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研究生:謝志正
研究生(外文):Chih-Cheng Hsieh
論文名稱:指數選擇權隱含波動率與股價指數報酬率之關連
論文名稱(外文):The Relationship between the Implied Volatility of Index Option and the Return of Stock Index
指導教授:王元章王元章引用關係王毓敏王毓敏引用關係
指導教授(外文):Yung-Jang WangYu-Min Wang
學位類別:碩士
校院名稱:國立嘉義大學
系所名稱:管理研究所
學門:商業及管理學門
學類:企業管理學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:94
中文關鍵詞:履約價隱含波動率變化股價指數報酬率因果關係
外文關鍵詞:exercise priceimplied volatility changereturn of stock indexcause-effect relation
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本研究以台指選擇權進行實證分析,所探討的議題及結論分為以下三部分:
首先,隱含波動率與履約價間關係的檢測上,台指買權在5分、30分、整體日資料及存續期間小於91天之日資料中,台指賣權在30分、整體日資料及存續期間小於31天之及日資料中,二者間皆呈正相關。此結果與Dennis and Mayhew(2002)、Bakshi, Madan, and Kapadia(2003)、Bollen and Whaley(2004)之研究結論並不一致,本研究認為:此一現象應是市場中投機需求較避險需求為強烈所造成。
其次,同時期的隱含波動率變化與股價指數報酬率間關係之檢測,台指買權在5分、30分及每日等資料頻率中,二者間皆呈現反向及不對稱關係,顯現先前文獻中(Fleming, Ostdiek, and Whaley,1995;Simon,1997;Davidson et al.,2001;盧佳鈺,2003)以日資料為主之證實結果,亦適用於高頻資料中。而此一關係主要是由距到期日31至90天之價外買權所引起(其估計係數最為顯著),顯示「槓桿效應理論」較「與時俱變的風險溢酬理論」適合解釋上述關係。換言之,在因果關係上,股價變化是「因」,隱含波動率變化是「果」。
然而,台指賣權在5分及30分等兩種資料頻率中,隱含波動率變化與股價指數報酬率間皆呈正相關,此實證結果與Chan, Cheng, and Lung(2003)所得之結論並不一致,本研究認為此一現象應是由於台指賣權之避險需求通常較高所引起。此外,在日資料部分,當距到期日大於或等於91天時,價內及價平賣權皆符合反向及不對稱關係,且價內賣權的反向關係最為顯著,此一結果亦支持「槓桿效應理論」的成立。值得注意的是,買權及賣權在同時期關係上的實證結果不盡相同,顯現先前以買權為主的實證研究(Fleming, Ostdiek, and Whaley,1995;Simon,1997;Davidson et al.,2001)之推論,並不適用於台指選擇權市場中,而此一結論亦與Chan, Cheng, and Lung(2003)的實證結果相異。
最後,在強健性檢定中,同時期關係的實證結果與上述結論相似。而把樣本期間分為前後兩期進行比較時,發現選擇權交易量的巨幅變化,會使台指買權之同時期關係較為顯著;而對台指賣權則無一致性的影響。此外,股票交易量對於同時期關係之影響並非相當顯著,而隱含波動率變化的落後效果則有顯著的影響,此二項結果與Chan, Cheng, and Lung(2003)所得到的結論一致。另一方面,就整體而言,選擇權交易量的干擾效果較股票交易量的干擾效果顯著。

This study takes the Taiwan Index Option (TXO) to an empirical analysis. The topics we explore and their conclusions can be devided into the following three parts.
First, we discuess the relationship between the implied volatility and the exercise prices. For the call options of every 5 minutes, every 30 minutes, daily, and and daily data of with maturity less than 91 days, and the put options of every 30 minutes, daily, and and daily data with maturity less than 31 days, implied volatilities are positivly related to exercise prices. This result is not consistent with the conclusions of Dennis and Mayhew (2002), Bakshi, Madan, and Kapadia (2003), and Bollen and Whaley (2004). We think this is because speculative demands are stronger than hedging demands in this market.
Second, we discuess the contemporary relation of implied volatility changes and the return of stock index. The emprical evidence of call options indicates that volatility changes are inversely related to equity price changes, and the asymmetric responses of volatility changes to equity price changes do exist for every 5 minutes, every 30 minutes, and daily data. This finding suggests that the results from prior research (i.e., Fleming, Ostdiek, and Whaley, 1995; Simon, 1997; Davidson et al., 2001; Chia-Yu Lu, 2003) on daily data can be generalized to high frequency data. Besides, this relation is driven by out-of-the-money call options with maturity between 31 to 90 days, which indicates that the “leverage-effect theory” can provide better explaination for the relationship between implied volatility changes and equity price changes than the “time-varying risk premium theory” can. In other words, it implies a cause-effect relation from equity price changes to volatility changes.
However, the emprical evidence of put options indicates that volatility changes are positively related to equity price changes for every 5 minutes, and every 30 minutes data. This result is not consistent with the conclusions of Chan, Cheng, and Lung (2003), and we think it is owing to higher hedging demand of put options. Besides, for daily data of in-the-money and at-the money put options with maturity over 91 days, we can find both inverse and asymmetric relation from them and the most significant inverse relation for in-the-money put options. This result also supports the “leverage-effect theory”. It worth notice that the empirical evidences of contemporary relation for call options and put options are not similar, which suggests that inferences of previous studies (i.e., Fleming, Ostdiek, and Whaley, 1995; Simon, 1997; Davidson et al., 2001) based on call options are not applicable to Taiwan Index Option market. Otherwise, this conclusion is different from the empirical evidences of Chan, Cheng,
and Lung (2003) either.
At last, the empirical results of contemporary relation are similar to previous conclusions in the robust tests. When deviding the sample periods into two parts, we find the huge change of option trading volumes will make the contemporary relation of call options more significant, but it will not have a consistent influence on put option. Besides, equity trading volumes do not have a significant effect on contemporary relation, but the legged implied volatility changes do. These results are consistent with the conclusions of Chan, Cheng, and Lung (2003). On the other hand, the confounding effect of option trading volumes is more siginficant than that of equity trading volumes.

目錄
壹、前言
一、研究背景………………………………………………………………1
二、研究動機………………………………………………………………2
三、研究目的………………………………………………………………4
四、研究架構………………………………………………………………8
貳、文獻探討
一、選擇權之基礎理論……………………………………………………10
二、波動率的分類與計算…………………………………………………15
三、波動率變化與股票報酬率間關係……………………………………19
四、槓桿效應理論 vs. 與時俱變的風險溢酬理論………………………20
五、ADF單根檢定與一般動差法……………………………………………25
參、研究方法
一、檢測波動率與履約價間之關係………………………………………28
二、同時期的隱含波動率變化與股價指數報酬率間之關連……………29
三、市場微結構的探討……………………………………………………33
四、市場中資訊流動的方向………………………………………………35
五、強健性檢定……………………………………………………………36
六、小結……………………………………………………………………38
肆、實證分析
一、樣本選取與資料來源…………………………………………………40
二、資料處理與實證流程…………………………………………………41
三、敘述性統計與單根檢定………………………………………………43
四、同時期的隱含波動率變化與股價指數報酬率間關係檢測…………52
五、強健性檢定……………………………………………………………62
伍、結論
一、研究結論………………………………………………………………83
二、研究建議………………………………………………………………86
參考文獻
一、中文部分………………………………………………………………88
二、英文部分………………………………………………………………88
附錄
附錄一:臺指選擇權契約規格重點說明…………………………………93

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