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다변량 혼합 정규분포 GARCH 모형을 이용한 선물시장의 동학헤지 성과분석
Reports NRF is supported by Research Projects( 다변량 혼합 정규분포 GARCH 모형을 이용한 선물시장의 동학헤지 성과분석 | 2007 Year | 정상국(인제대학교) ) data is submitted to the NRF Project Results
Researcher who has been awarded a research grant by Humanities and Social Studies Support Program of NRF has to submit an end product within 6 months(* depend on the form of business)
  • Researchers have entered the information directly to the NRF of Korea research support system
Project Number B00263
Year(selected) 2007 Year
the present condition of Project 종료
State of proposition 재단승인
Completion Date 2009년 05월 13일
Year type 결과보고
Year(final report) 2009년
Research Summary
  • Korean
  • 최근에 선물계약은 개별 기업의 차원에서 위험관리의 일반적인 수단으로 간주되고 있다. 일반적으로 위험은 분산과 동일한 것으로 가정하는데, 이러한 상황에서 최적의 선물헤지전략은 현물포지션에 대한 선물포지션의 비율이 선물수익의 조건부 분산에 대한 현-선물 수익율간의 조건부 공분산의 비율과 동일해야 한다는 것을 의미한다. 실증분석을 통해서 헤지비율은 과거의 현-선물수익율과 같은 정보를 조건부로 변화한다는 것이다.

    초기의 연구는 현물수익율을 선물수익율에 회귀분석을 통해서 헤지전략의 성과를 기술하고 있다. 최근의 연구로부터 헤지비율은 시간에 따라 변화하는 것으로 분석되고 있고, 따라서 GARCH 모형을 이용하여 동학적인 헤지전략의 성과가 기존의 전통적인 헤지전략에 비해서 우월한 것으로 밝혀졌다.

    ARCH, GARCH 모형 등이 개발된 이후로 일련의 혼합정규분포 GARCH 모형이 최근에 발표되고있다. 이 모형은 특별히 금융 시계열의 변동성을 예측하고 분석하는데 적합한 것으로 판단된다. 이러한 혼합정규분포 GARCH 모형은 조건부-무조건부 수익분포에서 자부 발견되는 왜도나 첨도를 설명하는데 있어서 매우 유용하다.

    금융분야에서는 대부분의 연구들은 본질적으로 다변량의 성격을 갖고 있으며, 따라서 다른 자산간의 종속구조를 이해할 필요가 있지만 현재까지의 대부분의 연구들은 단별량 혼합정규분포 GARCH 모형에 국한되어 있다.

    이 연구는 기존의 BEKK 모형과 CCC 모형에 이변량 혼합정규분포 GARCH 과정을 결합하는 형태의 새로운 모형을 이용하여 헤지전략을 비교분석하고자 한다. 결과적으로 혼합정규분포 GARCH 모형으로부터 추정된 헤지비율은 시간 가변적이고 비대칭의 성격을 갖는다. 이 연구에서 고려하는 모든 모형을 CBOT에서 거래되는 두 개의 선물계약, 옥수수와 밀 등에 적용할 것이다. 특별히 혼합정규분포 BEKK-GARCH 모형의 헤지성과는 전통적인 CCC와 BEKK-GARCH 모형, 혼합정규분포 CCC-GARCH, OLS 모형 등을 통한 헤지성과와 비교하게 될 것이다. 헤지성과에 대한 비교는 표본외 예측을 통한 헤지기간 별 각 모형의 헤지포트폴리오의 분산의 감소에 의해서 이루어지고 있다. 또한 이러한 헤지성과의 차이가 통계학적으로 얼마나 유의적인지를 검증하기 위해서 최근에 개발된 SPA 검증방법을 이용하였다.

    이 연구를 통해서 중요한 연구결과는 다음과 같다. 첫째, 옥수수와 밀 선물시장의 현-선물 수익률에 적용한 이변량 혼합정규분포 GARCH 모형의 결과는 무엇보다 데이터의 중요한 특징을 충분히 설명하고 있다는 것이다. 둘째, 비교적 단기의 헤지기간에 걸쳐 일반적인 BEKK-GARCH 모형이 다른 모형에 비해서 통계적으로 유의한 것으로 나타났다. 셋째, 헤지기간이 10일 이후의 장기에 걸쳐있는 경우 혼합정규분포 BEKK-GARCH 모형이 가장 우월한 결과를 보이고 있다.
  • English
  • Recently futures contracts are becoming more popular instruments for risk management in specific firm level. Assuming the convention that equates risk to variance, the best futures hedging strategy is that the ratio of the futures position to the spot position should equal to the ratio of the conditional covariance between spot and futures returns to the conditional variance of the futures return. In empirical applications, the hedge ratio varies according to the conditioning information adopted such as the history of both spot and futures prices.

