CARR模型之實證研究---以台股指數為例

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劉炳麟(Bin-Lin Liu) 查詢紙本館藏

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財務金融學系

論文名稱

CARR模型之實證研究---以台股指數為例
(An empirical study of the CARR model: an axample of the Taiwan Stock Index)

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摘要(中)

波動性在財務上扮演著關鍵的角色，若能適當的描述波動性模型，將有助於投資組合配置的最適化，進而能有效的控管風險。ARCH/GARCH族模型在波動性的預測上已被廣泛的應用，而且也能在實證上得到良好的成效。然而Chou(2002)將GARCH模型結合變幅在波動性預測上的優勢進一步提出CARR(Conditional Auto-Regressive Range)模型，並且在S&P500股價指數波動性預測實證上獲得優於GARCH模型的結論，本文想驗證是否在台股指數上也能得到相同的結論。
本文中將簡單的介紹CARR模型及其性質，並以台股指數為研究對象，分別進行CARR模型和GARCH模型在樣本內及樣本外波動性的預測能力比較。本文的實證結果可推論CARR模型在刻畫波動性方面優於GARCH模型，此與Chou(2002)的論述一致。另外，本文隨機選取了10檔個股資料，並比較其樣本內波動性預測能力用以強化論證的完整性。除此之外，本研究並推廣CARR模型的應用層面，考慮財務槓桿效應及漲跌幅限制的影響，並探討其背後所隱含的經濟意義。

摘要(英)

In finance, volatility plays a key role in several sub-fields. Whether the construct of portfolio is optimal or not, partly depends on the control of volatility. Since 1982, ARCH/GARCH family models have been used in the forecast of volatilities, and have performed well in many empirical studies. Recently, Chou(2002) proposed the CARR (Conditional Auto-Regressive Range) model as an alternative volatility model. The main concept of the CARR model is to use a simple dynamic structure for range to characterize the volatility process. In Chou(2002), comparing the CARR model and traditional GARCH model, the former is better in the volatility forecasting based on the data of the S&P 500 index. The main motivation in this paper is to explore the forecasting power of the CARR model based on the trading data of the Taiwan Stock Exchange Capitalization Weighted Stock Index. Our emperical results show that in both the in-sample forecast and the out-of-sample forecast the CARR model is preferable to the GARCH model in the volatility forecasting, supporting the claims of Chou(2002). In order to strenghten the completeness of our demonstration, we arbitrarily choose 10 stocks in Taiwan to compare the two models again in the in-sample volatilities forecasting. Moreover, we also consider the economic implications of financial leverage effect and price limit by utilizing the CARR model.

關鍵字(中)

★ CARR
★ GARCH
★ 變幅
★ 波動性
★ 財務槓桿效應
★ 漲跌幅限制

關鍵字(英)

★ CARR
★ GARCH
★ Range
★ Volatility
★ Leverage Effect
★ Price Limit

論文目次

目錄
頁數
第一章前言 1
第二章文獻回顧 2
第三章研究方法 4
第一節 CARR模型的介紹 4
第二節預測能力的比較 7
第三節考量漲跌幅限制的模型 10
第四章資料分析 11
第一節台灣股票指數週資料的樣本敘述統計量 12
第二節台灣股票指數日資料樣本敘述統計量 14
第三節個股日資料及週資料樣本的敘述統計量 16
第五章實證分析 19
第一節 CARR模型及GARCH模型樣本內預測能力的比較 19
一、以台灣發行量加權股價指數週資料為研究標的 19
二、以台灣發行量加權股價指數日資料為研究標的 25
三、以台灣集中市場個股週資料及日資料為研究標的 27
第二節 CARR模型及GARCH模型樣本外預測能力的比較 30
第三節財務槓桿效應 35
第四節漲跌幅限制的影響 36
第六章結論 39
參考文獻 41
表次
頁次
表1：台灣股價指數週資料之統計特性分析 13
表2：台灣股價指數日資料之統計特性分析 15
表3：個股股價日變幅之統計特性分析 17
表4：個股股價週變幅之統計特性分析 18
表5：CARR模型比較（以CARR(1,1)、CARR(1,2)及CARR(2,1)為例） 20
表6：GARCH模型的比較（以GARCH(1,1)、GARCH(1,1)及GARCH(2,1)為例） 21
表7：CARR(1,1)及GARCH(1,1)在大盤指數週資料的預測能力比較 22
表8：CARR(1,1)及GARCH(1,1)在大盤指數日資料的預測能力比較 26
表9：CARR(1,1)及GARCH(1,1)在個股週資料的預測能力比較 27
表10：CARR(1,1)及GARCH(1,1)在個股日資料的預測能力比較 29
表11：CARR模型及GARCH模型在大盤指數週資料的樣本外預測(SSDR) 31
表12：CARR模型及GARCH模型在大盤指數週資料的樣本外預測(WRSQ) 32
表13：CARR模型及GARCH模型在大盤指數週資料的樣本外預測(WRNG) 33
表14：CARR模型及GARCH模型在大盤指數週資料的樣本外預測(AWRET) 34
表15：CARR(1,1)模型與CARRX(1,1)模型大盤指數日資料參數估計上比較 36
表16：漲跌幅更動表（1985年1月1日起至2001年4月30日） 37
表17：考慮漲跌幅限制的CARR模型表現情形 38
表18：隨著漲跌幅限制改變CARRX(1,1)模型係數的表現情形 39
圖次
頁次
圖1：台灣股價指數週變幅及週報酬率走勢圖 14
圖2：台灣股價指數日變幅及日報酬率走勢圖 15
圖3：SSDR、FV(CARR)及FV(GARCH)樣本內預估圖形 24
圖4：WRSQ、FV(CARR)及FV(GARCH)樣本內預估圖形 24
圖5：WRNG、FV(CARR)及FV(GARCH)樣本內預估圖形 25
圖6：AWRET、FV(CARR)及FV(GARCH)樣本內預估圖形 25
圖7：CARR模型及GARCH模型在大盤指數週資料的樣本外預測比較圖(SSDR) 32
圖8：CARR模型及GARCH模型在大盤指數週資料的樣本外預測比較圖(WRSQ) 33
圖9：CARR模型及GARCH模型在大盤指數週資料的樣本外預測比較圖(WRNG) 34
圖10：CARR模型及GARCH模型在大盤指數週資料的樣本外預測比較圖(AWRET) 35

參考文獻

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指導教授

周雨田、周賓凰
(Ray Y. Chou、Pin-Huang Chou)

審核日期

2003-1-8

推文