论文信息 - Value at risk using hyperbolic distributions

Value at risk using hyperbolic distributions

Abstract This article deals with the Value at Risk concept as it is used in practice. We show that, like the Gaussian distribution, elliptical distributions lend themselves to simple practical computations. All necessary computations are detailed for the symmetric hyperbolic distributions. A test on real stock market and exchange rate data shows the new distributions fit the data better and outperform equivalent estimators used in RiskMetrics™. 1 1 Keywords: Hyperbolic distribution; Elliptical distributions; Value at risk JEL classification: C5; G1

Christian Bauer | C. Bauer

[1] O. Barndorff-Nielsen. Exponentially decreasing distributions for the logarithm of particle size , 1977, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[2] A. C. Atkinson,et al. The Simulation of Generalized Inverse Gaussian and Hyperbolic Random Variables , 1982 .

[3] Michael M. Sørensen,et al. A hyperbolic diffusion model for stock prices , 1996, Finance Stochastics.

[4] P. Blæsild. The two-dimensional hyperbolic distribution and related distributions, with an application to Johannsen's bean data , 1981 .

[5] Stephen E. Fienberg,et al. A Celebration of Statistics , 1985 .

[6] Ermittlung von Eigenkapitalanforderungen mit "Internen Modellen" : eine empirische Studie zur Messung von Zins-, Währungs- und Optionsrisiken mit Value-at-Risk-Ansätzen , 1997 .

[7] O. E. Barndorff-Nielsen,et al. Wind shear and hyperbolic distributions , 1989 .

[8] K. Fang,et al. Generalized Multivariate Analysis , 1990 .

[9] E. Eberlein,et al. Hyperbolic distributions in finance , 1995 .

[10] O. Barndorff-Nielsen,et al. The pattern of natural size distributions , 1980 .

[11] R. Chou,et al. ARCH modeling in finance: A review of the theory and empirical evidence , 1992 .

[12] Jens Ledet Jensen,et al. The Fascination of Sand , 1985 .