臺灣博碩士論文加值系統

本研究旨在探討現貨市場與權證市場之互動是否產生權證定價之錯價效果，模型則修正Black-Scholes（1973）之股價變動方程式，分別建立價格效果與波動性效果模型，藉由數值分析模擬理論價格，探討互動效果是否降低系統性誤差。
經由本文研究發現，根據九支權證之分析效果與傳統Black-Scholes模型比較後發現，當權證市場與現貨市場存在互動效果時，現貨價格為價外與價平時溢價效果最大，但溢價效果隨著現貨價格價內程度加深，溢價效果隨之降低。另外，間斷複製所產生之誤差雖會影響上述推論，但權證市場與現貨市場存在互動效果所產生之溢價效果依然存在。
若就互動效果所形成不同錯價效果成因加以分析，均可解釋為何產生溢價現象。但發現上述效果均隨價內、價平與價外效果之不同而不同。其主因為透過不同之影響管道，所修正現貨波動幅度，會透過Gamma產生錯價效果。而Gamma值在價外至價平之間較大，故進而溢價效果也較顯著。

This research focus on the devalue facts of warrants, and try to explain that in a new prospects of interaction mechanism between warrant and stock markets. In order to describe such mechanism, we have modified the partial difference function of Black and Scholes (1973). Finite difference method was used to simulate the new models, and compare the difference with traditional model.
We found that the simulation results of nine samples from warrant market can support the prospects of interaction effects. New model can explain the pricing error facts. But it depend on stock price is in-the-money, at-the-money
or out-the-money. We found that stock price was out-the-money, or it changed to at-the-money, new model performed better that traditional model. But stock price changed to in-the-money, the performance is weaker. By the way, discrete replication problem was matter. But after excluding the discrete replication effects, interaction mechanism still can explain the facts.
If we discuss different interaction mechanism, such as price interaction mechanism and volatility interaction mechanism, we will have the same result. To explain that, all the interaction effects have modified volatility by the Gamma value. Gamma value is higher in at-the-money situation. That is why stock price is at-the-money, modified model can explain better than traditional model.

第一章 緒 論 1
第一節 研究背景與目的 1
第二節 論文架構與研究流程 3
第二章 文獻回顧 4
第一節 傳統選擇權評價模型及其修正 4
第二節 美式選擇權定價模型 7
第三節 數值分析法之介紹 9
第四節 實證文獻 14
第三章 研究方法 18
第一節 研究模型 18
第二節 數值分析方法 20
第三節 資料來源及參數估計 24
第四章 實證結果 29
第一節 參數分析 29
第二節 模型實證分析 35
第五章 結論與建議 39
第一節 結論 39
第二節 未來研究方向 40
參考文獻 41
附錄A：價格效果模型 44
附錄B：價格與波動性效果模型 47
附錄C：權證與現貨之因果檢定 50
附錄D：權證在不同模型下的價格差異值 51
附錄E：權證模擬結果 65

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