Abstract
Distributional assumptions of financial return data are an important issue for asset-pricing and portfolio management as well as risk controlling. In order to capture the departure of empirical observations of financial return data from normality the Student’s t-distribution has been proposed as an alternative fat-tailed distribution in the literature. In this paper we (i) briefly summarize the Student’s t-distribution; (ii) compare the tail behavior of the Student’s t-distribution with empirical data; and (iii) discuss some implications of the empirical results on the risk management based on Value-at-Risk. We also suggest a simple statistic as a measure of tail-thickness based on the sample quantile and the first absolute moment.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
BACHELIER, L.J.B.A. (1900): Théorie de la spéculation. Gauthier-Villars, Paris. Reprinted in P.H. Cootner (ed.): The Random Character of Stock Market. M.I.T. Press, Cambridge, 1964, 17–78.
BASLE COMMITTEE ON BANKING SUPERVISION (1996): Amendment to the capital accord to incorporate market risks. Basle.
BLATTBERG, R.C. and GONEDES N.J. (1974): A comparison of the stable and Student distributions as statistical models for stock prices. Journal of Business, 47, 244–280.
BOLLERSLEV, T. (1987): A conditional heteroskedastic time series model for speculative prices and rates of return. Review of Economics and Statistics, 69, 542–547.
BOLLERSLEV, T., ENGLE, R.F. and NELSON, D. (1994): ARCH models. In: R.F. Engle and D.L. McFadden (eds.): Handbook of Econometrics, Vol. 4, Amsterdam, North-Holland, 2959–3038.
DUMOUCHEL, W.H. (1973): Stable distributions in statistical inference: 1. Symmetric stable distributions compared to other symmetric long-tailed distributions. Journal of the American Statistical Association, 68, 469–477.
DUFFIE, D. and PAN, J. (1997): An overview of value at risk. The Journal of Derivatives, 4, 7–49.
ENGLE, R.F. (1982): Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation. Econometrica, 50, 987–1008.
HAMILTON, J.D. and SUSMEL, R. (1994): Autoregressive conditional heteroskedasticity and changes in regime. Journal of Econometrics, 64, 307–333.
HUSCHENS, S. and KIM, J.-R. (1998): Measuring risk in value-at-risk in the presence of infinite variance. Dresdner Beiträge zu Quantitativen Verfahren, Vol. 25, Technische Universität Dresden.
JORION, P. (1997): Value at Risk: The New Benchmark for Controlling Market Risk, McGraw-Hill, New York.
MANDELBROT, B. (1963): The variation of certain speculative prices. Journal of Business, 36, 394–419.
MERTON, R.C. (1973): An intertemporal capital asset pricing model. Econometrica, 41, 867–887.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin · Heidelberg
About this paper
Cite this paper
Huschens, S., Kim, JR. (1999). Measuring Risk in Value-at-Risk Based on Student’s t-Distribution. In: Gaul, W., Locarek-Junge, H. (eds) Classification in the Information Age. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60187-3_48
Download citation
DOI: https://doi.org/10.1007/978-3-642-60187-3_48
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65855-9
Online ISBN: 978-3-642-60187-3
eBook Packages: Springer Book Archive