Value-at-risk measures and value-at-risk based hedging approach

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Title:	Value-at-risk measures and value-at-risk based hedging approach
Other Titles:	風險值衡量與風險值避險法
Authors:	洪瑞成;Hung, Jui-cheng
Contributors:	淡江大學財務金融學系博士班邱建良;Chiu, Chien-liang
Keywords:	風險值;跳躍;絕對風險值避險比率;雙變量馬可夫狀態轉換模型;多期絕對風險值避險比率;最小變異避險比率;Value-at-Risk;Jump;zero-VaR hedge ratio;Bivariate Markov regime switching model;Multi-period zero-VaR hedge ratios;Minimum hedge ratios
Date:	2007
Issue Date:	2010-01-11 01:15:13 (UTC+8)
Abstract:	本論文著重在風險值的衡量與以風險值為基礎的避險比率上，共包含三個部份，分別為「在動態跳躍與訊息不對稱下的風險值計算」、「絕對風險值避險比率」與「以雙變量馬可夫狀態轉換模型估計多期的絕對風險值避險比率與最小變異避險比率」。將此三部份的內容簡敘如下。第一部分使用GARJI、ARJI與不對稱GARCH等三個模型在估計一天的相對風險值之績效。本文使用此三個模型計算兩個股價指數(道瓊指數與S&P 500指數)與一個匯率(日圓)的多部位風險值，其用意在於探討價格跳躍與訊息不對稱效果對於衡量風險值績效的影響。實證結果發現，在資產報酬率具有隨時間變動的跳躍現象以及訊息不對稱的效果下，由GARJI與ARJI模型所估算出來的風險值無論信心水準的高低，均能提供令人信賴的準確度。另外，由MRSB顯示，GARJI所估算出的風險值最具效率性。第二部份本文以風險值為基礎，推出以絕對風險值為目標函數的絕對風險值避險比率。當期貨報酬率服從單純平賭過程或是風險趨避程度趨於無窮大的條件下，絕對風險值避險比率將縮減成為最小變異避險比率。於實證過程中，本文採用包含誤差修正項的雙變量固定相關係數GARCH(1,1)模型估計計算最小變異避險比率所需的參數，並且比較其與Hsin et al. (1994)所提出的以極大化效用函數為目標的避險比率。第三部份本文推廣單期的絕對風險值避險比率(Hung et al., 2006)成為多期的情況，並使用四狀態雙變量馬可夫轉換模型和雙變量對角化VECH GARCH(1,1)模型估計道瓊指數與S&P 500的絕對風險值避險比率與最小變異避險比率。與Bollen et al. (2000)不同之處在於，本文分別從樣本內與樣本外避險績效的角度，探討在雙變量的情況下，狀態轉換與GARCH這兩種方法何者對於樣本內的配適度以及樣本外的變異數預測較佳。實證結果顯示狀態轉換的方式提供較佳的樣本內配適度；然而，於大多數的情況下，GARCH在樣本外的變異數預測上較具有優勢。 This study focuses on VaR measurement and VaR-based hedge ratio, and it contains three parts. The first part is titled “Estimation of Value-at-Risk under Jump Dynamics and Asymmetric Information”, the second part is named “Hedging with Zero-Value at Risk Hedge Ratio”, and the last one is “Bivariate Markov Regime Switching Model for Estimating Multi-period zero-VaR Hedge Ratios and Minimum Variance Hedge Ratios”. A brief introduction of these three parts is described as follow: The first part employs GARJI, ARJI and asymmetric GARCH models to estimate the one-step-ahead relative VaR and compare their performances among these three models. Two stock indices (Dow Jones industry index and S&P 500 index) and one exchange rate (Japanese yen) are used to estimate the model-based VaR, and we investigate the influences of price jumps and asymmetric information on the performance of VaR measurement. The empirical results demonstrate that, while asset returns exhibited time-varying jump and the information asymmetric effect, the GARJI-based and ARJI-based VaR provide reliable accuracy at both low and high confidence levels. Moreover, as MRSB indicates, the GARJI model is more efficient than alternatives. In the second part, a mean-risk hedge ratio is derived on the foundation of Value-at-Risk. The proposed zero-VaR hedge ratio converges to the MV hedge ratio under a pure martingale process or an infinite risk-averse level. In empirical section, a bivariate constant correlation GARCH(1,1) model with an error correction term is adopted to calculate zero-VaR hedge ratio, and we compare it with the one proposed by Hsin et al. (1994) which maximized the utility function as their objective. The last part extends one period zero-VaR hedge ratio (Hung et al., 2006) to the multi-period case, and also employed a four-regime bivariate Markov regime switching model and diagonal VECH GARCH(1,1) model to estimate both zero-VaR and MV hedge ratios for Dow Jones and S&P 500 stock indices. Dissimilar with Bollen et al. (2000), the in-sample fitting abilities and out-of-sample variance forecasts between regime-switching and GARCH approaches are investigated in a bivariate case through in- and out-of-sample hedging performances. The empirical evidences show that the regime switching approach provides better in-sample fitting ability; however, GARCH approach has better out-of-sample variance forecast ability for most cases.
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