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研究生：	邱馨儀 Chiu, Hsin-i
論文名稱：	由隱含波動率曲面預測未來實際波動率 Local Volatility Forecasts from Implied Volatility Surfaces
指導教授：	王澤世 Wang, Tse-shih
學位類別：	碩士 Master
系所名稱：	管理學院 - 財務金融研究所 Graduate Institute of Finance
論文出版年：	2007
畢業學年度：	95
語文別：	英文
論文頁數：	61
外文關鍵詞：	Forecasting, Implied volatility, Deterministic volatility models
相關次數：	點閱：78 下載：2
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The major objective of this paper is to investigate the predictive ability of the one-factor stochastic volatility model by extracting helpful information from the implied volatility surface. This model is compared to the GARCH (1, 1) model with respect to forecasting future realized volatility of the underlying asset. We construct the one-factor stochastic volatility model consistent with the theory of implied tree models, which are suggested by Rubinstein (1994), Dupire (1994) and Derman and Kani (1994), and apply the transformation by Kreisler (1998), in which the implied volatility function is included.
We analyze the Dow Jones Industrial Average (DJIA) index options and find that the implied volatility surfaces may really exist through estimation process. In predicting the future realized volatility of the underlying asset, the evidence shows that the GARCH (1, 1) model performs better than the one-factor stochastic volatility model and the ad hoc model. Nevertheless, for a 1-week forecast horizon, the one-factor stochastic volatility model’s correlation coefficient between the realized and the forecasted volatility is much more significant than the GARCH (1, 1) model and the ad hoc model, indicating that the one-factor stochastic volatility model subsumes additional information that others do not take into account.

Chapter 1 Introduction .......................................................................................................1
1.1 Research Background ..................................................................................................1
1.2 Objectives and Major Findings ...................................................................................1
1.3 Research Framework ...................................................................................................2
Chapter 2 Literature Review ..............................................................................................4
2.1 Can Implied Volatilities Predict Future Volatilities? .................................................. 4
2.2 Why is the deterministic volatility model? ..................................................................7
2.3 What is the Contribution of Our Study? ....................................................................11
Chapter 3 Methodology ....................................................................................................12
3.1 Implied Volatility and the One-Factor Stochastic Volatility Model ..........................12
3.2 Implied Volatility Surface and the Ad Hoc Approach ...............................................16
3.3 The GARCH (1, 1) Model .........................................................................................17
3.4 Datasets .....................................................................................................................18
Chapter 4 Empirical Results ........................................................................................... 20
4.1 Estimations for the Implied Volatility Surfaces .........................................................20
4.2 Local Volatility Forecasts and the GARCH (1, 1) .....................................................21
4.3 Comparisons ..............................................................................................................22
Chapter 5 Conclusions and Suggestions ..........................................................................26
References ..........................................................................................................................28
Appendix A .........................................................................................................................32
Appendix B .........................................................................................................................34

List of Tables 
Table 1  Implied Volatility Surface of DJIA Index Options .............................................37
Table 2  Ad Hoc Implied Volatility Surface of DJIA Index Options ................................43
Table 3  Volatility Forecasts from the Implied Volatility Surface ....................................49
Table 4  Volatility Forecasts from the Ad Hoc Implied Volatility Surface ......................51
Table 5  Volatility Forecasts from the GARCH (1, 1) Model ...........................................53
Table 6  Forecast Errors ....................................................................................................55
Table 7  The Correlation Matrix between the Forecasted and the Realized Volatilities ...56
















List of Figures
Figure 1  Implied Volatility Surface and Local Volatility Forecast
         Observation Date: 08/30/2006 ...........................................................................57
Figure 2  Implied Volatility Surface and Local Volatility Forecast
         Observation Date: 09/06/2006 ...........................................................................58
Figure 3  Implied Volatility Surface and Local Volatility Forecast
         Observation Date: 09/13/2006 ...........................................................................59
Figure 4  Implied Volatility Surface and Local Volatility Forecast
         Observation Date: 09/20/2006 ...........................................................................60
Figure 5  Implied Volatility Surface and Local Volatility Forecast
         Observation Date: 09/27/2006 ...........................................................................61
                                    

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校內：2012-06-27公開
校外：2017-06-27公開

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