Generalized Inverse Gaussian Generator, Communications in Statistics - Simulations 18: 703-710.

26
Danielsson, J., Hartmann, P. and De Vries, C.G. (1998). The cost of conservatism: Extreme returns, value at risk and the Basle multiplication factor, Risk 11: 101-103.

27
Dowd, K. (2002). Measuring Market Risk, Wiley.

28
Duffie, D. and Pan, J. (1997). An overview of value at risk, Journal of Derivatives 4: 7-49.

29
DuMouchel, W.H. (1971). Stable Distributions in Statistical Inference, Ph.D. Thesis, Department of Statistics, Yale University.

30
DuMouchel, W.H. (1973). On the Asymptotic Normality of the Maximum-Likelihood Estimate when Sampling from a Stable Distribution, Annals of Statistics 1(5): 948-957.

31
Eberlein, E. and Keller, U. (1995). Hyperbolic distributions in finance, Bernoulli 1: 281-299.

32
Eberlein, E., Keller, U. and Prause, K. (1998). New insights into the smile, mispricing and Value at Risk: The hyperbolic model, Journal of Business 71: 371-406.

33
Embrechts, P., Kluppelberg, C. and Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance, Springer.

34
Embrechts, P., Lindskog, F. and McNeil, A.J. (2003). Modelling Dependence with Copulas and Applications to Risk Management, in S.T. Rachev (ed.) Handbook of Heavy-tailed Distributions in Finance, North Holland.

35
Embrechts, P., McNeil, A.J. and Straumann, D. (2002). Correlation and Depend-ence in Risk Management: Properties and Pitfalls, in M.A.H. Dempster (ed.) Risk Management: Value at Risk and Beyond, Cambridge Univ. Press, Cambridge.

36
Fama, E.F. (1965). The behavior of stock market prices, Journal of Business 38: 34-105.

37
Fama, E.F. and Roll, R. (1971). Parameter Estimates for Symmetric Stable Distributions, Journal of the American Statistical Association 66: 331-338.

38
Fang, K.-T., Kotz, S. and Ng, K.-W. (1987). Symmetric Multivariate and Related Distributions, Chapman & Hall, London.

39
Fofack, H. and Nolan, J.P. (1999). Tail Behavior, Modes and Other Characteristics of Stable Distributions, Extremes 2: 39-58.

40
Franke, J., Härdle, W. and Stahl, G. (2000). Measuring Risk in Complex Stochastic Systems, Springer. See also: http://www.xplore-stat.de/ebooks/ebooks.html.

41
Genest, C. and MacKay, J. (1986). The Joy of Copulas: Bivariate Distributions with Uniform Marginals, The American Statistician 40: 280-283.

42
Guillaume, D.M., Dacorogna, M.M., Dave, R.R., Müller, U.A., Olsen, R.B. and Pictet, O.V. (1997). From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets, Finance & Stochastics 1: 95-129.

43
Härdle, W., Klinke, S. and Müller, M. (2000). XploRe Learning Guide, Springer. See also: http://www.xplore-stat.de/ebooks/ebooks.html.

44
Härdle, W., Kleinow, T. and Stahl, G. (2002). Applied Quantitative Finance, Springer. See also: http://www.xplore-stat.de/ebooks/ebooks.html.

45
Härdle, W. and Simar, L. (2003). Applied Multivariate Statistical Analysis, Springer. See also: http://www.xplore-stat.de/ebooks/ebooks.html.

46
Holt, D.R. and Crow, E.L. (1973). Tables and graphs of the stable probability density functions, Journal of Research of the National Bureau of Standards B 77B: 143-198.

47
Janicki, A. and Kokoszka, P. (1992). Computer investigation of the rate of convergence of LePage type series to alpha-stable random variables, Statistica 23: 365-373.

48
Janicki, A. and Weron, A. (1994a). Can one see $ \alpha $-stable variables and processes, Statistical Science 9: 109-126.

