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研究生:郭姿儀
研究生(外文):Tzu-YiKuo
論文名稱:探討Black-Scholes模型中的Delta是否隱含S&P500指數之預測訊息?
論文名稱(外文):Does Delta in Black-Scholes model contain predictive information for S&P 500 index?
指導教授:王澤世王澤世引用關係
指導教授(外文):Tse-Shih Wang
學位類別:碩士
校院名稱:國立成功大學
系所名稱:財務金融研究所
學門:商業及管理學門
學類:財務金融學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:英文
論文頁數:80
中文關鍵詞:隱含波動率選擇權Delta領先落後關係
外文關鍵詞:Implied volatilityOptionDeltaLead-lag relationship
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本研究探討選擇權市場對於股票市場的價格變動是否擁有預測能力,我們利用delta法來檢驗股票市場與選擇權市場彼此所隱含的資訊是否有所異同,就本文的假說而言,選擇權若擁有較大的delta值,則對於預期的股票價格易於變動,也就是說具有較大delta值的選擇權其隱含波動率之預測能力相對於較小delta值的選擇權為佳。再者我們根據「淨賣壓」理論(Bollen and Whaley,2004)來解釋本文觀點,選擇權的供給曲線並不是水平,因此選擇權的價格會偏離從模型計算出的價值。本文利用Corrado and Miller 模型計算選擇權之隱含波動率,此模型可廣泛適用於不同內含價值的選擇權,同時避免Black-Scholes模型設定上之偏誤。其實證雖然無強烈地顯著證據證明選擇權之隱含波動率具有對股票報酬的預測能力,但仍顯示出一些趨勢符合假說的現象。
除此之外,本研究亦探討S&P 500 指數選擇權與其現貨之間是否存在領先落後關係,其實證結果顯示現貨市場相較於選擇權市場存在一些優勢的領先資訊,這似乎呼應著無強烈顯著的證據顯示選擇權之隱含波動率對股票報酬具有預測能力。

In this study we analyze option market whether have the predictive ability for stock market. By using delta method we examine the stock market and the option market whether contain differential information. For the proposition of this study, implied volatilities of options with larger absolute delta are more sensitive to change in expected price of underlying asset and thus contain more information. That is to say the options have better predictive ability. In addition our argument can be explained by the “net buying pressure” [Bollen and Whaley, 2004] in which the supply curve of options is not horizontal, and thus the option price will deviate from the model value. In this study the implied volatility of option is calculated from Corrado and Miller model. It not only extends the range of accuracy to a wide band of option moneyness but also avoids the misspecification of Black-Scholes model. Using S&P 500 index options, we still can find some evidences that in-the-money call and put options with larger absolute delta tend to have more predictive power for index return although the partial results are not very significant. Finally we examine the lead-lag relationship between the S&P500 index option market and the stock market. The results show that the stock market does contain relevant information and leads the option market. It seems to respond the partial results that the predictive ability of implied volatility for the index returns are not very significant.
Chapter 1 Introduction 1
Chapter 2 Delta method 13
2.1 Proposition 14
2.2 Corollary 16
2.2.1 Corollary 1 16
2.2.2 Corollary 2 17
Chapter 3 Methodology 18
3.1 The calculation method of implied volatility 18
3.2 Regression model 19
3.3 Vector autoregressive model 21
3.4 Granger Causality 22
Chapter 4 Data and empirical results 26
4.1 Data 26
4.2 Empirical results 28
Chapter 5 Conclusion 37
References 39

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