臺灣博碩士論文加值系統

本文透過S&P500、NASDAQ、DJIA股價指數探討實現變幅、隱含波動性對於實現變異之關係，發現實現變幅與隱含波動性對於實現變異具有良好的解釋能力，因此代表實現變幅與隱含波動性亦可當做波動性的代理變數。在GARCH模型與CARR模型之比較方面，在樣本內預測方面，可以發現CARR模型之結果優於GARCH模型，代表變幅對於表現波動性的行程確實優於報酬率，在考慮槓桿效果與隱含波動性後，確實可以提高波動性模型得配適能力。最後，在樣本外預測方面，可以發現CARR模型在樣本外的預測能力是比GARCH模型來得好，考慮槓桿效果與隱含波動性後，短期而言確實可以提高模型在樣本外的預測能力；但長期來說卻未必可以提高模型在樣本外的預測能力，不過就資產評價與風險管理而言，波動性短期預測所提供的資訊已經足夠。

By using S&P 500, NASDAQ and DJIA stock index, in this paper we examine the relationships among realized return, realized range and implied volatility, finding that the realized range and implied volatility are possessed of excellent explanation power toward the realized return, and thereby can be presented as proxy variables for volatilities. On the other hand, in comparison with the empirical performance on the CARR model and GARCH model. Whatever in-of-sample or out-of-sample volatility forecast, we found that the result from CARR model is better than from GARCH model, which means that range has a better ability than return to present the descriptions of volatilities. Finally, we find that leverage effect and implied volatility can actually increase the explanation power of volatility in short time.

中文摘要 i
英文摘要 ii
致 謝 iii
目 錄 iv
表目錄 v
圖目錄 vi
符號說明 vii
壹、緒論 1
貳、文獻回顧 2
一、變幅資料估計波動性之探討 2
二、隱含波動性之探討 4
參、研究方法 5
一、波動性的衡量方法 5
二、實現變異、實現變幅與隱含波動性關係之探討 7
三、以報酬為基礎之擴增型GARCH模型 8
四、以變幅為基礎之擴增型CARR模型 10
肆、實證分析 11
一、敘述統計分析 11
二、實現變異、實現變幅與隱含波動性關係之實證分析 15
三、擴增型GARCH模型之實證探討 18
四、擴增型CARR模型之實證探討 21
五、樣本內預測之探討 26
六、樣本外預測之探討 33
七、變幅資料與隱含波動性在石油市場之應用 41
伍、結論 44
參考文獻 46

1. 周雨田、巫春洲和劉炳麟，2004。「動態波動模型預測能力之比較與實證」，財務金融學刊。12卷，1期，1-25。
2. Agnolucci, P., 2009. Volatility in crude oil futures: A comparison of the predictive ability of GARCH and implied volatility models, Energy Economics 31, 316-321.
3. Alizadeh, S., M. W. Brandt and F. X. Diebold, 2002. Range-based estimation of stochastic volatility models, Journal of Finance 57, 1047-1091.
4. Beckers, S., 1983. Variances of security price returns based on high, low, and closing prices, Journal of Business 56, 97-112.
5. Bollerslev, T., 1986. Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics 31, 307-327.
6. Brandt, M. W. and C. S. Jones, 2006. Volatility forecasting with range-based EGARCH models, Journal of Business & Economic Statistics 24, 470-486.
7. Chou, R. Y., 2005. Forecasting financial volatilities with extreme values: The conditional autoregressive range (CARR) model, Journal of Money, Credit and Banking 37, 561-682.
8. Christensen, B. J. and N. R. Prabhala, 1998. The relation between implied and realized volatility, Journal of Financial Economics 50, 125-150.
9. Christensen, B. J. and C. S. Hansen, 2002. New evidence on the implied-realized volatility relation, The European Journal of Finance 8, 187-205.
10. Corrado, C. and C. Truong, 2007. Forecasting stock index volatility: Comparing implied volatility and the intraday high-low price range, Journal of Financial Research 30, 201-215.
11. Engle, R.F., 1982. Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation, Econometrica 50, 987-1008.
12. Engle, R.F., 2002. New frontiers for ARCH models, Journal of Applied econometrics 17, 425-446.
13. Engle, R.F. and G.M. Gallo, 2006. A multiple indicators model for volatility using intra-day data, Journal of Econometrics 131, 3-27.
14. Lam, K.P. and H. S. Ng, 2009. Intra-daily information of range-based volatility for MEM-GARCH, Mathematics and Computers in Simulation 79, 2625-2632
15. Li, S. and Q. Yang, 2009. The relationship between implied and realized volatility: evidence from the Australian stock index option market, Review of Quantitative Finance and Accounting 32, 405-419
16. Martens, M. and D. van Dijk, 2007. Measuring volatility with the realized range, Journal of Econometrics 138, 181-207.
17. Parkinson, M., 1980. The extreme value method for estimating the variance of the rate of return, Journal of Business 53, 61-66.
18. Regnier, Eva., 2007. Oil and energy price volatility, Energy Economics 29, 405-427.
19. Rogers, L. C. G. and S. E. Satchell, 1991, Estimating variance from high, low, and closing prices, The Annals of Applied probability 1, 504–512.
20. Tu, T. T., C. C. Wu and N. Liu, 2009, Latent information VIX for dynamic volatility structure, Working paper, Department of Finance, Ming Chuan University.
21. Yang, D. and Q. Zang, 2000. Drift-independent volatility estimation based on high, low, open, and close prices, Journal of Business 73, 477-491.