• The Korean Journal of Financial Management
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• v.20 no.1
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• pp.213-231
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• 2003

This paper uses the Efficient Method of Moments(EMM) of Gallant and Tauchen to estimate continuous-time stochastic volatility diffusion model for the Korean Composite Stock Price Index, sampled daily over $1995\sim2002$. The estimates display non-normality of stock index return, leptokurtic distribution, and stochastic volatility. Funker, this study suggests that two factor stochastic volatility model will be more desirable than one factor stochastic volatility model to estimate daily Korean stock return and also suggests that the stochastic volatility diffusions should allow for Poisson jumps of time-varying intensity.

• The Journal of the Korea Contents Association
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• v.13 no.12
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• pp.369-378
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• 2013

The Korean Won-Dollar exchange markets showed radical price movements in the late 1990s and 2008. Therefore it provides good sources for studying volatility phenomena. Using the GARCH option models, I analysed how the prices of foreign exchange options react volatilities in the foreign exchange spot prices. For this I compared the explanatory power of three option models(Black and Scholes, Duan, Heston and Nandi), using the Won-Dollar OTC option markets data from 2006 to 2013. I estimated the parameters using MLE and calculated the mean square pricing errors. According to the my empirical studies, the pricing errors of Duan, Black and Scholes models are 0.1%. And the pricing errors of the Heston and Nandi model is greatest among the three models. So I would like to recommend using Duan or Black and Scholes model for hedging the foreign exchange risks. Finally, the historical average of spot volatilities is about 14%, so trading the options around 5% may lead to serious losses to sellers.

• The Korean Journal of Applied Statistics
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• v.36 no.4
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• pp.295-307
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• 2023

The heterogeneous autoregressive (HAR) model is a simple linear model that is commonly used to explain long memory in the realized volatility. However, as realized volatility has more complicated features such as conditional heteroscedasticity, leverage effect, and volatility clustering, it is necessary to extend the simple HAR model. Therefore, to better incorporate the stylized facts, we propose a threshold HAR model with GARCH errors, namely the THAR-GARCH model. That is, the THAR-GARCH model is a nonlinear model whose coefficients vary according to a threshold value, and the conditional heteroscedasticity is explained through the GARCH errors. Model parameters are estimated using an iterative weighted least squares estimation method. Our simulation study supports the consistency of the iterative estimation method. In addition, we show that the proposed THAR-GARCH model has better forecasting power by applying to the realized volatility of major 21 stock indices around the world.

• The Korean Journal of Financial Management
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• v.26 no.3
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• pp.227-246
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• 2009

This study examines the dynamic hedging performances of the Black-Scholes model and Heston model when stock prices drift with stochastic volatilities. Using Monte Carlo simulations, stock prices consistent with Heston's(1993) stochastic volatility option pricing model are generated. In this circumstance, option traders are assumed to use the Black- Scholes model and Heston model to implement dynamic hedging strategies for the options written. The results of simulation indicate that the hedging performance of a mis-specified Black-Scholes model is almost as good as that of a fully specified Heston model. The implication of these results is that the efficacy of the dynamic hedging performances on evaluating the specifications of alternative option models can be limited.

• The Korean Journal of Applied Statistics
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• v.36 no.1
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• pp.85-100
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• 2023

The stochastic volatility (SV) model is one of the main methods of modeling time-varying volatility. In particular, SV model is actively used in estimation and prediction of financial market volatility and option pricing. This paper attempts to model the time-varying volatility of the bitcoin market price using SV model. Hidden Markov model (HMM) is combined with the SV model to capture characteristics of regime switching of the market. The HMM is useful for recognizing patterns of time series to divide the regime of market volatility. This study estimated the volatility of bitcoin by using data from Upbit, a cryptocurrency trading site, and analyzed it by dividing the volatility regime of the market to improve the performance of the SV model. The MCMC technique is used to estimate the parameters of the SV model, and the performance of the model is verified through evaluation criteria such as MAPE and MSE.

