• The Korean Journal of Applied Statistics
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• v.25 no.5
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• pp.757-773
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• 2012

Traditional value at risk(S-VaR) has a difficulity in predicting the future risk of financial asset prices since S-VaR is a backward looking measure based on the historical data of the underlying asset prices. In order to resolve the deficiency of S-VaR, an economic value at risk(E-VaR) using the risk neutral probability distributions is suggested since E-VaR is a forward looking measure based on the option price data. In this study E-VaR is estimated by assuming the generalized gamma distribution(GGD) as risk neutral density function which is implied in the option. The estimated E-VaR with GGD was compared with E-VaR estimates under the Black-Scholes model, two-lognormal mixture distribution, generalized extreme value distribution and S-VaR estimates under the normal distribution and GARCH(1, 1) model, respectively. The option market data of the KOSPI 200 index are used in order to compare the performances of the above VaR estimates. The results of the empirical analysis show that GGD seems to have a tendency to estimate VaR conservatively; however, GGD is superior to other models in the overall sense.

• The Korean Journal of Financial Management
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• v.26 no.3
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• pp.139-169
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• 2009

This paper introduces the modified VaR which takes into account the asymmetry and fat-tails of financial asset distribution, and then compares its out-of-sample forecast performance with traditional VaR model such as historical simulation model and Riskmetrics. The empirical tests using stock indices of 6 countries showed that the modified VaR has the best forecast accuracy. At the test of independence, Riskmetrics and GARCH model showed best performances, but the independence was not rejected for the modified VaR. The Monte Carlo simulation using skew t distribution again proved the best forecast performance of the modified VaR. One of many advantages of the modified VaR is that it is appropriate for measuring VaR of the portfolio, because it can reflect not only the linear relationship but also the nonlinear relationship between individual assets of the portfolio through coskewness and cokurtosis. The empirical analysis about decomposing VaR of the portfolio of 6 stock indices confirmed that the component VaR is very useful for the re-allocation of component assets to achieve higher Sharpe ratio and the active risk management.

• The Korean Journal of Applied Statistics
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• v.24 no.4
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• pp.597-607
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• 2011

Value at Risk(VaR) is being widely used as a simple tool for measuring financial risk. Although VaR has a few weak points, it is used as a basic risk measure due to its simplicity and easiness of understanding. However, it becomes very difficult to estimate the volatility of the portfolio (essential to compute its VaR) when the number of assets in the portfolio is large. In this case, we can consider the application of a dimension reduction technique; however, the ordinary factor analysis cannot be applied directly to financial data due to autocorrelation. In this paper, we suggest a dimension reduction method that uses the time-series factor analysis and DCC(Dynamic Conditional Correlation) GARCH model. We also compare the method using time-series factor analysis with the existing method using ordinary factor analysis by backtesting the VaR of real data from the Korean stock market.

• The Korean Journal of Applied Statistics
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• v.23 no.3
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• pp.471-485
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• 2010

VaR is used extensively as a tool for risk management by financial institutions. For convenience, the normal distribution is usually assumed for the measurement of VaR, but recently the method using extreme value theory is attracted for more accurate VaR estimation. So far, GEV and GPD models are used for probability models of EVT for the VaR estimation. In this paper, the PP model is suggested for improved VaR estimation as compared to the traditonal EV models such as GEV and GPD models. In view of the stochastic process, the PP model is regarded as a generalized model which include GEV and GPD models. In the empirical analysis, the PP model is shown to be superior to GEV and GPD models for the performance of VaR estimation.

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1065-1074
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• 2011

During several decades, many researchers in the field of finance have studied Value at Risk (VaR) to measure the market risk. VaR indicates the worst loss over a target horizon such that there is a low, pre-specified probability that the actual loss will be larger (Jorion, 2006, p.106). In this paper, we compare conditional copula method with two conventional VaR forecasting methods based on simple moving average and exponentially weighted moving average for measuring the risk of the portfolio, consisting of two domestic stock indices. Through real data analysis, we conclude that the conditional copula method can improve the accuracy of portfolio VaR forecasting in the presence of high kurtosis and strong correlation in the data.

• The Korean Journal of Applied Statistics
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• v.28 no.3
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• pp.541-559
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• 2015

VaR is now widely used as an important tool to evaluate and manage financial risks. In particular, it is important to select an appropriate volatility model for the rate of return of financial assets. In this study, both univariate and multivariate models are considered to evaluate VaR of the portfolio composed of KOSPI, Hang-Seng, Nikkei indexes, and their performances are compared through back testing techniques. Overall, multivariate models are shown to be more appropriate than univariate models to estimate the portfolio VaR, in particular DCC and ADCC models are shown to be more superior than others.

• The Korean Journal of Applied Statistics
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• v.29 no.1
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• pp.171-180
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• 2016

Basel committee suggests using Value-at-Risk (VaR) and expected shortfall (ES) as a measurement for market risk. Various estimation methods of VaR and ES have been studied in the literature. This paper compares semi-parametric methods, such as conditional autoregressive value at risk (CAViaR) and conditional autoregressive expectile (CARE) methods, and a Gaussian quasi-maximum likelihood estimator (QMLE)-based method through back-testing methods. We use unconditional coverage (UC) and conditional coverage (CC) tests for VaR, and a bootstrap test for ES to check the adequacy. A real data analysis is conducted for S&P 500 index and Hyundai Motor Co. stock price index data sets.

• The Korean Journal of Financial Management
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• v.24 no.3
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• pp.153-186
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• 2007

It is well known that the distributional properties of financial asset returns exhibit fatter-tails and skewer-mean than the assumption of normal distribution. The correct assumption of return distribution might improve the estimated performance of the Value-at-Risk(VaR) models in financial markets. In this paper, we estimate and compare the VaR performance using the RiskMetrics, GARCH and FIGARCH models based on the normal and skewed-Student-t distributions in two daily returns of the Korean Composite Stock Index(KOSPI) and Korean Won-US Dollar(KRW-USD) exchange rate. We also perform the expected shortfall to assess the size of expected loss in terms of the estimation of the empirical failure rate. From the results of empirical VaR analysis, it is found that the presence of long memory in the volatility of sample returns is not an important in estimating an accurate VaR performance. However, it is more important to consider a model with skewed-Student-t distribution innovation in determining better VaR. In short, the appropriate assumption of return distribution provides more accurate VaR models for the portfolio managers and investors.

• 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.

• Communications for Statistical Applications and Methods
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• v.25 no.6
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• pp.605-618
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• 2018

Risk management has been a crucial part of the daily operations of the financial industry over the past two decades. Value at Risk (VaR), a quantitative measure introduced by JP Morgan in 1995, is the most popular and simplest quantitative measure of risk. VaR has been widely applied to the risk evaluation over all types of financial activities, including portfolio management and asset allocation. This paper uses the implementations of multivariate GARCH models and copula methods to illustrate the performance of a one-day-ahead VaR prediction modeling process for high-dimensional portfolios. Many factors, such as the interaction among included assets, are included in the modeling process. Additionally, empirical data analyses and backtesting results are demonstrated through a rolling analysis, which help capture the instability of parameter estimates. We find that our way of modeling is relatively robust and flexible.