• Title/Summary/Keyword: VaR

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A rolling analysis on the prediction of value at risk with multivariate GARCH and copula

  • Bai, Yang;Dang, Yibo;Park, Cheolwoo;Lee, Taewook
    • 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.

Long Memory Properties in the Volatility of Australian Financial Markets: A VaR Approach (호주 금융시장 변동성의 장기기억 특성: VaR 접근법)

  • Kang, Sang-Hoon;Yoon, Seong-Min
    • International Area Studies Review
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    • v.12 no.2
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    • pp.3-26
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    • 2008
  • This article investigates the usefulness of the skewed Student-t distribution in modeling the long memory volatility property that might be present in the daily returns of two Australian financial series; the ASX200 stock index and AUD/USD exchange rate. For this purpose we assess the performance of FIGARCH and FIAPARCH Value-at-Risk (VaR) models based on the normal, Student-t, and skewed Student-t distribution innovations. Our results support the argument that the skewed Student-t distribution models produce more accurate VaR estimates of Australian financial markets than the normal and Student-t distribution models. Thus, consideration of skewness and excess kurtosis in asset return distributions provides appropriate criteria for model selection in the context of long memory volatility models in Australian stock and foreign exchange markets.

Value at Risk with Peaks over Threshold: Comparison Study of Parameter Estimation (Peacks over threshold를 이용한 Value at Risk: 모수추정 방법론의 비교)

  • Kang, Minjung;Kim, Jiyeon;Song, Jongwoo;Song, Seongjoo
    • The Korean Journal of Applied Statistics
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    • v.26 no.3
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    • pp.483-494
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    • 2013
  • The importance of financial risk management has been highlighted after several recent incidences of global financial crisis. One of the issues in financial risk management is how to measure the risk; currently, the most widely used risk measure is the Value at Risk(VaR). We can consider to estimate VaR using extreme value theory if the financial data have heavy tails as the recent market trend. In this paper, we study estimations of VaR using Peaks over Threshold(POT), which is a common method of modeling fat-tailed data using extreme value theory. To use POT, we first estimate parameters of the Generalized Pareto Distribution(GPD). Here, we compare three different methods of estimating parameters of GPD by comparing the performance of the estimated VaR based on KOSPI 5 minute-data. In addition, we simulate data from normal inverse Gaussian distributions and examine two parameter estimation methods of GPD. We find that the recent methods of parameter estimation of GPD work better than the maximum likelihood estimation when the kurtosis of the return distribution of KOSPI is very high and the simulation experiment shows similar results.

Conditional Value-at-Risk Optimization for Conversion of Convertible Bonds (전환사채 주식전환을 위한 조건부 VaR 최적화)

  • Park, Koo-Hyun;Shim, Eun-Tak
    • Korean Management Science Review
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    • v.28 no.2
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    • pp.1-16
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    • 2011
  • In this study we suggested two optimization models to answer a question from an investor standpoint : how many convertible bonds should one convert, and how many keep? One model minimizes certain risk to the minimum required expected return, the other maximizes the expected return subject to the maximum acceptable risk. In comparison with Markowitz portfolio models, which use the variance of return, our models used Conditional Value-at-Risk(CVaR) for risk measurement. As a coherent measurement, CVaR overcomes the shortcomings of Value-at-Risk(VaR). But there are still difficulties in solving CVaR including optimization models. For this reason, we adopted Rockafellar and Uryasev's[18, 19] approach. Then we could approximate the models as linear programming problems with scenarios. We also suggested to extend the models with credit risk, and applied examples of our models to Hynix 207CB, a convertible bond issued by the global semiconductor company Hynix.

VA-Tree : An Efficient Multi-Dimensional Index Structure for Large Data Set (VA-Tree : 대용량 데이터를 위한 효율적인 다차원 색인구조)

  • 송석일;이석희;조기형;유재수
    • Journal of Korea Multimedia Society
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    • v.6 no.5
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    • pp.753-768
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    • 2003
  • In this paper, we propose a multi-dimensional index structure, tailed a VA(Vector Approximate)-tree that is constructed with vector approximates of multi-dimensional feature vectors. To save storage space for index structures, the VA-tree employs vector approximation concepts of VA-file that presents feature vectors with much smaller number of bits than original value. Since the VA-tree is a tree structure, it does not suffer from performance degradation owing to the increase of data. Also, even though the VA-tree is MBR(Minimum Bounding Region) based tree structure like a R-tree, its split algorithm never allows overlap between MBRs. We show through various experiments that our proposed VA-tree is a suitable index structure for large amount of multi-dimensional data.

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Multivariate conditional tail expectations (다변량 조건부 꼬리 기대값)

  • Hong, C.S.;Kim, T.W.
    • The Korean Journal of Applied Statistics
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    • v.29 no.7
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    • pp.1201-1212
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    • 2016
  • Value at Risk (VaR) for market risk management is a favorite method used by financial companies; however, there are some problems that cannot be explained for the amount of loss when a specific investment fails. Conditional Tail Expectation (CTE) is an alternative risk measure defined as the conditional expectation exceeded VaR. Multivariate loss rates are transformed into a univariate distribution in real financial markets in order to obtain CTE for some portfolio as well as to estimate CTE. We propose multivariate CTEs using multivariate quantile vectors. A relationship among multivariate CTEs is also derived by extending univariate CTEs. Multivariate CTEs are obtained from bivariate and trivariate normal distributions; in addition, relationships among multivariate CTEs are also explored. We then discuss the extensibility to high dimension as well as illustrate some examples. Multivariate CTEs (using variance-covariance matrix and multivariate quantile vector) are found to have smaller values than CTEs transformed to univariate. Therefore, it can be concluded that the proposed multivariate CTEs provides smaller estimates that represent less risk than others and that a drastic investment using this CTE is also possible when a diversified investment strategy includes many companies in a portfolio.

