• The Korean Journal of Financial Studies
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• v.3 no.1
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• pp.329-357
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• 1996

본 논문은 확률적 변동성하의 통화옵션가격결정모형에 대하여 실증적으로 검증하였다. 연구결과 OTM, ATM, ITM에서 일정한 변동성을 가정하는 모형가격은 확률적 변동성하의 통화옵션가격결정모형에 비교하여 일치적으로 높게 나타나고 있으며 OTM옵션에 가격결정오차의 크기는 ATM 옵션보다 크게 나타나고 있다. 또한 옵션의 만기가 길수록 가격결정오차의 크기는 커진다는 것을 보여주고 있다. 확률적 변동성하의 통화옵션가격결정모형이 일정한 변동성을 가정하는 통화옵션가격결정모형보다 행사가격과 만기편의를 감소시키며 특히 단기의 만기를 가진 범위에서는 매우 큰 오차감소효과가 나타났다. 따라서 통화옵션가격결정모형을 이용하여 옵션가격을 예측함에 있어 환율변동성이 일정하다는 가정하에서 변동성을 모형에 투입하는 것보다는 환율변동성의 이분산성을 고려하여 추정된 변동성을 모형에 투입하는 것이 통화옵션가격의 예측력을 개선시킬 수 있다고 할 수 있다. 그리고 회귀분석결과 설명력을 나타내는 $R^2$값이 높게 나타나고 있으며, 확률적 변동성하의 통화옵션가격결정모형의 $R^2$값이 일정한 변동성을 가정하는 모형의 $R^2$보다는 높게 나타나고 있다.

• Journal of Korea Port Economic Association
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• v.30 no.3
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• pp.1-14
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• 2014

This paper aims at measuring how new information is incorporated into volatility estimates. Various GARCH models are compared and estimated with daily BDI(Baltic Dry Index) data. While most researchers agree that volatility is predictable, they differ on how this volatility predictability should be modelled. This study, hence, introduces the asymmetric or leverage volatility models, in which good news and bad news have different predictability for future. We provide the systematic comparison of volatility models focusing on the asymmetric effect of news on volatility. Specifically, three diagnostic tests are provided: the sign bias test, the negative size bias test, and the positive size bias test. From the Ljung-Box test statistic for twelfth-order serial correlation for the level we do not find any significant serial correlation in the unpredictable BDI. The coefficients of skewness and kurtosis both indicate that the unpredictable BDI has a distribution which is skewed to the left and significantly flat tailed. Furthermore, the Ljung-Box test statistic for twelfth-order serial correlations in the squares strongly suggests the presence of time-varying volatility. The sign bias test, the negative size bias test, and the positive size bias test strongly indicate that large positive(negative) BDI shocks cause more volatility than small ones. This paper, also, shows that three leverage models have problems in capturing the correct impact of news on volatility and that negative shocks do not cause higher volatility than positive shocks. Specifically, the GARCH model successfully reveals the shape of the news impact curve and is a useful approach to modeling conditional heteroscedasticity of daily BDI.

• The Korean Journal of Applied Statistics
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• v.29 no.7
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• pp.1213-1229
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• 2016

Cho and Shin (2016) recently demonstrated that an integrated HAR model has a forecast advantage over the HAR model of Corsi (2009). Recalling that realized volatilities of financial assets have asymmetries, we add a leverage term to the integrated HAR model, yielding the LIHAR model. Out-of-sample forecast comparisons show superiority of the LIHAR model over the HAR and IHAR models. The comparison was made for all the 20 realized volatilities in the Oxford-Man Realized Library focusing specially on the DJIA, the S&P 500, the Russell 2000, and the KOSPI. Analysis of the realized volatility data sets reveal apparent long-memory and asymmetry. The LIHAR model takes advantage of the long-memory and asymmetry and produces better forecasts than the HAR, IHAR, LHAR models.

• International Area Studies Review
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• v.14 no.2
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• pp.25-40
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• 2010

Accurate forecasting of volatility is of considerable interest in financial volatility research, particularly in regard to portfolio allocation, option pricing and risk management because volatility is equal to market risk. So, we attempted to delineate a model with good ability to forecast and identified stylized features of volatility, with a focus on volatility persistence or long memory in the Australian futures market. In this context, we assessed the long-memory property in the volatility of index futures contracts using three conditional volatility models, namely the GARCH, IGARCH and FIGARCH models. We found that the FIGARCH model better captures the long-memory property than do the GARCH and IGARCH models. Additionally, we found that the FIGARCH model provides superior performance in one-day-ahead volatility forecasts. As discussed in this paper, the FIGARCH model should prove a useful technique in forecasting the long-memory volatility in the Australian index futures market.

