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Spectral Risk Measures with an Application to Futures Clearinghouse Variation Margin Requirements

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  • John Cotter
  • Kevin Dowd

Abstract

This paper applies an AR(1)-GARCH (1, 1) process to detail the conditional distributions of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses the conditional distribution for these contracts to estimate spectral risk measures, which are coherent risk measures that reflect a user's risk-aversion function. It compares these to more familiar VaR and Expected Shortfall (ES) measures of risk, and also compares the precision and discusses the relative usefulness of each of these risk measures in setting variation margins that incorporate time-varying market conditions. The goodness of fit of the model is confirmed by a variety of backtests.

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Paper provided by arXiv.org in its series Papers with number 1103.5408.

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Date of creation: Mar 2011
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Handle: RePEc:arx:papers:1103.5408

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  1. Cotter, John, 2004. "Varying the VaR for Unconditional and Conditional Environments," MPRA Paper 3483, University Library of Munich, Germany.
  2. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
  3. Cotter, John & Dowd, Kevin, 2006. "Extreme spectral risk measures: An application to futures clearinghouse margin requirements," Journal of Banking & Finance, Elsevier, vol. 30(12), pages 3469-3485, December.
  4. Brennan, Michael J., 1986. "A theory of price limits in futures markets," Journal of Financial Economics, Elsevier, vol. 16(2), pages 213-233, June.
  5. Cotter, John, 2001. "Margin exceedences for European stock index futures using extreme value theory," Journal of Banking & Finance, Elsevier, vol. 25(8), pages 1475-1502, August.
  6. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
  7. Giannopoulos, Kostas & Tunaru, Radu, 2005. "Coherent risk measures under filtered historical simulation," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 979-996, April.
  8. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-26, March.
  9. G. Geoffrey Booth & John Paul Broussard & Teppo Martikainen & Vesa Puttonen, 1997. "Prudent Margin Levels in the Finnish Stock Index Futures Market," Management Science, INFORMS, vol. 43(8), pages 1177-1188, August.
  10. Bertsimas, Dimitris & Lauprete, Geoffrey J. & Samarov, Alexander, 2004. "Shortfall as a risk measure: properties, optimization and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1353-1381, April.
  11. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
  12. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  13. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  14. Bates, David & Craine, Roger, 1999. "Valuing the Futures Market Clearinghouse's Default Exposure during the 1987 Crash," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 31(2), pages 248-72, May.
  15. Theodore E. Day, 2004. "Margin Adequacy and Standards: An Analysis of the Crude Oil Futures Market," The Journal of Business, University of Chicago Press, vol. 77(1), pages 101-136, January.
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