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

Cotter, John and Dowd, Kevin (2006): Spectral Risk Measures with an Application to Futures Clearinghouse Variation Margin Requirements.

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.

• Item Type: MPRA Paper
• Language: English
• Subjects: G - Financial Economics > G1 - General Financial Markets; G - Financial Economics > G0 - General

References

REFERENCES Acerbi, C., 2002. Spectral measures of risk: a coherent representation of subjective risk aversion. Journal of Banking and Finance 26: 1505-1518. Acerbi, C., 2004. Coherent representations of subjective risk-aversion, in G. Szego (Ed), Risk Measures for the 21st Century, Wiley, New York, pp. 147-207. Artzner, P., F. Delbaen, J.-M. Eber, D. Heath, 1999. Coherent measures of risk. Mathematical Finance 9, 203-228. Barone-Adesi, G., K. Giannopoulos, and L. Vosper, 1999. VaR without correlations for portfolios of derivatives securities, Journal of Futures Markets, 19, 583-602. Bates, D., and R. Craine, 1999. Valuing the futures market clearinghouse's default exposure during the 1987 crash. Journal of Money, Credit, and Banking, 31, 248-272. Bawa, V. S., 1975. Optimal rules for ordering uncertain prospects. Journal of Financial Economics 2: 95-121. Bollerslev, T., Chou, R., and K. Kroner, 1992. ARCH modelling in finance: a review of the theory and empirical evidence, Journal of Econometrics, 52, 5-59. Booth, G. G., Brousssard, J.P., Martikainen, T., and Puttonen, V., 1997. Prudent margin levels in the Finnish stock index futures market. Management Science 43, 1177-1188. Brennan, M.J., 1986. A theory of price limits in futures markets, Journal of Financial Economics, 16, 213-233. Cotter, J. 2001. Margin exceedences for European stock index futures using extreme value theory. Journal of Banking and Finance 25, 1475-1502. Cotter, J., 2006, Varying the VaR for unconditional and conditional environments, Journal of International Money and Finance, Forthcoming. Cotter, J., Dowd, K., 2006, Extreme spectral risk measures: an application to futures, Electronically available on Science Direct: http://www.sciencedirect.com/science?_ob=ArticleListURL&_method=list&_Article ListID=477617306&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersio n=0&_userid=10&md5=e64db1df9db6e25e4c1394873d9aeb0d 21 Craine R., 1992. Are futures margins adequate? Working Paper, University of California – Berkley. Day, T.E., and C.M. Lewis, 2004, Margin adequacy and standards: an analysis of the crude oil futures markets. Journal of Business, 77, 101-135. Diebold, FX, TA Gunther, and AS Tay, 1998. “Evaluating density forecasts with applications to financial risk management.” International Economic Review 39: 863- 883. Edwards, F. R., and S. N. Neftci, 1988. Extreme price movements and margin levels in futures markets. Journal of Futures Markets 8, 639-655. Engle, R.F., 1981. Autoregressive conditional heteroskedasticity with estimates of the variance of UK Inflation, Econometrica, 50, 987-1008. Figlewski, S., 1984. Margins and market integrity: margin setting for stock index futures and options. The Journal of Futures Markets, 4, 385–416. Fishburn, P. C., 1977. Mean-risk analysis with risk associated with below-target returns. American Economic Review 67: 116-126. Giannopoulos, K., and R. Tunaru, 2005. Coherent risk measures under filtered historical simulation. Journal of Banking and Finance, 29, 979-996. Grootveld, H., Hallerbach, W. G., 2004. Upgrading value-at-risk from diagnostic metric to decision variable: a wise thing to do?, in G. Szegö (Ed.) Risk Measures for the 21st Century. Wiley, New York, pp. 33-50. Hsieh, D.A., 1993. Implications of nonlinear dynamics for financial risk management, Journal of Financial and Quantitative Analysis, 28, 41-64. Hull, J. C., 2003. Options, Futures, and other Derivatives, 5h edition, Prentice Hall, New Jersey. Jarque, CM, and AK Bera, 1987. “A test for normality of observations and regression residuals,” International Statistical Review 55: 163-172. Kreyszig, E. 1999. Advanced Engineering Mathematics. 8th edition. New York: Wiley. Kupiec, P., 1995. “Techniques for verifying the accuracy of risk management models”. Journal of Derivatives 3: 73-84. 22 Kusuoka, S., 2001. On law invariant coherent risk measures. Advances in Mathematical Economics 3: 83-95. Longin, F., 1999. Optimal margin levels in futures markets: extreme price movements. Journal of Futures Markets, 19, 127-152. McNeil, A. J., and R. Frey, 2000. Estimation of tail-related risk for heteroscedastic financial time series: an extreme value approach. Journal of Empirical Finance, 7, 271-300. Miranda, M. J., and P. L. Fackler, 2002. Applied Computational Economics and Finance. MIT Press, Cambridge MA and London. Warshawsky, M. J., 1989. The adequacy and consistency of margin requirements: the cash, futures and options segments of the equity markets. The Review of Futures Markets 8, 420–437.