• The Korean Journal of Financial Management
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• v.13 no.1
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• pp.203-220
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• 1996

본 연구에서는 우리나라 채권시장의 변동성 분석과 추정을 위하여 Markov-Switching ARCH (SWARCH)모형과 GMM모형 및 I-GARCH모형을 적용하였다. 관측된 자료는 1993년 1월에서부터 1996년 4월까지의 주별 91일물 양도성 예금증서 수익률이다. 본 연구에서 채권 수익률 분산과정의 추정을 위해 사용하는 SWARCH 모형은 경제나 채권시장의 국면전환으로 말미암아 채권수익률의 변동성이 이질적인 분포에서 오는 경우 서로 다른 분산 국면의 확률적 식별이 가능할 뿐만 아니라 지속성이 GARCH모형보다 작아서 조건부 변동성의 예측력이 뛰어난 모형으로 알려져 있다. 또한 SWARCH모형은 베이즈이론에 의한 확률의 개념으로 국면전환을 추정하기 때문에 주관적인 국면전환시점의 판단이 불필요하다는 장점을 가진다 여러 가지 모형들의 추정결과 I-GARCH 모형과 SWARCH 모형등이 우리나라 단기 채권수익률의 조건부 변동성을 비교적 잘 설명해 내는 것으로 나타났으며 우리나라 단기 채권시장은 1993년 6월부터 1993년 12월초까지, 1994년 7월경부터 1995년 5월경까지 비교적 높은 변동성을 유지하였으며 그후로는 변동성이 등락을 계속하는 것으로 추정되었다. 본 연구의 결과 아직은 태동단계에 머물러 있는 한국 채권시장의 시계열적 특성을 체계적으로 문서화하고 정교하고 다양한 최근 계량기법을 체계적으로 정리하고 응용하여 시장 참가자들의 기회비용과 시행착오의 기간을 단축시키는데 도움을 줄 수 있을 것으로 기대된다.

• Management & Information Systems Review
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• v.28 no.4
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• pp.93-108
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• 2009

This study examines the asymmetric volatility in the Korean bond market and stock market by using the KTB Prime Index and KOSPI. Because accurate estimation and forecasting of volatility is essential before investing assets, it is important to understand the asymmetric response of volatility in bond market. Therefore I investigate the existence of asymmetric volatility in Korean bond market unlike the previous studies which mainly focused on stock returns. The main results of the empirical analysis with GARCH and GJR-GARCH model are as follow. At first, it exists the asymmetric volatility on KOSPI returns like the previous studies. Also, I find that the GJR-GARCH is more suitable one than GARCH model for forecasting volatility. Second, it does not exist the asymmetric volatility on KTB Prime Index returns. This result is showed by that using the GARCH model for forecasting volatility in bond market is sufficient.

• The Korean Journal of Applied Statistics
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• v.26 no.1
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• pp.163-185
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• 2013

In this paper, we investigate the need to employ long-memory volatility models in terms of Value-at-Risk(VaR) estimation. We estimate the VaR of the KOSPI returns using long-memory volatility models such as FIGARCH and FIEGARCH; in addition, via back-testing we compare the performance of the obtained VaR with short memory processes such as GARCH and EGARCH. Back-testing says that there exists a long-memory property in the volatility process of KOSPI returns and that it is essential to employ long-memory volatility models for the right estimation of VaR.

