Saddlepoint approximations for the risk measures of linear portfolios based on generalized hyperbolic distributions

- Journal title : Journal of the Korean Data and Information Science Society
- Volume 27, Issue 4, 2016, pp.959-967
- Publisher : Korean Data and Information Science Society
- DOI : 10.7465/jkdi.2016.27.4.959

Title & Authors

Saddlepoint approximations for the risk measures of linear portfolios based on generalized hyperbolic distributions

Na, Jonghwa;

Na, Jonghwa;

Abstract

Distributional assumptions on equity returns play a key role in valuation theories for derivative securities. Elberlein and Keller (1995) investigated the distributional form of compound returns and found that some of standard assumptions can not be justified. Instead, Generalized Hyperbolic (GH) distribution fit the empirical returns with high accuracy. Hu and Kercheval (2007) also show that the normal distribution leads to VaR (Value at Risk) estimate that significantly underestimate the realized empirical values, while the GH distributions do not. We consider saddlepoint approximations to estimate the VaR and the ES (Expected Shortfall) which frequently encountered in finance and insurance as measures of risk management. We supposed GH distributions instead of normal ones, as underlying distribution of linear portfolios. Simulation results show the saddlepoint approximations are very accurate than normal ones.

Keywords

Expected shortfall;generalized hyperbolic distribution;saddlepoint approximation;value at risk;

Language

Korean

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