KOSPI 200 지수의 실현변동성 예측에서의 내재변동성 측정오차의 영향

정정현 ( Chung Hyun Chung ),김동회 ( Dong Hoe Kim ) 한국금융공학회 2008 금융공학연구 Vol.7 No.3

This paper investigates the error-in-variable problem of implied volatility in KOSPI 200 index option market during the period of 9 years from 1999 to 2007. The measurement error of implied volatility will cause the downward bias of OLS coefficient of implied volatility in predicting future realized volatility. The realized volatility and the historical volatility are measured as daily base and monthly base using daily return of KOSPI 200 index. And the volatility index (KoVIX) published by KRX is used to measure the implied volatility. For the daily data, the implied volatility of put option exhibits measurement error, while that of call option does not. It shows that the measurement error may be effected by the market liquidity. And the implied volatility doesn`t seem to be an unbiased estimator of the realized volatility. The historical volatility seems to have additional predictive information over the implied volatility. For the monthly data, the pattern of measurement error is similar with the daily data. But the implied volatility seems to be an unbiased estimator of the realized volatility. The historical volatility doesn`t have additional predictive information over the implied volatility.

변동성지수의 미래예측력에 대한 연구

엄영호 ( Young Ho Eom ),지현준 ( Hyun Jun Ji ),장운욱 ( Woon Wook Jang ) 한국금융학회 2008 금융연구 Vol.22 No.3

변동성지수는 옵션가격에 내재되어 있는 미래 변동성에 대한 기대를 지수화하여 표현한 것이며 미국, 독일 등의 증권거래소에서는 변동성지수의 발표뿐만 아니라 지수관련 파생상품도 거래되고 있다. 국내의 경우에는 아직까지 변동성지수를 공식적으로 발표하지 않고 있으나, 장외파생상품시장의 성장에 따른 변동성 헤지수요의 증가와 새로운 상품에 대한 수요의 증가 등으로 인해 변동성지수에 대한 관심이 크게 증가하고 있다. 변동성지수는 변동성에 대한 헤지기능과 함께 시장위험에 대한 지표의 기능을 할 수 있으며 미래 실제변동성에 대한 예측치의 역할을 할 수 있다. 미래 실제변동성에 대한 예측치로서 변동성지수 혹은 내재변동성의 유용성에 대한 기존연구 들에서는 일별 자료를 이용하여 변동성지수가 실제변동성의 불편추정량은 아니지만 실제변동성에 대해 예측력을 갖는 것으로 설명하고 있다. 그러나 실제 2차적률에는 위험중립 2차적률 뿐만 아니라 고차적률까지 포함될 수 있다는 Bakshi, Kapadia and Madan(2003)의 연구를 고려할 경우 계량경제학적으로 중요변수 누락문제(omitted variable problem)가 발생할 수 있으며, 이는 변동성지수의 불편성(unbiasedness) 및 예측력 검증과정에 영향을 미칠 수 있다. 이에 본 연구에서는 1999년부터 2006년까지의 KOSPI200 지수옵션자료를 이용하여 변동성지수를 월별로 산정하고 실제변동성에 대한 예측력을 살펴보았다. 연구결과 측정오차를 고려하거나 고차적률을 고려할 경우 변동성지수의 실제변동성에 대한 불편성을 기각하지 못하고 실제변동성의 과거변수에 비해서도 높은 예측력을 나타냈다. Since the introduction of volatility indices, futures and options on the index have been traded in some derivative exchanges in the US and some European countries. Introducing similar volatility index is also now considered by the Korea Stock Exchange because of the increasing needs of hedge instruments in the fast-growing OTC markets. Furthermore, volatility indices measure market expectations of near term volatilities implied in stock index option prices. Thus, volatility index is not only important in hedging market volatility risk, but also useful in predicting future volatility and measuring market`s fear. There have been many empirical tests about the predictability to the actual volatility and most of them were focused on the Black-Scholes implied volatility or the volatility index based on variance swap (hereafter VIX) or Black-Scholes implied volatility (hereafter VXO). Previous studies indicate that the volatility index or the Black-Scholes implied volatility has predictability to the future actual volatility though they are not unbiased estimators. However, there might be some econometric problems in testing the predictability to the actual volatility. One of classical problems is the measurement error problem caused by low-liquidity or non-synchronous data and an over-lapping data problem mentioned by Christensen and Prabhala (1998). Also, Bakshi, Kapadia and Madan(2003) showed that higher moments of risk-neutral measure can affect to the actual volatility and in this case there may be an omitted-variable problem, which may result in the biasedness in the tests. Besides these econometric problems, there are some measurement issues in estimating the actual volatility (the realized volatility based on intra-data and the sample standard deviation) and constructing the volatility index (VXO, VIX and splined VIX).The purpose of this study is to empirically test whether volatility index is an unbiased estimator of the future actual volatility. Firstly, according to the result of Bakshi, Kapadia and Madan(2003), we test the predictability of the volatility index with the risk-neutral higher moments. Secondly, we test the predictability with considerations of measurement error problems. We use the data of specific time in trading hour to avoid non-synchronous problem and monthly data for using non-overlapping data. We use an instrumental variable regression method in estimating as well. Also for the robustness test of the results, we construct various volatility indices with respect to data types and numericlal methods and investigate their effects on the predictablility power. Finally, in the test we use the realized volatility of Andersen et al. (2001) as well as a sample standard deviation as the proxy for the future true realized volatility. We test with the monthly volatility index constructed by the KOSPI200 index option data for the sample period covered from 1999 to 2006. The results indicate that the volatility index has predictability to the actual volatility and has higher predictability power than the historical volatility (past sample standard deviation). In case of the realized volatility, the volatility index is better than the past realized volatility in forecasting the actual volatility when considering measurement error. The volatility index is an unbiased estimator when we take the measurement error or the omitted-variable problem into account, while it`s a biased estimator in general regression test. The VIX index is predictable to the actual volatility as much as the VXO index, but the former is less sensitive to data or construction method. These results shows that the unbiasedness of the volatilty index to the actual volatility is not rejected when some econometric issues are considered and that the volatility index has higher predictability power than those of other volatility measures such as past actual volatilities.