    Early research illustrates the benefits of conventional hedging strategies derived from the regression of spot returns on futures returns. Recent studies recognize the hedge ratio is changing through time and adopt GARCH models to generate dynamic hedging strategies, which are found to perform better than the conventional strategies.

    Since the publication of the ARCH and GARCH models, family of mixed normal GARCH processes are recently proposed, in which they have been shown to be particularly well suited for analyzing and forecasting financial volatility. These mixed normal GARCH models, besides having a skewed leptokurtic conditional density, are capable of capturing the skewness and kurtosis detected in both conditional and unconditional return distributions.

    Most of applications in finance are inherently multivariate and require us to understand the dependence structure between assets, but the existing literature on normal mixture GARCH models is limited to univariate processes.

    This study develops hedge strategies using new models that extend the BEKK and constant conditional correlation (CCC) GARCH models with a bivariate mixed normal, respectively. As a consequence, the hedge ratio estimated from mixed normal GARCH models is both time varying and asymmetric. All competing models are applied to two agricultural futures contracts, corn and wheat, traded on the Chicago Board of Trade. Specifically, the hedge performances of a mixed normal BEKK-GARCH (MN-BEKK) model are compared with the conventional CCC and BEKK GARCH models, the other mixed normal CCC-GARCH (MN-CCC) model and Ordinary Least Square (OLS). Hedge performance comparisons are based on the percentage variance reduction of the hedged portfolio of each model with the use of out-of-sample point estimates and with respect to different hedge horizons, respectively. To test statistical significance of these differences in hedging performance, the SPA (superior predictive ability) is applied.

    Overall, three main empirical results are in order. First, upon fitting a bivariate mixed normal GARCH model to spot and futures returns of corn and wheat markets, we find that a parsimonious version of the model captures the salient features of the data rather well. Second, the standard BEKK-GARCH model significantly outperforms the CCC-GARCH model and the other mixed normal GARCH models at shorter horizons (from one day to 10-days) both under hedged performances and their statistical significance of SPA tests. Third, as the hedge horizon is extended to longer than 10 days, it is evident that the MN-BEKK model is the best at the usual significance level of 5%.
Research result report
  • Abstract
  • In this study we compare two standard bivariate GARCH models with new bivariate mixed normal GARCH models in terms of the percentage variance reduction of the out-of-sample hedged portfolio and the statistical significance test of the performance improvements using Hansen’s (2001) Superior Predictive Ability statistics. All competing models are applied to estimate time-varying hedge ratios for corn and wheat, traded on the Chicago Board of Trade. The out-of-sample evaluation is carried out by comparing hedged portfolio variances from all models over the one to 60 days horizons. The empirical results demonstrate that the standard BEKK-GARCH model significantly outperforms the other competing GARCH models at shorter horizons. However, as the hedge horizon is extended to longer than 10 days, it is evident that the mixed normal BEKK-GARCH model is the best at the usual significance level of 5%.
  • Research result and Utilization method
  • In this study new bivariate mixed normal GARCH models are proposed to estimate the time-varying hedge ratio. We employ standard bivariate GARCH models such as the CCC-GARCH(1,1) and BEKK-GARCH(1,1), in addition to bivariate mixed normal GARCH models of MN-CCC and MN-BEKK. The main goal is to evaluate the performance of different models in terms of their ability to reduce variances of out-of-sample hedged portfolio and to test the statistical significance of the performance improvements using SPA tests. The out-of-sample evaluation is carried out by comparing the hedged portfolio variances from all models over the one to 60 days horizons.
    Overall, three main empirical results are in order. First, upon fitting a bivariate mixed normal GARCH model to spot and futures returns of corn and wheat markets, we find that a parsimonious version of the model captures the salient features of the data rather well. Second, the standard BEKK-GARCH model significantly outperforms the CCC-GARCH model and the other mixed normal GARCH models at shorter horizons (from one day to 10-days) both under hedged performances and their statistical significance of SPA tests. Third, as the hedge horizon is extended to longer than 10 days, it is evident that the MN-BEKK model is the best at the usual significance level of 5%.
    Further research is however needed to build more parsimonious parameterizations for the component-specific volatility models and to allow for conditional forecasts of the next period regime, which is not possible within the iid mixed normal used in this study. As an anonymous referee noted, the hedging cost problem is occurred due to the expiration of corn and wheat futures on the CBOT when hedge horizon is approximately less than 90 days and also the results of this study can change on account of forecasting methods such as dynamic and static methods.
  • Index terms
  • Regime-dependent Correlations, Conditional Variance, Bivariate Mixed Normal BEKK GARCH, Dynamic Hedge Performances, SPA tests
  • List of digital content of this reports
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