• 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.

• 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.

• 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.

• Communications for Statistical Applications and Methods
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• v.28 no.1
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• pp.59-79
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• 2021

Value at Risk (VaR) is one of the most common risk management tools in finance. Since a portfolio of several assets, rather than one asset portfolio, is advantageous in the risk diversification for investment, VaR for a portfolio of two or more assets is often used. In such cases, multivariate distributions of asset returns are considered to calculate VaR of the corresponding portfolio. Copulas are one way of generating a multivariate distribution by identifying the dependence structure of asset returns while allowing many different marginal distributions. However, they are used mainly for bivariate distributions and are not widely used in modeling joint distributions for many variables in finance. In this study, we would like to examine the performance of various copulas for high dimensional data and several different dependence structures. This paper compares copulas such as elliptical, vine, and hierarchical copulas in computing the VaR of portfolios to find appropriate copula functions in various dependence structures among asset return distributions. In the simulation studies under various dependence structures and real data analysis, the hierarchical Clayton copula shows the best performance in the VaR calculation using four assets. For marginal distributions of single asset returns, normal inverse Gaussian distribution was used to model asset return distributions, which are generally high-peaked and heavy-tailed.

• Environmental and Resource Economics Review
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• v.16 no.4
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• pp.947-978
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• 2007

In this paper, we investigated a Value-at-Risk approach to the volatility of two crude oil markets (Brent and Dubai). We also assessed the performance of various VaR models (RiskMetrics, GARCH, IGARCH and FIGARCH models) with the normal and skewed Student-t distribution innovations. The FIGARCH model outperforms the GARCH and IGARCH models in capturing the long memory property in the volatility of crude oil markets returns. This implies that the long memory property is prevalent in the volatility of crude oil returns. In addition, from the results of VaR analysis, the FIGARCH model with the skewed Student-t distribution innovation predicts critical loss more accurately than other models with the normal distribution innovation for both long and short positions. This finding indicates that the skewed Student-t distribution innovation is better for modeling the skewness and excess kurtosis in the distribution of crude oil returns. Overall, these findings might improve the measurement of the dynamics of crude oil prices and provide an accurate estimation of VaR for buyers and sellers in crude oil markets.

• Communications for Statistical Applications and Methods
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• v.29 no.1
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• pp.85-101
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• 2022

Derivative-linked securities (DLS) is a type of derivatives that offer an agreed return when the underlying asset price moves within a specified range by the maturity date. The underlying assets of DLS are diverse such as interest rates, exchange rates, crude oil, or gold. A German 10-year bond rate-linked DLS and a USD-GBP CMS rate-linked DLS have recently become a social issue in Korea due to a huge loss to investors. In this regard, this paper accounts for the payoff structure of these products and evaluates their prices and fair coupon rates as well as risk measures such as Value-at-Risk (VaR) and Tail-Value-at-Risk (TVaR). We would like to examine how risky these products were and whether or not their coupon rates were appropriate. We use Hull-White Model as the stochastic model for the underlying assets and Monte Carlo (MC) methods to obtain numerical results. The no-arbitrage prices of the German 10-year bond rate-linked DLS and the USD-GBP CMS rate-linked DLS at the center of the social issue turned out to be 0.9662% and 0.9355% of the original investment, respectively. Considering that Korea government bond rate for 2018 is about 2%, these values are quite low. The fair coupon rates that make the prices of DLS equal to the original investment are computed as 4.76% for the German 10-year bond rate-linked DLS and 7% for the USD-GBP CMS rate-linked DLS. Their actual coupon rates were 1.4% and 3.5%. The 95% VaR and TVaR of the loss for German 10-year bond rate-linked DLS are 37.30% and 64.45%, and those of the loss for USD-GBP CMS rate-linked DLS are 73.98% and 87.43% of the initial investment. Summing up the numerical results obtained, we could see that the DLS products of our interest were indeed quite unfavorable to individual investors.

• International Journal of Naval Architecture and Ocean Engineering
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• v.13 no.1
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• pp.340-350
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• 2021

This paper proposes a decision support model for USVs to improve the accuracy of collision avoidance decision-making. It is formed by Navigation Safety Domain (NSD) and domain-based Collision Risk Index (CRI), capable of determining the collision stage and risk between multiple ships. The NSD is composed of a warning domain and a forbidden domain, which is constructed under the constraints of COLREGs (International Regulations for Preventing Collisions at Sea). The proposed domain based CRI takes the radius of NSD in various encounter situations as threshold parameters. It is found that the value of collision risk in any directions can be calculated, including actual value and risk threshold. A catamaran USV and 6 given vessels are taken as study objects to validate the proposed model. It is found that the judgment of collision stage is accurate and the azimuth range of risk exists can be detected, hence the ships can take direct and effective collision avoidance measures. According to the relation between the actual value of CRI and risk threshold, the decision support rules are summarized, and the specific terms of COLREGs to be followed in each encounter situation are given.

• Nuclear Engineering and Technology
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• v.56 no.3
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• pp.819-823
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• 2024

The main criteria used in NEI 18-04 to define SSCs as risk-significant include (1) the SSC is required to keep all LBEs within the F-C target, and (2) the total frequency with the SSC failed exceeds 1% of the limit for at least one of the three cumulative risk metrics used for evaluating the integrated plant risk. The first one is a reasonable criterion in determining the risk significant SSCs. However, the second criterion may not be adequate to serve the purpose of determining the risk significance of SSCs. In the second criterion, the cumulative risk metric values representing the integrated plant risk (less the preventive and mitigative effects of the SSC being evaluated) are compared to a risk limit that represents a very small contribution to the overall integrated plant risk, which corresponds appropriately to the contributions from individual SSCs. The easiest approach to redefine the NEI 18-04 definition of risk-significant SSCs in relation to the integrated plant risk metrics is to compare the difference, between the risk metric value calculated with the SSC failed and the risk metric value calculated with the SSC credited, with 1% of the risk limit established for the integrated plant risk metrics.

• Journal of the Korean Society of Marine Environment & Safety
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• v.26 no.3
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• pp.227-232
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• 2020

This paper develops a risk index based on an indicator of risk assessment in terms of coastal activity location and accident type. The risk index is derived from a formula which adds the consequence of failure to a vulnerability value, then subtracts the mitigation value. Specifically, the consequence of failure is the number of casualties in coastal activity locations. An indicator of vulnerability refers to coastal environment elements and social elements. A pointer of mitigation includes managerial and organizational elements that indicate the capabilities of coastal activities. A risk rating of coastal activity location is found from a risk matrix consisting of the accident location and type. The purpose of this study is to prevent accidents at coastal activity locations by allowing the Coastal police guard to monitor effectively and inform visitors of potential risks.

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.121-131
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• 2009

In this paper we examine the relation among law-invariant coherent risk measures with the Fatou property, distortion risk measures and spectral risk measures, and give a new proof of the relation among them. It is also shown that the spectral risk measure satisfies the monotonicity with respect to stochastic dominance and the comonotonic additivity.