本研究嘗試探討股價指數期貨選擇權的資訊內涵，並與股價指數選擇權及歷史波動度的資訊內涵加以比較。我們的研究標的為2000年2月至2003年3月的S&P 500指數、指數選擇權及指數期貨選擇權，首先說明三個資料序列的敘述統計量，並使用單根檢定以確定資料序列為定態，符合迴歸分析的假設，再來探討原始隱含波動度的資訊內涵，然後嘗試以門檻自我迴歸模型修正隱含波動度，但檢定發現隱含波動度門檻效果並不存在，接下來以Christensen and Prabhala (1998)提出的工具變數修正隱含波動度，並探討修正後隱含波動度的資訊內涵，最後使用包含迴歸模型比較指數選擇權及指數期貨選擇權對指數的資訊內涵。得出結論如下： 1.指數選擇權與指數期貨選擇權隱含波動度均具有指數已實現波動度充分資訊，指數選擇權的資訊內涵較指數期貨選擇權為高。指數選擇權與指數期貨選擇權隱含波動度均無法作為已實現波動度的不偏估計量。歷史波動度沒有隱含波動度未包含的資訊。隱含波動度的衡量誤差並不存在。 2.指數選擇權與指數期貨選擇權隱含波動度門檻效果均不存在。前一期隱含波動度與當期隱含波動度並不顯著相關，歷史波動度與當期隱含波動度相關性較高，但使用上述兩種工具變數修正隱含波動度並不能增加對已實現波動度的解釋能力。 3.指數選擇權對指數的資訊較指數期貨選擇權為多，但指數選擇權與指數期貨選擇權隱含波動度均含有對方所缺乏的解釋能力，沒有一個隱含波動度完全包含另外一個隱含波動度的資訊。

Black and Scholes (1973)對於報酬率提出以B-S模型配適，但B-S模型無法有效解釋報酬率不對稱高狹峰、波動度微笑、波動度叢聚、長記憶性的性質。Merton (1976)認為不尋常的訊息來臨會影響股價不連續跳躍，因此發展B-S模型加入不連續跳躍風險項的跳躍擴散模型，該模型可同時描述報酬率不對稱高狹峰和波動度微笑兩性質。Charles, Fuh and Lin (2011)加以考慮市場狀態提出狀態轉換跳躍模型，除了保留跳躍擴散模型可描述報酬率不對稱高狹峰和波動度微笑，更可以敘述報酬率的波動度叢聚和長記憶性。本文進一步拓展狀態轉換跳躍模型，考慮不連續跳躍風險項的帄均數與市場狀態相關，提出狀態轉換跳躍相關模型。並以道瓊工業指數與S&P 500指數1999年至2010年股價指數資料，採用EM和SEM分別估計參數與估計參數共變異數矩陣。使用概似比檢定結果顯示狀態轉換跳躍相關模型比狀態轉換跳躍獨立模型更適合描述股價指數報酬率。並驗證狀態轉換跳躍相關模型也可同時描述報酬率不對稱高狹峰、波動度微笑、波動度叢聚、長記憶性。最後利用Esscher轉換法計算股價指數選擇權定價公式，以敏感度分析模型參數對於定價結果的影響，並且市場驗證顯示狀態轉換跳躍相關模型會有最小的定價誤差。 / Black and Scholes (1973) proposed B-S model to fit asset return, but B-S model can’t effectively explain some asset return properties, such as leptokurtic, volatility smile, volatility clustering and long memory. Merton (1976) develop jump diffusion model (JDM) that consider abnormal information of market will affect the stock price, and this model can explain leptokurtic and volatility smile of asset return at the same time. Charles, Fuh and Lin (2011) extended the JDM and proposed regime-switching jump independent model (RSJIM) that consider jump rate is related to market states. RSJIM not only retains JDM properties but describes volatility clustering and long memory. In this paper, we extend RSJIM to regime-switching jump dependent model (RSJDM) which consider jump size and jump rate are both related to market states. We use EM and SEM algorithm to estimate parameters and covariance matrix, and use LR test to compare RSJIM and RSJDM. By using 1999 to 2010 Dow-Jones industrial average index and S&P 500 index as empirical evidence, RSJDM can explain index return properties said before. Finally, we calculate index option price formulation by Esscher transformation and do sensitivity analysis and market validation which give the smallest error of option prices by RSJDM.

台灣特殊的兩黨對立政治環境及幾乎每年都會有的固定選舉，使得政治的不確定性深深的影響著國內的投資環境及投資人心態。本研究便是要探討，2002/1/1~2006/1/16 研究期間台灣的投資人在選舉前後的投資行為，是否真如大家所預期的，會受到台灣選舉事件的影響。 本研究首先利用適當的機率密度函數模型及選擇權市場資訊來導出隱含的風險中立密度值。再利用這些風險中立密度值，求出各個選舉事件相對應的機率分配圖形，並透過其機率分配圖形及波動率指數等統計值於投票日前後的變化來觀察某一選舉事件前後投資者的反應。 研究結果發現：1. 選舉事件的發生確實會影響投資者的心理，且投資者會透過選擇權市場有效率的反應預期的未來股價指數分佈情況。2. 越大型、越具爭議且全國性的選舉結果，其選舉期間機率分配圖形及波動率指數具有較高的波動性。3. 一般而言，選舉過後市場不確定因素降低，將使投資者對於股市的預期較為一致和樂觀。而若這個選舉結果使投資者感到意外，因而增加了市場的不確定性，則選後機率分配圖形及波動率指數的改變反而會更為明顯。4. 在此研究下對數常態混合法比傳統的 Black-Scholes 方法產生較低的誤差值，因此就實證的分析上能提供更好的配適。 / This research examines the behavior of investors during election periods from January 1st 2002 to January 6th 2006 in Taiwan. The research includes a few steps. First, we adopted a proper probability density function composed of stock index options data to construct the implied distribution. Then, when changing the whole shape of the risk-neutral implied distribution, the volatility indexes, and the statistics of the implied distribution, we observed investors' response around a specific election event. According to the empirical results, we found that: 1. An election event would influence investors’ behavior, and investors tend to reflect their expectation of future stock index in the option market in an efficient way. 2. The result of a large-scale and more disputed nationwide election will cause a higher fluctuation in both the implied distribution and the volatility index. 3. In general, the factor resulting from investors’ uncertainty of the market is likely to reduce after the election, which makes investors’ relatively unanimous and optimistic expectation of the stock market. However, if this election result surprises investors, their uncertainty of the market will increase, and thus the changes of the implied distribution and the volatility index become quite obvious. 4. The in-sample performance of the lognormal mixtures method employed in the research is considerably better than that of the traditional Black-Scholes model by having a lower root mean squared error.