Realized FX Volatility : Statistical Properties and Applications

엄철준,박종원,Taisei Kaizoji,Enrico Scalas 한국파생상품학회 2018 선물연구 Vol.26 No.1

This paper empirically examines the statistical properties of realized volatility and the relationships between volatility and correlation measurements of realized volatility by using intraday high-frequency foreign exchange (FX) rates. Results regarding the distributional and dynamic properties of realized volatility are in agreement with the findings of previous studies. However, the positive correlation present in previous studies is not found in the case of JPY. On trading days with low volatility in the FX market, realized correlation coefficients between JPY and other currencies have positive values, while realized correlation coefficients on trading days with high volatility show negative values. These results are due to the Japanese government's intervention in the FX market, particularly during trading days with high volatility. In this regard, our results suggest that the positive relationships between volatility and correlations verified in previous studies are not a general phenomenon in the case of government intervention and government intervention may distort the efficiency of the FX market. In addition, we show that the multivariate measurement of realized volatility based on intraday high-frequency data can be a useful tool for determining the occurrence of external intervention in the FX market.

내재변동성 측정방법에 따른 실현변동성 예측력 분석

김태혁 ( Tae Hyuck Kim ),박종해 ( Jong Hae Park ) 한국금융공학회 2006 금융공학연구 Vol.5 No.2

Our Research is that Compare the implied volatility and econometircs literature for predicting realized volatility. We investigate various weighting schemes for calculating implied volatility and select implied volatility using our research. We calculate 9 implied volatilitis weighted various schemes, 2 historical volatilities using GARCH-type model and a realized volatility using high-frequency data. Next, we compare forecast accuracy between implied volatility and historical volatility using RMSE, MAE, MAPE. We find that VIX and NewVIX has strong predictive power and better than other implied volatility. GARCH-type volatility forecast better than implied volatility weighted by trading volume, but worst than any other implied volatility. According to measuring rule of implied volatility and econometrics models, predictive power is different.