• Communications for Statistical Applications and Methods
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• v.16 no.4
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• pp.605-614
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• 2009

TGARCH models characterized by asymmetric volatilities have been useful for analyzing various time series in financial econometrics. We are concerned with persistent volatility in the TGARCH context. Park et al. (2009) introduced I-TGARCH process exhibiting a certain persistency in volatility. This article applies I-TGARCH model to various financial time series in Korea and it is obtained that I-TGARCH provides a better fit than competing models.

• The Korean Journal of Applied Statistics
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• v.28 no.3
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• pp.429-442
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• 2015

Volatility forecasting in financial markets is an important issue because it is directly related to the profit of return. The volatility is generally modeled as time-varying conditional heteroskedasticity. A generalized autoregressive conditional heteroskedastic (GARCH) model is often used for modeling; however, it is not suitable to reflect structural changes (such as a financial crisis or debt crisis) into the volatility. As a remedy, we introduce the Markov regime switching GARCH (MRS-GARCH) model. For the empirical example, we analyze and forecast the volatility of the daily Korea Composite Stock Price Index (KOSPI) data from January 4, 2000 to October 30, 2014. The result shows that the regime of low volatility persists with a leverage effect. We also observe that the performance of MRS-GARCH is superior to other GARCH models for in-sample fitting; in addition, it is also superior to other models for long-term forecasting in out-of-sample fitting. The MRS-GARCH model can be a good alternative to GARCH-type models because it can reflect financial market structural changes into modeling and volatility forecasting.

• Environmental and Resource Economics Review
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• v.13 no.2
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• pp.175-194
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• 2004

Volumes of research have been implemented to estimate and predict the oil price. These models, however, fail in accurately predicting oil price as a model composed of only a few observable variables is limiting. Unobservable variables and news that have been overlooked in past research, yet have a high likelihood of affecting the oil price. Hence, this paper analyses the news impact on the price. The standard GARCH model fails in capturing some important features of the data. The estimated news impact curve for the GARCH model, which imposes symmetry on the conditional variances, suggests that the conditional variance is underestimated for negative shocks and overestimated for positive shocks. Hence, this paper introduces the asymmetric or leverage volatility models, in which good news and bad news have different impact on volatility. They include the EGARCH, AGARCH, and GJR models. The empirical results showed that negative shocks introduced more volatility than positive shocks. Overall, the AGARCH and GJR were the best at capturing this asymmetric effect. Furthermore, the GJR model successfully revealed the shape of the news impact curve and was a useful approach to modeling conditional heteroscedasticity.

• Proceedings of the Korea Inteligent Information System Society Conference
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• 2001.06a
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• pp.333-340
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• 2001

본 연구에서는 GARCH 모델과 이동평균법을 이용한 국내 외환 시장에 있어서의 변동성 척도가 비교 분석되었다. 즉 두가지 알고리듬을 통하여 정보의 내용과 외환시장 변동성의 변통성 예측력을 비교하였다. 그 결과 GARCH 모형에 의할 변동성 추정치는 예측력에 있어서는 이동평균 추정치 보다 낮은 수준이지만 정보내용의 측면에서 성과가 더 좋은 것으로 나타났다. 그리고 GARCH모형에 의한 추정치는 이동평균 추정치 보다 편의성(Bias)이 낮은 것으로 나타났다. 또한 변동성의 가치에 대해서 논의하고, 이러한 변통성 추정치를 통해서 실제 환율변동을 헷지하기 위한 옵션매매에 어떻게 적용할 수 있는지를 언급하였다.

• The Korean Journal of Applied Statistics
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• v.24 no.1
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• pp.61-69
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• 2011

In GARCH context, the conditional variance (or volatility) is of a quadratic function of the observation process. Examine standard ARCH/GARCH and their variant models in terms of quadratic formulations and it is interesting to note that most models in GARCH context have contained neither the first order term nor the interaction term. In this paper, we consider three models possessing the first order and/or interaction terms in the formulation of conditional variances, viz., quadratic GARCH, absolute value GARCH and bilinear GARCH processes. These models are investigated with a view to model comparisons and applications to financial time series in Korea