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研究生:湯麒國
研究生(外文):Patrick Tan
論文名稱:認購權證評價-二因子模型之應用
論文名稱(外文):An Empirical Study for Bivariate Binomial Tree Pricing Models of Covered Warrant
指導教授:周麗娟周麗娟引用關係
指導教授(外文):Zhou Li Jan
學位類別:碩士
校院名稱:銘傳大學
系所名稱:金融研究所
學門:商業及管理學門
學類:財務金融學類
論文種類:學術論文
論文出版年:2000
畢業學年度:88
語文別:中文
論文頁數:77
中文關鍵詞:Black & Scholes模型二因子二元樹模型異質變異模型認購權證波動度
外文關鍵詞:Black & Scholes ModelBivariate Binomial Tree Option ModelHeteroscdeasticitywarrantvolatility
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中文摘要
本研究以歷史波動度代入B-S模型,以GARCH-family模型代入Boyle(1989)多期二因子二元樹評價模型,得到認購權證理論價格,再透過與實際市場價格的比較,期望能發現一個有效的股價波動估計方法及適用於台灣認購權證市場的評價模型。
1. 整體而言,在權證上市期間,券商發行以電子類股為標的權證中除大華01的國巨、日盛04與京華02的台積電與元大02的華碩外,其餘電子股的報酬率分配在95%信賴水準下皆接受報酬率為常態分配的假設;然而券商發行非電子股為標的權證中在95%信賴水準下皆拒絕非電子股的報酬率為常態分配的假設。
2. 在樣本期間中,整體而言利用GARCH-family模型估計標的股未來波動度以(1)非電子股的效果較佳(2) GARCH(1,1)、EGARCH(1,1)與GARCH-M(1,1)模型的GARCH效果皆顯著。(3)槓桿效果在EGARCH(1,1)模型中皆不顯著。(4)風險溢酬在GARCH-M(1,1)模型中皆不顯著。
3. Boyle模型在非電子股權證與電子股權證中不論在價外與價平時其訂價偏誤明顯小於B-S模型;B-S模型只有在價內的電子股權證中才具有較小的訂價偏誤。
4. 評估價外與價平選擇權時,B-S與Boyle(1988)模型的理論價格傾向低於市價;評估價內選擇權時B-S與Boyle(1988)模型的理論價格部分高於市價,部份低於市價。
5. GARCH(1,1)、EGARCH(1,1)與GARCH-M(l,l)三種異質變異性模型對未來波動的預測能力並無顯著的差異。
關鍵詞:Black & Scholes 模型、二因子二元樹模型、一般化自我迴
歸條件異質變異模型、認購權證、波動度
Abstract
This research acquires a warranty binominal theoretic pricing by taking historic volatility into B-S Model and taking GARACH-family Model into Boyle(1989) Bivariate Binominal Tree Pricing Model and through comparing with realistic market pricing for expecting to find out an effective evaluating formula of stock pricing fluctuation and a pricing model which is applicable to Taiwan warranty binominal market.
1. General speaking, during the period of the warranty binominal going on sale, among all Electronic underlying warranty binominals issued by stock brokers, the remunerative ratio distribution of electronic stocks being located at significant level of 95%, almost can accept and take remunerative ratio as hypothesis under normal distribution ,However while stock brokers issuing non-electronic stocks underlying warranty binominal all of them reject to take remunerative ratio as normal distribution hypothesis under 95% of significant level.
2. During sampling, considering of whole situation, to use GARCH-family model to evaluate the future volatility of underlying stocks:
(1) the effect of non-electronic stock is better
(2) the GARCH effect of GARCH(1,1), EGARCH(1,1), and GARCH-M (1,1) model is remarkable
(3) the leverage effect on EGARCH(1,1) model is not obviously
(4) the premium on GARCH-M(1,1) model is not obviously
3. Between non-electronic stock warranty binominal and electronic stock warranty binominal , the ordering price difference of Boyle model is obviously smaller than B-S model, no matter out of money or at money. Only the electronic stock warranty binominal is in the money, B-S model carries a smaller ordering price difference.
4. While evaluating the choosing right on out of money and at money, the theoretic pricing of B-S and Boyle(1988) Model incline under market pricing. But during studying in the money choosing right, some of theoretic pricing of B-S and Boyle(1988) models are higher than market pricing, but some are lower.
5. For 3 kinds of Heteroscdeasticity Models GARCH(1,1), EGARCH(1,1) and GARCH-M(1,1), they don''t make an obvious difference on future fluctuation predicated ability.
Keyword : Black & Scholes Model, Bivariate Binominal Tree
Option Model ,Warrant, Heteroscdeasticity, Volatility
目 錄
第一章 緒論.........................................1
第一節 研究背景與動機.................................1
第二節 研究目的.......................................2
第三節 研究範圍與限制.................................3
第四節 研究流程.......................................4
第二章 文獻回顧.......................................6
第一節 Black& Scholes選擇權評價模型...................6
第二節 固定彈性變異模型...............................12
第三節 隨機波動選擇權訂價模型.........................16
第四節 選擇權數值模擬文獻.............................17
第三章 研究方法.......................................26
第一節 波動度預測模式.................................26
第二節 選擇權評價模式之探討...........................31
第四章 實證結果.......................................37
第一節 資料描述與處理.................................37
第二節 進行步驟.......................................39
第三節 估計波動度.....................................40
第四節 訂價能力比較...................................56
第五章 結論與建議.....................................71
第一節 結論...........................................71
第二節 後續研究建議...................................72
參考文獻..............................................73
附 圖、附 表
圖1-1 研究流程圖…………………………………………………………………..5
表3-1 二因子二元樹跳躍型態表…………………………………………………34
圖3-1 二因子二元樹擴散過程圖…………………………………………………36
表4-1 權證基本資料表……………………………………………………………37
表4-2 認購權證上市期間標的股報酬率統計值…………………………………43
表4-3 認購權證歷史波動度統計表………………………………………………46
表4-4 GARCH(1,1)模型參數估計值……….……….………………….……….. 47
表4-5 EGARCH(1,1)模型參數估計值……………………………………………50
表4-6 GARCH-M(1,1)模型參數估計值…………………..………………………53
表4-7 權證訂價誤差表……………………………………………………………57
表4-8 非電子股權證訂價誤差……………………………………………………67
表4-9 電子股權證訂價誤差………………………………………………………67
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