Exponential Spectral Risk Measures

Cotter, John and Dowd, Kevin (2007): Exponential Spectral Risk Measures.

Abstract

Spectral risk measures are attractive risk measures as they allow the user to obtain risk measures that reflect their subjective risk-aversion. This paper examines spectral risk measures based on an exponential utility function, and finds that these risk measures have nice intuitive properties. It also discusses how they can be estimated using numerical quadrature methods, and how confidence intervals for them can be estimated using a parametric bootstrap. Illustrative results suggest that estimated exponential spectral risk measures obtained using such methods are quite precise in the presence of normally distributed losses.

• Item Type: MPRA Paper
• Institution: University College Dublin
• Language: English
• Subjects: G - Financial Economics > G1 - General Financial Markets > G10 - General; G - Financial Economics > G0 - General

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.” Pp. 147-207 in G. Szegö (Ed.) Risk Measures for the 21st Century, New York: Wiley. Artzner, P., F. Delbaen, J.-M. Eber, and D. Heath, (1997) “Thinking coherently.” Risk, 10 (November), 68-71. Artzner, P., F. Delbaen, J.-M. Eber, and D. Heath, (1999) “Coherent Measures of Risk.” Mathematical Finance, 9, 203-228. Bawa, V. S., (1975) “Optimal Rules for Ordering Uncertain Prospects.” Journal of Financial Economics, 2, 95-121. Borse, G. J. (1997) Numerical Methods with MATLAB: A Resource for Scientists and Engineers. Boston: PWS Publishing Company. Bertsimas, D., G. J. Lauprete, and A. Samarov, (2004) “Shortfall as a Risk Measure: Properties, Optimization and Applications.” Journal of Economic Dynamics and Control, 28, 1353 – 1381. Cotter, J., and K. Dowd, (2006) “Extreme Spectral Risk Measures: An Application to Futures Clearinghouse Margin Requirements.” Journal of Banking and Finance, 30, 3469-3485. Dowd, K., (2005) Measuring Market Risk. Second edition, Chichester: John Wiley and Sons. Fishburn, P. C., (1977) Mean-Risk Analysis with Risk Associated with Below- Target Returns.” American Economic Review, 67, 116-126. Grootveld, H., and W. G. Hallerbach, (2004) “Upgrading Value-at-Risk from Diagnostic Metric to Decision Variable: A Wise Thing to Do?” Pp. 33-50 in G. Szegö (Ed.) Risk Measures for the 21st Century, Wiley, New York. Kreyszig, E. (1999) Advanced Engineering Mathematics. 8th edition. Wiley, New York. Miranda, M. J., and P. L. Fackler, (2002) Applied Computational Economics and Finance. Cambridge, MA and London: MIT Press.