외환시장의 변동성과 거래량의 관계 분석: 충격정보 확률변동성 모형 이용

박범조 한국은행 2008 經濟分析 Vol.14 No.4

Modifying the MDH(mixture of distribution hypothesis) theory, Park(2007) showed that the effect of ‘surprising information’ on the relationship between volatility and trading volumes contrasts with that of general information. On the basis of his study, this paper proposes surprising-information-stochastic- volatility(SISV) model to capture their nonlinear relationship that is caused by the state change of volatility due to the surprising information flow. To estimate the SISV model efficiently this paper also suggests Markov chain Monte Carlo(MCMC) method. Strong evidence in favor of SISV model over the standard stochastic volatility model is based on empirical application with high frequency data of Won/Dollar exchange rates. Interestingly, while their positive relationship is not significant in the stochastic volatility model with a volume variable, it becomes significant and the persistence of volatility is remarkably reduced in the SISV model. According to the estimation results of the bivariate SISV model, furthermore, the surprising information flow increases the volatility of returns highly, whereas it little changes the volatility of trading volume. These empirical findings are consistent with the modified MDH and imply that ignoring the feature of surprising information can lead to a model misspecification. 충격정보가 자산시장의 변동성과 거래량의 관계에 미치는 영향이 일반정보와 다르다는 수정된 혼합분포가설(MDH)(박범조, 2007)에 기초하여 본 연구는 충격정보의 유입에 따라 변동성의 상태(states)가 변함으로써 발생되는 두 변수의 비선형적 관계를 동태적으로 고려하기 위한 충격정보 확률변동성(surprising-information-stochastic volatility: SISV) 모형을 새롭게 제안하였다. 이 모형을 추정하기 위해 효율적인 베이지언 추정법인 마코프 체인 몬테칼로(MCMC) 알고리즘을 적용하고 고빈도 원/달러 환율 자료와 일별 거래량 자료를 이용하여 실증분석을 수행하였다. 거래량 변수만을 포함한 단변량 확률변동성 모형을 이용한 분석결과에 의하면 GARCH 유형의 모형을 이용한 일반적 연구결과와 다르게 변동성과 거래량이 통계적으로 유의한 관계를 갖지 않았다. 하지만 충격정보를 고려할 경우 유의한 관계를 가지게 되며 변동성의 지속성도 현격히 감소하였다. 한편 동시편의(simultaneity bias) 문제 없이 두 변수의 관계를 동태적으로 분석할 수 있는 이변량 SISV 모형에서도 유사한 결과를 보여줄 뿐만 아니라 충격정보가 유입되는 경우 수익률의 변동성은 통계적으로 유의하게 증가되지만 거래량의 변동성은 유의하게 변화되지 않는다는 흥미로운 사실을 보여주었다. 이런 실증분석 결과들은 수정된 혼합분포가설과 일치하며 변동성 모형에 충격정보를 고려하지 않는 경우 심각한 모형설정 오류가 발생할 수 있음을 암시한다.

외부충격과 실현변동성의 이질적 자기회귀모형

엄철준,장욱,박종원 한국재무학회 2016 한국재무학회 학술대회 Vol.2016 No.11

본 연구는 외부충격변수(ES)가 실현변동성의 이질적 자기회귀(HAR-RV)모형에서 미래 기간 실현변동성의 변화에 대한 내표본 설명력 개선과 외표본 예측력 개선에 유용한 정보효과를 갖는지를 중점적으로 분석하였다. 실현변동성은 2004년 1월부터 2016년 6월까 지 KOSPI 200 시장지수의 일중 5분 단위 고빈도 수익률 자료를 이용하여 산출한다. 외부충격변수는 요인분석을 이용하여 구한 외부충격의 속성을 갖는 10가지 자료들을 결합 한 단일 시계열자료이다. 주요 검증결과는 다음과 같다. 첫째, 제안된 방법으로 생성된 단일 외부충격변수의 시계열자료는 국제적으로 알려진 시장충격의 중요한 흐름을 잘 반 영하고, 실현변동성이 급격하게 상승하는 시장붕괴 시점에서 유사한 움직임을 보였다. 둘째, 내표본 분석에서 외부충격뱐수를 새로운 독립변수로 추가한 이질적 자기회귀모형 (HAR-RV-J-ES모형)은 미래기간 일별과 주별 실현변동성의 변화를 유의적으로 설명하 는 정보효과를 가졌다. 셋째, 외표본 분석에서 외부충격변수는 이질적 자기회귀모형의 미래기간 일별 실현변동성의 예측력 개선에 유의한 증거를 보였다. 넷째, 확인된 외부충 격변수의 설명력과 예측력 개선은 변동성 레버리지효과에 영향을 받지 않는 고유한 정보 효과임을 확인하였다. 이러한 결과는 미래기간 실현변동성의 변화를 설명하고 예측하는 데 본 연구에서 사용된 외부충격변수가 유용한 정보가치를 가짐을 보여주는 것이며, 본 연구에서 제안한 외부충격의 속성을 갖는 다양한 자료들을 결합하여 단일의 외부충격변수를 생성하는 방법이 향후 관련 연구에 새로운 시각을 제공할 수 있음을 의미한다. We examine the information effect of external shocks on the realized volatility based on the HAR-RV (heterogeneous autoregressive realized volatility) model in Korean stock market. For the study, we estimate the realized volatility using the five minute intraday high-frequency KOSPI return data from Jan. 2004 to June 2016. And we develop and use the single external shock variable (ES) which is constructed from the 10-external shock variables representing changes of international stock, crude oil, gold, foreign exchange market prices, and interest rate. We use factor analysis to develop the ES from the 10-external shock variables. The main results are as follows. First, the developed external shock variable (ES) represents well the shocks in international market prices and the time-series patterns of ES are similar to the realized volatility patterns of KOSPI, especially in the market crash period. Second, in In-sample analysis using the HAR-RV-ES model which is the model added the ES variable to HAR-RV model as a new explanatory variable, the ES variable shows a significant explanatory power on changes of daily and weekly realized volatility. Third, in Out-of-sample analysis, the ES variable has a significant predictive power on future realized volatility. Fourth, The information effects of ES variable are robust to volatility leverage effect. These results suggest that the developed ES variable in this study is useful variable with additive and independent information effect for explaining and predicting the future volatility in the HAR-RV model, and the proposed method for developing the ES variable is helpful for the improvement of HAR-RV model.