• The Korean Journal of Financial Studies
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• v.3 no.2
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• pp.157-185
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• 1996

본 연구는 한국증권시장에서 변동성의 정보비대칭효과를 조건부 이분산모형을 이용하여 검증하고자 하였다. 검증방법으로는 Engle과 Ng (1993)의 연구에 기초하여 정보반응곡선(News impact curve)으로 분석하였다. 분석자료로 1980년 부터 1995년 까지의 한국종합주가지수, 일별 초과수익률자료를 사용하였다. 정보반응곡선에 이용한 모형은 GARCH 모형, EGARCH 모형, TGARCH 모형, AGARCH 모형등 4개의 조건부 이분산 모형이다. 무조건 분산을 이용한 정보 반응곡선의 함수형태로 보면, 분산의 정보반응에 있어서 GARCH 모형은 대칭적으로 반응하며 나머지 조건부 이분산 모형인 EGARCH 모형, TGARCH 모형, 그리고 AGARCH 모형은 비대칭적으로 반응하는 모형임을 알 수 있었다. 실증분석결과 정보반응곡선을 통하여 악재(bad news)정보에 따라 예측하지 못한 주식수익률의 하락이 호재(good news)에 따른 예측하지 못한 주식수익률의 상승보다 더 큰 변동성을 발견할 수 있었다. 그러나 비대칭성의 크기는 그다지 큰 것으로 보이지 않았다. 모형적합성 검정에서도 4개의 조건부 이분산 모형은 모두 적합한 것으로 보인다. 그중에서도 EGARCH 모형과 TGARCH 모형이 상대적으로 주가예측력이 뛰어나 보인다. 그러나 변동성의 정보 비대칭반응을 통계적으로 유의적인 것으로 확인한 모형은 TGARCH모형 뿐이었다.

• Journal of Intelligence and Information Systems
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• v.16 no.2
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• pp.19-32
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• 2010

Volatility plays a central role in both academic and practical applications, especially in pricing financial derivative products and trading volatility strategies. This study presents a novel mechanism based on generalized autoregressive conditional heteroskedasticity (GARCH) models that is able to enhance the performance of intelligent volatility trading systems by predicting Korean stock market volatility more accurately. In particular, we embedded the concept of the volatility asymmetry documented widely in the literature into our model. The newly developed Korean stock market volatility index of KOSPI 200, VKOSPI, is used as a volatility proxy. It is the price of a linear portfolio of the KOSPI 200 index options and measures the effect of the expectations of dealers and option traders on stock market volatility for 30 calendar days. The KOSPI 200 index options market started in 1997 and has become the most actively traded market in the world. Its trading volume is more than 10 million contracts a day and records the highest of all the stock index option markets. Therefore, analyzing the VKOSPI has great importance in understanding volatility inherent in option prices and can afford some trading ideas for futures and option dealers. Use of the VKOSPI as volatility proxy avoids statistical estimation problems associated with other measures of volatility since the VKOSPI is model-free expected volatility of market participants calculated directly from the transacted option prices. This study estimates the symmetric and asymmetric GARCH models for the KOSPI 200 index from January 2003 to December 2006 by the maximum likelihood procedure. Asymmetric GARCH models include GJR-GARCH model of Glosten, Jagannathan and Runke, exponential GARCH model of Nelson and power autoregressive conditional heteroskedasticity (ARCH) of Ding, Granger and Engle. Symmetric GARCH model indicates basic GARCH (1, 1). Tomorrow's forecasted value and change direction of stock market volatility are obtained by recursive GARCH specifications from January 2007 to December 2009 and are compared with the VKOSPI. Empirical results indicate that negative unanticipated returns increase volatility more than positive return shocks of equal magnitude decrease volatility, indicating the existence of volatility asymmetry in the Korean stock market. The point value and change direction of tomorrow VKOSPI are estimated and forecasted by GARCH models. Volatility trading system is developed using the forecasted change direction of the VKOSPI, that is, if tomorrow VKOSPI is expected to rise, a long straddle or strangle position is established. A short straddle or strangle position is taken if VKOSPI is expected to fall tomorrow. Total profit is calculated as the cumulative sum of the VKOSPI percentage change. If forecasted direction is correct, the absolute value of the VKOSPI percentage changes is added to trading profit. It is subtracted from the trading profit if forecasted direction is not correct. For the in-sample period, the power ARCH model best fits in a statistical metric, Mean Squared Prediction Error (MSPE), and the exponential GARCH model shows the highest Mean Correct Prediction (MCP). The power ARCH model best fits also for the out-of-sample period and provides the highest probability for the VKOSPI change direction tomorrow. Generally, the power ARCH model shows the best fit for the VKOSPI. All the GARCH models provide trading profits for volatility trading system and the exponential GARCH model shows the best performance, annual profit of 197.56%, during the in-sample period. The GARCH models present trading profits during the out-of-sample period except for the exponential GARCH model. During the out-of-sample period, the power ARCH model shows the largest annual trading profit of 38%. The volatility clustering and asymmetry found in this research are the reflection of volatility non-linearity. This further suggests that combining the asymmetric GARCH models and artificial neural networks can significantly enhance the performance of the suggested volatility trading system, since artificial neural networks have been shown to effectively model nonlinear relationships.

