不同模型之股價波動度預測比較

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游舒淳(Shu-Chun Yu) 查詢紙本館藏

畢業系所

財務金融學系

論文名稱

不同模型之股價波動度預測比較
(The Comparison of forecasting performance under Different Models)

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摘要(中)

本研究探討四種不同計算方式的波動度之預測能力，共計算了美國304家公司的四種不同的股價波動率，樣本期間從1999年1月4日至2004年12月31日。這四種波動度分別為：model-free隱含波動率、Black-Scholes隱含波動率、Relized波動率(使用高頻率的日內報價資料計算而得)，以及GJR模型的波動率。參考Taylor, Tadav and Zhang (2006) 的model-free隱含波動率計算方法，結果發現利用前一天的資料來預測今天的波動度，有54%公司是使用五分鐘股票報價所計算的Relized波動率表現最好。而當要預測股票選擇權履約後下個交易日至履約日這段期間的波動度時，則是Black-Scholes隱含波動率的解釋力最高，約有62%的公司適用此波動率。整體來說，無論是使用前一天的資料來預測，還是預測選擇權履約的這段期間之波動度，model-free隱含波動率的預測力來得比Black-Scholes隱含波動率還要差。

摘要(英)

This paper discusses the forecasting abilities of different volatility estimates for 304 U.S. firms during the period from January 4, 1999 to December 31, 2004. The volatility estimates include the model-free implied volatility, the Black-Scholes implied volatility, the realized volatility (calculated by high-frequency intraday data) and the conditional volatility under GJR model. The model-free implied volatility is based on the work of Taylor, Yadav and Zhang (2006). For one-day-ahead estimation, 54% of firms indicate that the realized volatility measured by 5-minute interval returns outperforms other estimates. The Black-Scholes implied volatility has the best performance for 62% of firms when the forecast horizon agrees with the period form the closed day after expiration date to next expiration. The empirical results show the forecasting performance of model-free implied volatility is worse than that of Black-Scholes implied volatility whether the estimation of one-day-ahead or monthly prediction.

關鍵字(中)

★ 隱含波動率
★ 波動率
★ model-free隱含波動率
★ ARCH模型
★ Relized波動率
★ 高頻率資料

關鍵字(英)

★ Realized volatility
★ Model-free volatility
★ Implied volatility
★ Volatility
★ High-frequency data
★ ARCH model

論文目次

1. INTRODUCTION___________________________________________1
2. MODEL-FREE IMPLIED VOLATILITY__________________________3
　2.1 FORMULA_____________________________________________3
　2.2 CALCULATION OF THE MODEL-FREE IMPLIED VOLATILITY____4
3. DATA AND VOLATILITY CALCULATION________________________7
　3.1 CONSTRUCTION OF THE MODEL-FREE AND BLACK-SCHOLES
　　　IMPLIED VOLATILITY__________________________________8
　3.2 CONSTRUCTION OF THE REALIZED VOLATILITY____________10
4. EMPIRICAL METHODOLOGY AND RESULT______________________13
　4.1 DESCRIPTIVE STATISTICS_____________________________13
　4.2 ARCH SPECIFICATIONS________________________________14
　　4.2.1 Description of Model___________________________14
　　4.2.2 Parameter Estimation___________________________15
　　4.2.3 Model Fitting__________________________________18
　4.3 OLS REGRESSION_____________________________________19
　　4.3.1 Description of Model___________________________19
　　4.3.2 Parameter Estimation and Explanation
　　　 Performance__________________________________19
　4.4 COMPARISONS OF THE PERFORMANCE_____________________21
　　4.4.1 Comparison for groups defined by
　　　 average available strike prices______________21
　　4.4.2 Comparison for groups defined by
　　　 intermediate delta options___________________22
5. CONCLUSIONS___________________________________________24
REFERENCES_______________________________________________25
APPENDIX_________________________________________________42
　APPENDIX A. PROOF OF EQUATION (1)______________________42
　APPENDIX B. PERFORMANCES UNDER VARIANCE
　　 AND LOGARITHM REGRESSION MODELS____________43
　APPENDIX C. PERFORMANCE OF DIFFERENT CURVE
　　 FITTING METHODS____________________________44

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指導教授

張傳章(Chuang-Chang Chang)

審核日期

2007-7-11

推文