Abstract
Value at Risk (<VaR >) is a notion meant to measure the risk linked to the holding of an asset or a portfolio of diverse assets. It is defined as the amount of money that one might lose with a certain confidence level and within a given time horizon. It is used by bankers because it allows them to measure, compare and consolidate “risk” that is linked to their trading activities. As it has recently been recommended to bankers by many financial institutions, it may increasingly become more and more widespread, with the possibility of becoming a market standard. Within a given time horizon, the portfolio return should not drop below a stated VaR number more often than predicted by the confidence interval. This paper aims to test this assertion under different methods of estimating VaR. Much of the current literature is devoted to the prediction of volatility, another measure of risk commonly used by bankers. However, the predictive power of Value-at-Risk has not been tested so far.
We show that “classical” ways of estimating VaR are valid only in reasonable ranges of confidence intervals. If bankers are looking at very low quantiles, then they might be advised to employ more sophisticated models.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. Bachelier, Théorie de la speculation. Annales de l’Ecole Normale Superieure 3, 17, 21–86, 1990.
J. Bollerslev, A conditional heteroskedastic time series model for speculative prices and rates of return. Review of Economics and Statistics, 69, 542–547, 1987.
T. Bollerslev, Generalized autoregressive conditional heterskedasticity. Journal of Econometrics, 31, 307–327, 1986.
J. Bollerslev, T. Chou, S.A. and Kroner, K.F. Arch modelling in finance. Journal of Econometrics, 7, 229–264, 1992.
J. Boudoukh, M. Richardson, and R. Whitelaw. The stochastic behavior of interest rates. Working paper, Stern School of Business, New York University, 1995.
J.P. Bouchaud, D. Sornette, C. Walter, and J.P. Aguilar. Taming large events; optimal portfolio theory for strongly fluctuating assets. Working paper Stern School of Business, New York University, 1995.
L. Canina and S. Figlewski. The information content of implied volatility. Review of Financial Studies, 6, 659–681, 1993.
T. Day and C. Lewis. Stock market volatility and the information content of stock index options. Journal of Econometrics, 52, 267–287, 1992.
E. Eberlein and H. Keller. Hyperbolic distributions in finance. Technical Report Inst. für Math., Stochastik, Univ. Freiburg, 1995.
R.F. Engle. Autoregressive conditional heterskedasticity with estimates of the variance of U.K. inflation. Econometrica, 50, 987–1008, 1995.
W. Feller. An introduction to probability theory and its applications. Vol 2 Wiley Eastern Ltd., New York, 1965.
B. Gamrowski and S.T. Rachev. A testable version of the Pareto-stable CAPM. Working paper Department of Statistics 6.4 Applied Probability, UCSB, Santa Barbara.
C. Harvey and R. Whaley. S & P 100 index option volatility. Journal of Finance, 46, 1551–1561, 1991.
C. Harvey and R. Whaley. Market volatility prediction and the efficiency of the S & P 100 index option market. Journal of Financial Economics, 31, 43–74, 1992.
B.M. Hill. A simple general approach to inference about the tail of a distribution. Annals of Statistics, 3, 1163–1174, 1975.
P. Jorion. Predicting volatility in the foreign exchange market. Journal of Finance, 50/2, 507–528, 1995.
L.B. Klebanov, J.A. Melamed, S. Mittnik and S.T. Rachev. Integral and asymptotic representations of geo-stable densities. To appear in Applied Mathematics Letters 1995.
T.J. Kozubowski. Geometric stable laws: estimation and applications. Working paper, Department of Mathematics UTC, Chattanooga, 1995.
M. Loretan and P.C.B. Phillips. Testing the variance stationarity of heavy-tailed time series. Journal of Empirical Finance, 1, 211–248, 1994.
B.B. Mandelbrot. The fractal geometry of nature. W.M.Freeman 61 Co., New York, 1977.
J.H. McCulloch. Simple consistent estimators of stable distribution parameters. Communications in Statistics Computation and Simulation, 15, 1109–1136, 1986.
S. Mittnik and S.T. Rachev. Modelling asset returns with alternative stable distributions. Econometric Reviews, 12/3, 261–330, 1993a.
S. Mittnik and S.T. Rachev. Reply to comments on modeling asset returns with alternative stable distributions. Econometric Reviews, 12/3, 347–389, 1993b.
S. Mittnik and S.T. Rachev, S.T. Modeling financial assets with alternative stable models. To appear in Wiley series in Financial Economics and Quantitative analysis, Wiley 1995a.
S. Mittnik and S.T. Rachev. Tail estimation of the stable index a. Working paper, Department of Statistics & Applied Probability, 1995b.
S. Mittnik, A. Panorska and S.T. Rachev. Stable GARCH models for financial time series. Applied Mathematics Letters, 8/5, 33–37, 1995.
E.E. Peters. Fractal market analysis, Wiley & Sons, 1994.
G. Samorodnitsky and M.S. Tagqu. Stable non-gaussian random processes. Chapman and Hall, London, 1994.
V.M. Zolotarev. One dimensional stable distributions. Translation of Mathematical monographs, American Mathematical Society, Vol.65, 1983.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Science+Business Media New York
About this paper
Cite this paper
Gamrowski, B., Rachev, S. (1996). Testing the Validity of Value-at-Risk Measures. In: Heyde, C.C., Prohorov, Y.V., Pyke, R., Rachev, S.T. (eds) Athens Conference on Applied Probability and Time Series Analysis. Lecture Notes in Statistics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0749-8_22
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0749-8_22
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94788-4
Online ISBN: 978-1-4612-0749-8
eBook Packages: Springer Book Archive