Operational Research

, 4:167 | Cite as

Selecting Value-at-Risk methods according to their hidden characteristics

  • Lampros Kalyvas
  • Nikolaos Dritsakis
  • Costas Siriopoulos
  • Chris Grose
Article

Abstract

The foremost concern of a modern risk manager is to estimate Value-at-Risk (VaR), that is the maximum loss likely to occur over the next two weeks for a given confidence level. Although widely spread as a standard measure for quantifying market risk, most of the techniques involved in measuring VaR are based on unrealistic assumptions. The purpose of this paper is to highlight the deficiencies of these techniques and to illustrate the exact steps for the estimation of portfolio-VaR according to all basic methods, namely, the variance-covariance (VC), the historical simulation method (HS) and the Monte Carlo simulation method (MC). Furthermore, the paper examines the accuracy of both the HS and the MC methods according to the Basel II regulatory framework.

Keywords

Traditional VaR methods Historical Simulation Basel Committee Back Testing 
This is a preview of subscription content, log in to check access.

References

  1. Alexander, C. O. and Leigh, C. T. (1997). On the Covariance Matrices used in Value-at-Risk Models. Journal of Derivatives, 4: 3, 50–62.CrossRefGoogle Scholar
  2. Barone-Adesi, G., Giannopoulos, K. and Vosper, L. (1999). VaR without Correlations for Portfolios of Derivative Securities. Journal of Futures Markets, 19, 583–602.CrossRefGoogle Scholar
  3. Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31, 1986, 307–327.CrossRefGoogle Scholar
  4. Boudoukh, J., Richardson, M. and Whitelaw, R. (1998). The Best of Both Worlds. RISK, 11, 64–67.Google Scholar
  5. Brailsford, T. J. and Faff, R. W. (1996). An evaluation of volatility forecasting techniques. Journal of Banking and Finance, Vol. 20.Google Scholar
  6. Campa, J. and Chang, P. K. (1998). The forecasting ability of correlations implied in foreign exchange options. Journal of International Money and Finance, 17, 855–880.CrossRefGoogle Scholar
  7. Chew, L. (1994). Shock Treatment. RISK, 7, 9, 63–70.Google Scholar
  8. Cho, D. C. and Frees, E. W. (1988). Estimating the volatility of discrete stock prices. Journal of Finance.Google Scholar
  9. Cuthbertson, K. and Nitzsche, D. (2001). Financial Engineering: Derivatives and Risk Management. Wiley.Google Scholar
  10. Dodgson, N. A. (1997), Quadratic Interpolation for Image Resampling. IEEE Transactions on Image Processing, Vol. 6, No. 9, 1322–1326.CrossRefGoogle Scholar
  11. Duffie, D. and Pan, J. (1997). An overview of value at risk. The Journal of Derivatives, Vol. 4, No. 3., 7–49.Google Scholar
  12. Engle, R. F. (1982). Autoregressive Conditional Heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987–1007.CrossRefGoogle Scholar
  13. Fallon, W. (1996), Calculating Value at Risk. Working Paper, The Wharton School.Google Scholar
  14. Figlewski, S. (1994). Forecasting volatility using historical data. Working Paper, New York University.Google Scholar
  15. Group of Thirty (1993). Derivatives: Practices and Principles.Google Scholar
  16. Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press.Google Scholar
  17. Hendricks, D. (1996). Evaluation of Value-at-Risk models using historical data. Economy Policy Review, Federal Reserve Bank of New York.Google Scholar
  18. Hicks, J. R. (1939). Value and Capital, Clarendon Press. Oxford, UK.Google Scholar
  19. Holton, G. A. (2003). Value at Risk: Theory and Practice. Academic Press.Google Scholar
  20. Hull, J. (2003). Options, Futures and Other Derivatives. Prentice Hall.Google Scholar
  21. Hull, J. C. and White, A. (1987). The pricing of options on assets with stochastic volatilities. Journal of Finance, 42, 281 -300.CrossRefGoogle Scholar
  22. Jackson, P., Maude, D. J. and Perraudin, W. (1998). Bank Capital and Value at Risk. Working Paper, Bank of England.Google Scholar
  23. Jorion, P. (2001). Financial Risk Manager Handbook. Wiley.Google Scholar
  24. Jorion, P. (1995). Predicting Volatility in the Foreign Exchange Markets. Journal of Finance, 50, 2, 507–528.CrossRefGoogle Scholar
  25. Jorion, P. (2002). Fallacies about the effects of market risk management systems. Financial Stability Review, 115–127.Google Scholar
  26. Kalyvas, L., Kiosse, P. and Mylonidis, N. (2003). Further Evidence on Modeling Option Volatility: A Comparative Analysis, Working Paper, University of Ioannina.Google Scholar
  27. Lawrence, D. (1996). Measuring and Managing Derivative Market Risk. International Thomson Business Press.Google Scholar
  28. Macaulay, F. R. (1938). The Movement of Interest Rates, Bond Yields, and Stock Prices in the United States Since 1856. National Bureau of Economic Research, New York.Google Scholar
  29. McNeil, A. J. and Frey, R. (2000). Estimation of tail-related risk measures for heteroskedastic financial time series: an Extreme Value Approach. Journal of Empirical Finance, 7, 271–300.CrossRefGoogle Scholar
  30. Poterba, J. M. and Summers, L. H. (1986). The persistence of volatility and stock market fluctuations. American Economic Review, No. 71.Google Scholar
  31. Ritchken, P. (1996), Derivative Markets: Theory, Strategy, and Applications, Case Western Reserve University, 1996.Google Scholar
  32. RiskMetrics Technical Document (1996). J.P. Morgan / Reuters, 4th Edition, New York.Google Scholar
  33. Deutsch, H. P. (2004). Derivatives and Internal Models. Palgrave, 3rd edition, London.Google Scholar
  34. Hull, J. and White, A. (1998). Incorporating Volatility Updating into the Historical Simulation Method for Value at Risk. Journal of Risk.Google Scholar
  35. Schwert, W. G. (1990). Stock market volatility. Financial Analysts Journal.Google Scholar
  36. Schoess, S. (1999). Value-at-Risk. Amsterdam Institute of Finance, Amsterdam.Google Scholar
  37. Scott, L. O. (1987). Option Pricing When the Variance Changes Randomly: Theory, Estimation and an Application. Journal of Financial and Quantitative Analysis, 22, 419–438.CrossRefGoogle Scholar
  38. Shastri, K. and Tandon, K. (1986). Valuation of foreign currency options: some empirical tests, Journal of Financial and Quantitative Analysis.Google Scholar
  39. Wiggins, J. B. (1987). Option values under stochastic volatility: Theory and Empirical Estimates. Journal of Financial Economics, 19, 351–372.CrossRefGoogle Scholar

Copyright information

© Hellenic Operational Research Society 2004

Authors and Affiliations

  • Lampros Kalyvas
    • 1
  • Nikolaos Dritsakis
    • 2
  • Costas Siriopoulos
    • 3
  • Chris Grose
    • 4
  1. 1.Department for the Supervision of Credit and Financial InstitutionsBank of GreeceAthensGreece
  2. 2.Department of Applied InformaticsUniversity of MacedoniaThessalonikiGreece
  3. 3.Department of Business AdministrationUniversity of PatrasPatrasGreece
  4. 4.Investors Relations OfficeCompucon S.A.ThermiGreece

Personalised recommendations