Document Type : Original Article

Authors

1 Department of Statistics, Yazd University, Yazd, Iran

2 Department of Mathematics, Yazd University, Yazd, Iran

3 Department of Statistics, Yazd University, Yazd, Iran.

Abstract

Value at risk and expected shortfall are the two most popular measures for calculating financial risk.
To calculate these measures (Value at risk and expected shortfall) there are many approaches, which can be divided into two main categories; parametric and non-parametric. In parametric approach it is supposed that the distribution of asset return belongs to a specific class of distributions. For some distributions we can claculate easily the mentioned measures. In this paper the the relation of epected shortfall has been proved for four symetric distribution.

Keywords

Main Subjects

Acerbi, C., & Tasche, D. (2002). On the coherence of expected shortfall. Journal of banking & finance26(7), 1487-1503.
Artzner, P. (1997). Thinking coherently. Risk, 68-71.
Artzner, P., Delbaen, F., Eber, J. M., & Heath, D. (1999). Coherent measures of risk. Mathematical finance9(3), 203-228.
Nadarajah, S., Zhang, B., & Chan, S. (2014). Estimation methods for expected shortfall. Quantitative finance14(2), 271-291.
Oh, S., & Moon, S. J. (2006). Comparative analysis of portfolio risk measures based on EVT-copula approach during financial crises. Asia-Pacific journal of financial studies35(3), 175-205.
Rockafellar, R. T., & Uryasev, S. (2002). Conditional value-at-risk for general loss distributions. Journal of banking & finance26(7), 1443-1471.
Taylor, J. W. (2008). Estimating value at risk and expected shortfall using expectiles. Journal of financial econometrics6(2), 231-252.
Yamai, Y., & Yoshiba, T. (2002). Comparative analyses of expected shortfall and value-at-risk: their estimation error, decomposition, and optimization. Monetary and economic studies20(1), 87-121.