• Journal of Intelligence and Information Systems
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• v.23 no.2
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• pp.107-122
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• 2017

Volatility in the stock market returns is a measure of investment risk. It plays a central role in portfolio optimization, asset pricing and risk management as well as most theoretical financial models. Engle(1982) presented a pioneering paper on the stock market volatility that explains the time-variant characteristics embedded in the stock market return volatility. His model, Autoregressive Conditional Heteroscedasticity (ARCH), was generalized by Bollerslev(1986) as GARCH models. Empirical studies have shown that GARCH models describes well the fat-tailed return distributions and volatility clustering phenomenon appearing in stock prices. The parameters of the GARCH models are generally estimated by the maximum likelihood estimation (MLE) based on the standard normal density. But, since 1987 Black Monday, the stock market prices have become very complex and shown a lot of noisy terms. Recent studies start to apply artificial intelligent approach in estimating the GARCH parameters as a substitute for the MLE. The paper presents SVR-based GARCH process and compares with MLE-based GARCH process to estimate the parameters of GARCH models which are known to well forecast stock market volatility. Kernel functions used in SVR estimation process are linear, polynomial and radial. We analyzed the suggested models with KOSPI 200 Index. This index is constituted by 200 blue chip stocks listed in the Korea Exchange. We sampled KOSPI 200 daily closing values from 2010 to 2015. Sample observations are 1487 days. We used 1187 days to train the suggested GARCH models and the remaining 300 days were used as testing data. First, symmetric and asymmetric GARCH models are estimated by MLE. We forecasted KOSPI 200 Index return volatility and the statistical metric MSE shows better results for the asymmetric GARCH models such as E-GARCH or GJR-GARCH. This is consistent with the documented non-normal return distribution characteristics with fat-tail and leptokurtosis. Compared with MLE estimation process, SVR-based GARCH models outperform the MLE methodology in KOSPI 200 Index return volatility forecasting. Polynomial kernel function shows exceptionally lower forecasting accuracy. We suggested Intelligent Volatility Trading System (IVTS) that utilizes the forecasted volatility results. IVTS entry rules are as follows. If forecasted tomorrow volatility will increase then buy volatility today. If forecasted tomorrow volatility will decrease then sell volatility today. If forecasted volatility direction does not change we hold the existing buy or sell positions. IVTS is assumed to buy and sell historical volatility values. This is somewhat unreal because we cannot trade historical volatility values themselves. But our simulation results are meaningful since the Korea Exchange introduced volatility futures contract that traders can trade since November 2014. The trading systems with SVR-based GARCH models show higher returns than MLE-based GARCH in the testing period. And trading profitable percentages of MLE-based GARCH IVTS models range from 47.5% to 50.0%, trading profitable percentages of SVR-based GARCH IVTS models range from 51.8% to 59.7%. MLE-based symmetric S-GARCH shows +150.2% return and SVR-based symmetric S-GARCH shows +526.4% return. MLE-based asymmetric E-GARCH shows -72% return and SVR-based asymmetric E-GARCH shows +245.6% return. MLE-based asymmetric GJR-GARCH shows -98.7% return and SVR-based asymmetric GJR-GARCH shows +126.3% return. Linear kernel function shows higher trading returns than radial kernel function. Best performance of SVR-based IVTS is +526.4% and that of MLE-based IVTS is +150.2%. SVR-based GARCH IVTS shows higher trading frequency. This study has some limitations. Our models are solely based on SVR. Other artificial intelligence models are needed to search for better performance. We do not consider costs incurred in the trading process including brokerage commissions and slippage costs. IVTS trading performance is unreal since we use historical volatility values as trading objects. The exact forecasting of stock market volatility is essential in the real trading as well as asset pricing models. Further studies on other machine learning-based GARCH models can give better information for the stock market investors.