Comparison of Vinyl Acetate Contents of Poly(Ethylene-co-Vinyl Acetate) Analyzed by IR, NMR, and TGA

  • Kim, Eunha;Choi, Sung-Seen
    • Elastomers and Composites
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    • v.50 no.1
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    • pp.18-23
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    • 2015
  • Vinyl acetate (VA) contents of poly(ethylene-co-vinyl acetate) (EVA) analyzed by infrared spectroscopy (IR), nuclear magnetic spectroscopy (NMR), and thermogravimetric analysis (TGA) were compared. Four grade EVAs supplied by Aldrich Co. and four grade EVAs manufactured by DuPont Co. were used. For IR analysis, VA contents were determined using calibration curve (absorbance ratio of $1739cm^{-1}/2922cm^{-1}$ or $609cm^{-1}/1464cm^{-1}$) of reference EVAs. Correlation coefficients of the calibration curves were not sufficiently high ($r^2{\leq}0.96$). For NMR analysis, VA contents were determined using peaks of $CH_3$, $CH_2$, and CH. VA contents determined by NMR analysis were less than those marked by suppliers more than 10%. For TGA, VA contents were determined using weight loss through deacetylation. VA contents determined by TGA were slightly different with those marked by suppliers. Difference in the VA contents determined by different analytical methods was discussed, and difference in the analytical results according to the EVA suppliers was also examined.

Estimation of VaR and Expected Shortfall for Stock Returns (주식수익률의 VaR와 ES 추정: GARCH 모형과 GPD를 이용한 방법을 중심으로)

  • Kim, Ji-Hyun;Park, Hwa-Young
    • The Korean Journal of Applied Statistics
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    • v.23 no.4
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    • pp.651-668
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    • 2010
  • Various estimators of two risk measures of a specific financial portfolio, Value-at-Risk and Expected Shortfall, are compared for each case of 1-day and 10-day horizons. We use the Korea Composite Stock Price Index data of 20-year period including the year 2008 of the global financial crisis. Indexes of five foreign stock markets are also used for the empirical comparison study. The estimator considering both the heavy tail of loss distribution and the conditional heteroscedasticity of time series is of main concern, while other standard and new estimators are considered too. We investigate which estimator is best for the Korean stock market and which one shows the best overall performance.

Operational Characteristics of the Anaerobic Sequencing Batch Reactor Process at a Thermophilic Temperature (연속 회분식 고온 혐기성 공정의 운전특성 연구)

  • Lee, Jong Hoon;Chung, Tai Hak;Chang, Duk
    • Journal of Korean Society of Water and Wastewater
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    • v.11 no.1
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    • pp.33-41
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    • 1997
  • An attempt was made to enhance anaerobic treatment efficiency by adopting the anaerobic sequencing batch reactor(ASBR) process at a thermophilic temperature. Operational characteristics of the ASBR process were studied using laboratory scale reactors and concentrated organic wastewater composed of soluble starch and essential nutrients. Effects of fill to react ratio (F/R) were examined in the Phase I experiment, where the equivalent hydraulic retention time(HRT) was maintained at 5 days with the influent COD of 10g/L. A continuous stirred tank reactor(CSTR) was operated in parallel as a reference. Treatment efficiency was higher for the ASBRs because of continuous accumulation of volatile suspended solids(VSS) compared to the CSTR. However, the rate of gas production and organic removal per unit VSS in the ASBRs was much lower than the CSTR. This was caused by reduced methane fermentation due to accumulation of volatile acids(VA), especially for the case of low F/R, during the fill period. When the F/R was high, maximum VA was low and the VA decreased in short period. Consequently, more stable operation was possible with higher F/R. Effects of hydraulic loading rate on the efficiency was studied in the Phase II experiment, where the organic loading rate was elevated to 3333mg/L-d with the F/R of 0.12. Reduction of organic removal along with rapid increase of VA was observed and the stability of reaction was seriously impaired, when the influent COD was doubled. However, operation of the ASBR was quite stable, when the hydraulic loading rate was doubled and a cycle time was adjusted to 12 hour. It is essential to avoid rapid accumulation of VA during the fill period in order to maintain operational stability of the ASBR.

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Optimal Portfolio Selection in a Downside Risk Framework (하방위험을 이용한 위험자산의 최적배분)

  • Hyung, Nam-Won;Han, Kyu-Sook
    • The Korean Journal of Financial Management
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    • v.24 no.3
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    • pp.133-152
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    • 2007
  • In this paper, we examine a portfolio selection model in which a safety-first investor maximizes expected return subject to a downside risk constraint. We use the Value-at-Risk as the downside risk measure. We exploit the fact that returns are fat-tailed, and use a semi-parametric method suggested by Jansen, Koedijk and de Vries(2000). We find a more realistic asset allocation than the one suggested by the literature based on the traditional mean-variance framework. For the robustness check, we provide empirical analyses using empirical quantiles. The results highlight that for optimal portfolio selection involving downside risks that are far in the tails of the distribution, our mean-VaR model with a fat-tailed distribution is superior.

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