Summary
The paper presents a consistent approach to the modeling of general and specific market risk as defined in regulatory documents. It compares the statistically based beta-factor model with a class of benchmark models that use a broadly based index as major building block for modeling. The investigation of log-returns of stock prices that are expressed in units of the market index reveals that these are likely to be Student t distributed. A corresponding discrete time benchmark model is used to calculate Value-at-Risk for equity portfolios.
Similar content being viewed by others
References
Alexander, C. (1996). Handbook of Risk Management and Analysis. Wiley, Chichester.
Artzner, P., F. Delbaen, J. M. Eber, & D. Heath (1997). Thinking coherently. Risk 10, 68–71.
Barndorff-Nielsen, O. (1978). Hyperbolic distributions and distributions on hyperbolae. Scand. J. Statist 5, 151–157.
Barndorff-Nielsen, O. (1995). NormalInverse Gaussian processes and the modelling of stock returns. Technical report, University of Aarhus. 300.
Basle (1996a). Amendment to the Capital Accord to Incorporate Market Risks. Basle Committee on Banking and Supervision, Basle, Switzerland.
Basle (1996b). Modifications to the Market Risk Amendment. Basle Committee on Banking and Supervision, Basle, Switzerland.
Black, F. & M. Scholes (1973). The pricing of options and corporate liabilities. J. Political Economy 81, 637–659.
Dacorogna, M., U. A. Müller, O. V. Pictet, & C. G. De Vries (2001). Extremal forex returns in extremely large data sets. Extremes 4(2), 105–127.
Duffie, D. & J. Pan (1997). An overview of Value at Risk. J. of Derivatives 4(3), 7–49.
Duffie, D. & J. Pan (2001). Analytic Value at Risk with jumps and credit risk. Finance Stoch. 5, 155–180.
Eberlein, E. & U. Keller (1995). Hyperbolic distributions in finance. Bernoulli 1, 281–299.
Embrechts, P., A. McNeal, & D. Straumann (2002). Correlation and dependencies in risk management: Properties and pitfalls. In Risk Management: Value at Risk and Beyond, pp. 176–223. Cambridge Univ. Press.
Fang, K. T., S. Kotz, & K. W. Ng (1990). Symmetric Multivariate and Related Distributions. Chapman Hall, London.
Gibson, M. S. (2001). Incorporating event risk into Value at Risk. Discussion Paper Federal Reserve Bord, Washington (http://www.gioriamundi.org).
Hurst, S. R. & E. Platen (1997). The marginal distributions of returns and volatility. In Y. Dodge (Ed.), L 1 -Statistical Procedures and Related Topics, Volume 31 of IMS Lecture Notes — Monograph Series, pp. 301–314. Institute of Mathematical Statistics Hayward, California.
Huschens, S. & Y. Kim (1999). Measuring risk in Value-at-Risk based on Student’s t-distribution. In W. Gaul and H. Locarek-Junge (Eds.), Proceedings of the GfKl-Conference in Dresden 1998, pp. 453–459. Berlin, Springer.
Jorion, P. (2000). Value at Risk: The New Benchmark for Controlling Market Risk (2nd ed.). Irwin, Chicago.
Kelly, J. R. (1956). A new interpretation of information rate. Bell Syst. Techn. J. 35, 917–926.
Madan, D. B. & E. Seneta (1990). The variance gamma (V.G.) model for share market returns. J. Business 63, 511–524.
Merton, R. C. (1973). An intertemporal capital asset pricing model. Econometrica 41, 867–888.
Platen, E. (2001). A minimal financial market model. In Trends in Mathematics, pp. 293–301. Birkhäuser.
Platen, E. (2002). Arbitrage in continuous complete markets. Adv. in Appl. Probab. 34(3), 540–558.
Platen, E. (2003). Diversified portfolios in a benchmark framework. Technical report, University of Technology, Sydney. QFRG Research Paper 87.
Praetz, P. D. (1972). The distribution of share price changes. J. Business 45, 49–55.
Rao, C. R. (1973). Linear Statistical Inference and Its Applications (2nd ed.). Wiley, New York.
RiskMetrics (1996). Technical Document (4th ed.).
Author information
Authors and Affiliations
Additional information
The views in this paper should not be construed as endorsed by the GFSA.
Rights and permissions
About this article
Cite this article
Platen, E., Stahl, G. A Structure for General and Specific Market Risk. Computational Statistics 18, 355–373 (2003). https://doi.org/10.1007/BF03354603
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03354603