Browse > Article
http://dx.doi.org/10.7465/jkdi.2014.25.6.1171

Saddlepoint approximations for the risk measures of portfolios based on skew-normal risk factors  

Yu, Hye-Kyung (Public Procurement Service)
Na, Jong-Hwa (Department of Information and Statistics/Business Data Convergence, Chungbuk National University)
Publication Information
Journal of the Korean Data and Information Science Society / v.25, no.6, 2014 , pp. 1171-1180 More about this Journal
Abstract
We considered saddlepoint approximations to VaR (value at risk) and ES (expected shortfall) which frequently encountered in finance and insurance as the measures of risk management. In this paper we supposed univariate and multivariate skew-normal distributions, instead of traditional normal class distributions, as underlying distribution of linear portfolios. Simulation results are provided and showed the suggested saddlepoint approximations are very accurate than normal approximations.
Keywords
Expected shortfall; saddlepoint approximation; skew normal; value at risk;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 Acerbi, C. and Tasche, D. (2002). Expected shortfall: A natural coherent alternative to value at risk. Economic Notes, 31, 379-388.   DOI   ScienceOn
2 Antonov, A., Mechkov, H. and Misirpashaev, T (2005). Analytical techniques for synthetic CDOs and credit default risk measures, Technical Report, Numerix, New York.
3 Artzner, P., Delbaen, F., Eber, J. and Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9, 203-228.   DOI
4 Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12, 171-178.
5 Azzalini, A. (1986). Further results on a class of distributions which includes the normal ones. Statistica, 46, 199-208.
6 Azzalini, A. (2005). The skew-normal distribution and related multivariate families(with discussion). Scandinavian Journal of Statistics, 32, 159-188.   DOI   ScienceOn
7 Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew normal distributions. Journal of the Royal Statistical Society B, 61, 579-602.   DOI   ScienceOn
8 Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika, 83, 715-726.   DOI   ScienceOn
9 Barndorff-Nielsen, O. E. and Cox, D. R. (1979). Edgeworth and saddlepoint approximations with statistical applications(with discussion). Journal of the Royal Statistical Society B, 41, 279-312.
10 Byun, B. G., Yoo, D.S. and Lim, J. T. (2013). Validity assessment of VaR with Laplacian distribution. Journal of the Korean Data & Information Science Society, 24, 1263-1274.   과학기술학회마을   DOI   ScienceOn
11 Daniels, H. E. (1954). Saddlepoint approximations in statistics. The Annals of Mathematical Statistics, 25, 631-650.   DOI   ScienceOn
12 Huang, X. and Oosterlee C. W. (2009). Saddlepoint approximations for expectations. preprint.
13 Lane, M. N. (2002). Pricing risk transfer transactions, ASTIN Bulletin, 30, 259-293.
14 Lugannani, R. and Rice, S. (1980). Saddlepoint approximations for the distribution of the sum of independent random variables. Advances in Applied Probability, 12, 475-490.   DOI   ScienceOn
15 McNeil, A., Frey, R. and Embrechts, P. (2005). Quantitative risk management: Concepts, techniques and tools, Princeton University Press, New Jersey.
16 Na, J. H. (2008). Saddlepoint approximation to quadratic form and application to intraclass correlation coefficient. Journal of the Korean Data & Information Science Society, 19, 497-504.   과학기술학회마을
17 Na, J. H. and Yu, H. K. (2013). Saddlepoint approximation for distribution function of sample mean of skew-normal distribution. Journal of the Korean Data & Information Science Society, 24, 1211-1219.   과학기술학회마을   DOI   ScienceOn
18 Rogers, L. C. G. and Zane, O. (1999). Saddlepoint approximations to option prices. The Annals of Applied Probability, 9, 493-503.   DOI
19 Vernic, R.(2006). Multivariate skew-normal distributions with applications in insurance. Insurance Mathematics and Economics, 38, 413-426.   DOI   ScienceOn
20 Yang, J., Hurd, T. and Zhang, X. (2006). Saddlepoint approximation method for pricing CDOs. Journal of Computational Finance, 10, 1-20.