Neural network heterogeneous autoregressive models for realized volatility

Kim, Jaiyool,Baek, Changryong The Korean Statistical Society 2018 Communications for statistical applications and me Vol.25 No.6

In this study, we consider the extension of the heterogeneous autoregressive (HAR) model for realized volatility by incorporating a neural network (NN) structure. Since HAR is a linear model, we expect that adding a neural network term would explain the delicate nonlinearity of the realized volatility. Three neural network-based HAR models, namely HAR-NN, $HAR({\infty})-NN$, and HAR-AR(22)-NN are considered with performance measured by evaluating out-of-sample forecasting errors. The results of the study show that HAR-NN provides a slightly wider interval than traditional HAR as well as shows more peaks and valleys on the turning points. It implies that the HAR-NN model can capture sharper changes due to higher volatility than the traditional HAR model. The HAR-NN model for prediction interval is therefore recommended to account for higher volatility in the stock market. An empirical analysis on the multinational realized volatility of stock indexes shows that the HAR-NN that adds daily, weekly, and monthly volatility averages to the neural network model exhibits the best performance.

Quantile forecasts for financial volatilities based on parametric and asymmetric models

Choi, Ji-Eun,Shin, Dong Wan Elsevier 2019 Journal of the Korean Statistical Society Vol.48 No.1

<P><B>Abstract</B></P> <P>For financial volatilities such as realized volatility and volatility index, a new parametric quantile forecast strategy is proposed, focusing on forecast interval and value at risk (VaR) forecast. This fully addresses asymmetries in 3 parts: mean, volatility and distribution. The asymmetries are addressed by the LHAR (leverage heterogeneous autoregressive) model of McAleer and Medeiros (2008) and Corsi and Reno (2009) for the mean part, by the EGARCH model for the volatility part, and by the skew-t distribution for the error distribution part. The method is applied to the realized volatilities and the volatility indexes of the US S&P 500 index, the US NASDAQ index, the Korea KOSPI index in which significant asymmetries are identified. Considerable out-of-sample forecast improvements of the forecast interval and VaR forecast are demonstrated for the volatilities: forecast intervals of volatilities have better coverages with shorter lengths and VaR forecasts of volatility indexes have better violations if asymmetries are properly addressed rather than ignored. The proposed parametric method reveals considerably better out-of-sample performance than the recently proposed semiparametric quantile regression approach of Zikes and Barunik (2016).</P>

Information Uncertainty and Implied Volatilities

홍종운,박형진 한국무역연구원 2019 무역연구 Vol.15 No.2

In the U.S. stock and options markets from January 1996 to December 2013, we examine whether information uncertainty explains the discrepancy between historical and implied volatilities in Goyal and Saretto (2009). In addition, we clarified the impact of the uncertainty on the stock market as well as on the options market. In particular, we calculated the performance of our zero-investment option portfolio selling option straddle positions of stocks in the first decile with the lowest discrepancy between the two volatilities and purchasing option straddle positions in the last decile with the highest discrepancy. Moreover, we estimate the returns of these portfolios held by until to the earnings announcement days as well as the returns of the portfolios held by one month. In our results, changes in information uncertainty are in tandem with changes in implied volatility and reduce the predictability of implied volatility for the future realized volatility. Additionally, we show an insignificant change in volatility skew during the time of a significant change in volatility implied from ATM options. Conclusively, we provide novel evidence that the uncertainty of information concerning a firm’s fundamental underlying volatility proposed in Hirshleifer (2001) significantly affects implied volatility.

Asymmetric volatility connectedness among G7 Stock Markets

Hahn S. Lee,Woo Suk Lee 한국재무학회 2020 한국재무학회 학술대회 Vol.2020 No.08

This paper investigates asymmetries in volatility connectedness among the G7 stock markets. Using daily realized semi-volatility indices, obtained from intra-day data, we provide ample evidence for the asymmetric volatility connectedness. We find that the impact of bad volatility strictly dominates that of good volatility in generating connectedness across financial markets. In particular, the global financial crisis and the European debt crisis have witnessed most influential episodes of volatility connectedness. We also discuss that the effect of the US stock market on other countries has been largely due to bad volatility.