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研究生： 蔡瓊梅
Tsai, Chiung-Mei
論文名稱： 利用隱含波動率價差來探討S&P500指數選擇權與其現貨之間的價格領先落後關係
指導教授： 王澤世
Wang, Alan T.
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： 2005
畢業學年度： 93
語文別： 中文
論文頁數： 51
中文關鍵詞： 隱含波動率價差 、指數選擇權 、領先落後關係
外文關鍵詞： Index option, Volatility spreads, Lead-lag relations
相關次數： 點閱：201  下載：7 
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    • 　　本研究為探討 S&P 500指數選擇權與其現貨之間的價格是否存在領先或落後的關係。本文利用隱含波動率價差（即買權的隱含波動率減去賣權的隱含波動率）來衡量此一領先和落後關係。我們預測若選擇權投資人預期現貨市場未來價格走勢上漲時，會買進買權，使得買權的隱含波動率上升，即相對於賣權的隱含波動率為高;而若選擇權投資人預期現貨市場未來價格走勢下跌時，會買進賣權，使得賣權的隱含波動率上升，即相對於買權的隱含波動率為高。因此，我們是以隱含波動率價差來代表選擇權交易者對於現貨市場未來價格走勢的看法。實證發現S&P 500指數選擇權市場和其股票市場為一個回饋系統，也就是兩市場互為領先和落後關係。另外，我們也有考慮非同步收盤時間的影響，結果發現指數選擇權收盤價的確存在一些優勢的領先資訊；我們發現選擇權收盤價裡所蘊含的資訊，並不會百分之百完全地在隔天股票市場開盤時立即反應出來，而是有一部分資訊是在隔天股票市場開盤後和收盤前才反應。這意謂著選擇權市場的確包含了並非純粹是因為非同步交易資料效果的優勢資訊。

    　In this study we investigate the lead-lag relations between the S&P 500 index option market and the stock market at the aggregate level. We apply volatility spreads, the difference between the implied volatilities of calls and puts, to represent the option market's view for future stock market movements and explore their relations. The results show that the causality between the implied volatility differences and stock index returns is bi-directional on a daily basis. In particular, the implied volatility difference does contain relevant information which is not reflected in the open price of the stock index immediately on the next day. As a result, the finding that options lead stocks is not purely due to the nonsynchroneity.

    第一章 緒論………………………………………………………………1 1.1 研究背景……………………………………………………………..1 1.2 研究動機和目的……………………………………………………..2 1.3 章節架構……………………………………………………………..3 第二章 文獻回顧…………………………………………………………4 2.1 效率市場與價格發現………………………………………………7 2.2 指數選擇權和現貨之間的關聯性…………………………………8 2.3 隱含波動率……………………………………………………….11 第三章 研究方法…………………………………………………………13 3.1 樣本資料說明…………………………………………………….13 3.2 時間序列穩定性檢定…………………………………………….14 3.3 簡單線性迴歸模型……………………………………………….16 3.4 向量自我迴歸模型（VAR）………………………………………17 3.5 Probit model 和 Logit model…………………………………19 第四章 實證結果與分析…………………………………………………22 4.1 基本敘述統計…………………………………………………….23 4.2 現貨報酬率與隱含波動率價差的相關係數…………………….27 4.3 自我相關函數檢定……………………………………………….28 4.4 單根檢定………………………………………………………….29 4.5 檢驗現貨市場指數報酬率與隱含波動價差之間的因果關係….30 4.6 二元向量自我迴歸模型（VAR 模型）………………………….32 4.7 區分非同步交易的資訊效果…….………………………………34 4.8 Probit 和 Logit 模型…………………………………….....37 4.9 現貨指數報酬率與買權和賣權隱含波動率的關係…………….38 4.10 現貨市場交易量的變化和選擇權市場交易量的變化的關係..40 第五章 結論與後續研究建議……………………………………………46 5.1 結論……………………………………………………………….46 5.2 後續研究建議…………………………………………………….47 參考文獻………………………………………………………………….48 表 4-1 基本敘述統計量…………………………………………………23 表 4-2 現貨報酬率與隱含波動價差之相關係數矩陣表……..………27 表 4-3 現貨市場報酬率與隱含波動價差之單根檢定結果……..……30 表 4-4 選擇權市場和股票市場間的領先落後關係………………..…31 表 4-5 各落後期數之AIC 值…………………………………………..32 表 4-6 VAR 模型檢定結果……………………………………………..33 表 4-7 利用隱含波動率價差來預測現貨指數報酬率（CTO & OTC）.35 表 4-8 在當CTO也是解釋變數時候，利用隱含波動率價差來預測現貨 指數報酬OTC………………………………………………………......36 表 4-9 利用隱含波動率價差來預測現貨指數報酬率（Probit model）37 表 4-10 利用隱含波動率價差來預測現貨指數報酬率（Logit model）38 表 4-11 檢驗指數報酬率是否能預測買權和賣權的隱含波動率…….39 表 4-12 以買權交易量變化來預測現貨市場交易量變化…………….40 表 4-13 以賣權交易量變化來預測現貨市場交易量變化…………….41 表 4-14 以前一期現貨市場交易量變化來預測買權和賣權市場交易量 變化…………………………………………………………….........42 表 4-15 實證結果綜合整理…………………………………………….44 圖 4-1 現貨市場報酬率的分配圖……………………………………24 圖 4-2 買權隱含波動率的分配圖……………………………………24 圖 4-3 賣權隱含波動率的分配圖……………………………………25 圖 4-4 買權和賣權隱含波動率價差的分配圖………………………25 圖 4-5 現貨市場報酬率的趨勢圖……………………………………26 圖 4-6 買權和賣權的隱含波動率和其波動率價差的趨勢圖………26 圖 4-7 現貨市場指數報酬率的ACF圖……………………………….28 圖 4-8 隱含波動率價差的ACF圖…………………………………….29

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