49
Janicki, A. and Weron, A. (1994b). Simulation and Chaotic Behavior of $ \alpha $-Stable Stochastic Processes, Marcel Dekker.

50
Joe, H. (1997). Multivariate Models and Dependence Concepts, Chapman & Hall, London.

51
Jorion, P. (2000). Value at Risk: The New Benchmark for Managing Financial Risk, McGraw-Hill.

52
Karlis, D. (2002). An EM type algorithm for maximum likelihood estimation for the Normal Inverse Gaussian distribution, Statistics and Probability Letters 57: 43-52.

53
Khindarova, I., Rachev, S. and Schwartz, E. (2001). Stable Modeling of Value at Risk, Mathematical and Computer Modelling 34: 1223-1259.

54
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.

55
Koponen, I. (1995). Analytic approach to the problem of convergence of truncated Levy flights towards the Gaussian stochastic process, Physical Review E 52: 1197-1199.

56
Koutrouvelis, I.A. (1980). Regression-Type Estimation of the Parameters of Stable Laws, Journal of the American Statistical Association 75: 918-928.

57
Küchler, U., Neumann, K., Sørensen, M. and Streller, A. (1999). Stock returns and hyperbolic distributions, Mathematical and Computer Modelling 29: 1-15.

58
Laha, R.G. and Rohatgi, V.K. (1979). Probability Theory, Wiley.

59
Leobacher, G. and Pillichshammer, F. (2002). A Method for Approximate Inversion of the Hyperbolic CDF, Computing 69: 291-303.

60
LePage, R., Woodroofe, M. and Zinn, J. (1981). Convergence to a stable distribution via order statistics, Annals of Probability 9: 624-632.

61
Lévy, P. (1925). Calcul des Probabilites, Gauthier Villars.

62
Lillestöl, J. (2001). Bayesian Estimation of NIG-parameters by Markov chain Monte Carlo Methods, Discussion paper 2001/3, Department of Finance and Management Science, The Norwegian School of Economics and Business Administration.

63
Madan, D.B. and Seneta, E. (1990). The variance gamma (V.G.) model for share market returns, Journal of Business 63: 511-524.

64
Mandelbrot, B.B. (1963). The variation of certain speculative prices, Journal of Business 36: 394-419.

65
Mantegna, R.N. (1994). Fast, accurate algorithm for numerical simulation of Levy stable stochastic processes, Physical Review E 49: 4677-4683.

66
Mantegna, R.N. and Stanley, H.E. (1994). Stochastic processes with ultraslow convergence to a Gaussian: The truncated Lévy flight, Physical Review Letters 73: 2946-2949.

67
Mantegna, R.N. and Stanley, H.E. (1995). Scaling behavior in the dynamics of an economic index, Nature 376: 46-49.

68
Marshall, A.W. and Olkin, I. (1988). Families of Multivariate Distributions, Journal of the American Statistical Association 83: 834-841.

69
Matacz, A. (2000). Financial Modeling and Option Theory with the Truncated Lévy Process, International Journal of Theoretical and Applied Finance 3(1): 143-160.

70
McCulloch, J.H. (1986). Simple Consistent Estimators of Stable Distribution Parameters, Communications in Statistics - Simulations 15: 1109-1136.

71
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.

72
McCulloch, J.H. (1997). Measuring Tail Thickness to Estimate the Stable Index $ \alpha $: A Critique, Journal of Business & Economic Statistics 15: 74-81.

73
McCulloch, J.H. (1998). Numerical Approximation of the Symmetric Stable Distribution and Density, in R. Adler, R. Feldman, M. Taqqu (eds.), A Practical Guide to Heavy Tails, Birkhauser, pp. 489-500.

74
Michael, J.R., Schucany, W.R. and Haas, R.W. (1976). Generating Random Variates Using Transformations with Multiple Roots, The American Statistician 30: 88-90.

75
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.

76
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.

