• The Korean Journal of Applied Statistics
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• v.34 no.6
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• pp.875-887
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• 2021

Value at Risk (VaR) is the most popular measure for market risk. In this paper, we consider the VaR estimation of portfolio consisting of a variety of assets based on multivariate copula model known as vine copula. In particular, sparse vine copula which penalizes too many parameters is considered. We show in the simulation study that sparsity indeed improves out-of-sample forecasting of VaR. Empirical analysis on 60 KOSPI stocks during the last 5 years also demonstrates that sparse vine copula outperforms regular copula model.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1171-1180
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• 2014

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.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1479-1494
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• 2015

Since the Markowitz's mean-variance framework for portfolio analysis, the topic of portfolio optimization has been an important topic in finance. Traditional approaches focus on maximizing the expected return of the portfolio while minimizing its variance, assuming that risky asset returns are normally distributed. The normality assumption however has widely been criticized as actual stock price distributions exhibit much heavier tails as well as asymmetry. To this extent, in this paper we employ the genetic algorithm to find the optimal portfolio under the Value-at-Risk (VaR) constraint, where the tail of risky assets are modeled with the generalized Pareto distribution (GPD), the standard distribution for exceedances in extreme value theory. An empirical study using Korean stock prices shows that the performance of the proposed method is efficient and better than alternative methods.

• Journal of the Korean Data and Information Science Society
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• v.27 no.4
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• pp.959-967
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• 2016

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.