臺灣博碩士論文加值系統

台指選擇權已成為避險者、投資客最熱門的金融商品，而最常使用的模型即是Black & Scholes (1973)評價模型，利用B-S模型與選擇權市價可反推隱含波動率，隱含波動率有一特殊現象，即隨價內外程度不同而改變，出現兩邊高中間低的微笑現象(Smile effect)。
Bollen & Whaley (2004)提出利用delta取代傳統價性(K/S)來區分選擇權價內外程度，因delta考慮標的資產的波動率(σ)和到期期間(T)；因此本文用delta對台指選擇權作價內外程度分組，統計每組買賣權交易量之比例，選取交易量較大區間(價內至深價外)研究；依不同到期期間分類，利用傳統價性與delta分別詮釋微笑現象，研究微笑程度在不同到期期間的變化。
實證結果如下：
1.傳統價性詮釋微笑現象優於delta。
2.去除極端值前之微笑程度並不隨到期期間減少而增加。
3.在去除極端值後，買權微笑程度隨到期期間減少而增加，但賣權並無此現象。
4.觀察不同到期期間每日微笑程度四分位數，可知賣權微笑程度高於買權，買賣權微笑程度不具一致性。

Taiwan stock index option has already become the most popular financial derivative for hedgers and investors. The most well-known method for the price options is the Black & Scholes model (1973). One can use the Black & Scholes formula to deduce the implied volatility of the underlying asset. The implied volatility has a special characteristic; that is the Smile Effect, resulting from the changes of the different option prices. Bollen & Whaley (2004) proposed a method of using the delta instead of the traditional moneyness to categorize the option data because the delta considers the volatility of the underlying asset and the maturity time. This research uses delta to divide the Index option data into several groups, computes the proportions of each volume for the call and put options, and chooses the groups which have larger volume amount as our target samples of this study. Moreover we use the maturity time as the criterion to sort the selected samples. This study attempts to explain the smile phenomenon according to different maturity time.

The empirical results are shown as follows:

1. The ability of the traditional moneyness to explain the smile phenomenon is better than delta.

2. The smile degree before deleting the outliers does not increase as the expiration period decreases.

3. After omitting the outlier, the smile degree of the call option increases when the maturity period is decreasing. However, it does not happen to put option.

4. Observing the quartiles of the smile degree during different maturity time, this study found that the smile degree of the put option is greater than the call option, and the smile degrees of put options and call options are not consistent.

中文摘要……………………………………………………………Ⅰ
英文摘要……………………………………………………………Ⅱ
誌謝…………………………………………………………………Ⅲ
目錄…………………………………………………………………Ⅳ
表目錄………………………………………………………………Ⅴ
圖目錄………………………………………………………………Ⅵ
第一章 緒論…………………………………………………………1
第一節 研究背景……………………………………………………1
第二節 研究動機與目的……………………………………………5
第三節 研究架構……………………………………………………6
第四節 研究架構……………………………………………………7
第二章 文獻回顧……………………………………………………8
第一節 重述Black-Scholes評價模型……………………………… 8
第二節 賣權-買權恆等式的回顧…………………………………10
第三節 隱含波動度微笑現象 (Smile effect)………………………12
第三章 研究方法………………………………………………… 17
第一節 資料來源與選取………………………………………… 17
第二節 隱含波動率……………………………………………… 19
第三節 選擇權的價性 (Moneyness)……………………………… 20
第四節 模型設計………………………………………………… 21
第四章 實證結果與分析………………………………………… 23
第一節 交易量分布……………………………………………… 23
第二節 微笑程度 (Agree of smile)……………………………… 25
第三節 去除極端值之微笑程度………………………………… 32
第四節 每日微笑程度分析……………………………………… 39
第五章 結論與建議……………………………………………… 44
第一節 結論……………………………………………………… 44
第二節 後續研究建議…………………………………………… 45
參考文獻……………………………………………………………46

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