77
Nelder, J.A. and Mead, R. (1965). A Simplex Method for Function Minimization, The Computer Journal 7: 308-313.

78
Nelsen, R.B. (1999). An Introduction to Copulas, Springer, New York.

79
Nolan, J.P. (1997). Numerical Calculation of Stable Densities and Distribution Functions, Communications in Statistics - Stochastic Models 13: 759-774.

80
Nolan, J.P. (1999). An Algorithm for Evaluating Stable Densities in Zolotarev's (M) Parametrization, Mathematical and Computer Modelling 29: 229-233.

81
Nolan, J.P. (2001). Maximum Likelihood Estimation and Diagnostics for Stable Distributions, in O.E. Barndorff-Nielsen, T. Mikosch, S. Resnick (eds.), Lévy Processes, Brikhäuser, Boston.

82
Officer, R.R. (1972). The Distribution of Stock Returns, Journal of the American Statistical Association 67: 807-812.

83
Ojeda, D. (2001). Comparison of stable estimators, Ph.D. Thesis, Department of Mathematics and Statistics, American University.

84
Prause, K. (1999). The Generalized Hyperbolic Model: Estimation, Financial Derivatives, and Risk Measures, Ph.D. Thesis, Freiburg University, http://www.freidok.uni-freiburg.de/volltexte/15.

85
Press, S.J. (1972). Estimation in Univariate and Multivariate Stable Distribution, Journal of the American Statistical Association 67: 842-846.

86
Press, W., Teukolsky, S., Vetterling, W. and Flannery, B. (1992). Numerical Recipes in C, Cambridge University Press. See also: http://www.nr.com.

87
Rachev, S. and Mittnik, S. (2000). Stable Paretian Models in Finance, Wiley.

88
Rank, J. and Siegl, T. (2002). Applications of Copulas for the Calculation of Value-at-Risk, in W. Härdle, T. Kleinow, G.P. Stahl (eds.) Applied Quantitative Finance, Springer.

89
Rydberg, T.H. (1997). The Normal Inverse Gaussian Lévy Process: Simulation and Approximation, Communications in Statistics - Simulations 13(4): 887-910.

90
Samorodnitsky, G. and Taqqu, M.S. (1994). Stable Non-Gaussian Random Processes, Chapman & Hall.

91
Schmidt, R. (2004). Tail dependence, in P. Cizek, W. Härdle, R. Weron (eds.) Statistical Tools for Finance and Insurance, Springer.

92
Shuster, J. (1968). On the Inverse Gaussian Distribution Function, Journal of the American Statistical Association 63: 1514-1516.

93
Stahl, G. (1997). Three cheers, Risk 10: 67-69.

94
Stute, W., Manteiga, W.G. and Quindimil, M.P. (1993). Bootstrap Based Goodness-Of-Fit-Tests, Metrika 40: 243-256.

95
Teichmoeller, J. (1971). A Note on the Distribution of Stock Price Changes, Journal of the American Statistical Association 66: 282-284.

96
Temme, N.M. (1975). On the numerical evaluation of the modified Bessel function of the third kind, Journal of Computational Physics 19: 324-337.

97
Venter, J.H. and de Jongh, P.J. (2002). Risk estimation using the Normal Inverse Gaussian distribution, The Journal of Risk 4: 1-23.

98
Weron, R. (1996). On the Chambers-Mallows-Stuck Method for Simulating Skewed Stable Random Variables, Statistics and Probability Letters 28: 165-171. See also R. Weron (1996) Correction to: On the Chambers-Mallows-Stuck Method for Simulating Skewed Stable Random Variables, Research Report HSC/96/1, http://www.im.pwr.wroc.pl/~hugo/Publications.html.

99
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.

100
Zolotarev, V.M. (1964). On representation of stable laws by integrals, Selected Translations in Mathematical Statistics and Probability 4: 84-88.

101
Zolotarev, V.M. (1986). One-Dimensional Stable Distributions, American Mathematical Society.



Subsections