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A Structure for General and Specific Market Risk

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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.

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References

  • Alexander, C. (1996). Handbook of Risk Management and Analysis. Wiley, Chichester.

    Google Scholar 

  • Artzner, P., F. Delbaen, J. M. Eber, & D. Heath (1997). Thinking coherently. Risk 10, 68–71.

    Google Scholar 

  • Barndorff-Nielsen, O. (1978). Hyperbolic distributions and distributions on hyperbolae. Scand. J. Statist 5, 151–157.

    MathSciNet  MATH  Google Scholar 

  • 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.

    Google Scholar 

  • Basle (1996b). Modifications to the Market Risk Amendment. Basle Committee on Banking and Supervision, Basle, Switzerland.

    Google Scholar 

  • Black, F. & M. Scholes (1973). The pricing of options and corporate liabilities. J. Political Economy 81, 637–659.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • Duffie, D. & J. Pan (1997). An overview of Value at Risk. J. of Derivatives 4(3), 7–49.

    Article  Google Scholar 

  • Duffie, D. & J. Pan (2001). Analytic Value at Risk with jumps and credit risk. Finance Stoch. 5, 155–180.

    Article  MathSciNet  Google Scholar 

  • Eberlein, E. & U. Keller (1995). Hyperbolic distributions in finance. Bernoulli 1, 281–299.

    Article  Google Scholar 

  • 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.

    Book  Google Scholar 

  • Gibson, M. S. (2001). Incorporating event risk into Value at Risk. Discussion Paper Federal Reserve Bord, Washington (http://www.gioriamundi.org).

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Jorion, P. (2000). Value at Risk: The New Benchmark for Controlling Market Risk (2nd ed.). Irwin, Chicago.

    Google Scholar 

  • Kelly, J. R. (1956). A new interpretation of information rate. Bell Syst. Techn. J. 35, 917–926.

    Article  MathSciNet  Google Scholar 

  • Madan, D. B. & E. Seneta (1990). The variance gamma (V.G.) model for share market returns. J. Business 63, 511–524.

    Article  Google Scholar 

  • Merton, R. C. (1973). An intertemporal capital asset pricing model. Econometrica 41, 867–888.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Rao, C. R. (1973). Linear Statistical Inference and Its Applications (2nd ed.). Wiley, New York.

    Book  Google Scholar 

  • RiskMetrics (1996). Technical Document (4th ed.).

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Platen, E., Stahl, G. A Structure for General and Specific Market Risk. Computational Statistics 18, 355–373 (2003). https://doi.org/10.1007/BF03354603

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