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研究生:林慧芳
研究生(外文):Hwei-Fang Lin
論文名稱:結構性改變下Black-Scholes與Hull-White評價模型之應用–以台灣股價選擇權為例
論文名稱(外文):Evaluate Black-Scholes and Hull-White assess models on TAIEX option with structure changes
指導教授:陳文典陳文典引用關係
指導教授(外文):Wen-Den Chen
學位類別:碩士
校院名稱:東海大學
系所名稱:經濟系
學門:社會及行為科學學門
學類:經濟學類
論文種類:學術論文
論文出版年:2006
畢業學年度:94
語文別:中文
論文頁數:41
中文關鍵詞:台指選擇權結構性改變Black-Scholes模型Hull-White模型GARCH模型
外文關鍵詞:TAIEX optionsstructure changeBlack-Scholes modelHull-White modelGARCH model
相關次數:
  • 被引用被引用:9
  • 點閱點閱:819
  • 評分評分:
  • 下載下載:122
  • 收藏至我的研究室書目清單書目收藏:2
多數實證研究所使用的波動估計模型,皆隱含假設在樣本觀察期間內,波動(或波動的參數)為固定不變,此隱含假設了市場結構是沒有發生改變,也就是波動路徑的形式是一致的,本研究認為此隱含假設其實並不盡合理。因此,本文將傳統計量方法中,對於結構性改變之檢定運用至此情況,以檢測樣本期間內是否存在著結構性改變。若確實存有結構性改變,則找出結構性改變之時間點,據此將研究期間加以分割,求得並非永遠是固定不變之待估參數,進而求出更適合模型的波動,以增加模型的績效。
本研究以Black-Scholes與Hul-White兩評價模型分別搭配歷史波動與GARCH模型,對台灣股價指數選擇權進行實證研究,所得之實證結果如下:
(1) 在樣本期間內,對歷史波動模型,本文找出了3個結構性改變時間點,運用在Black-Scholes模型下,發現除了遠月賣權之少數情形外(例如深價內與價內),平均而言,“考慮結構性改變後”之訂價誤差明顯小於“不考慮結構性改變”。
(2) 對GARCH模型,則找出了1個結構性改變點將全樣本區分為2個區段,運用至Hull-White評價模型下,也有同樣之結論,即“考慮結構性改變”能明顯改善模型的績效,並降低訂價誤差。。
自從Black, F., and M. Scholes,在1973年發表了著名的B-S模型後,後續許多學者為了減少訂價誤差、改善模型,無不費盡心思;但在繁複的數學代價下,所獲得的可能只是誤差的些微改善。在此本文提供了另一種思維來增進績效,我們不改變先天模型的設定,而是從後天實務操作上著手做修改。
In traditional approaches the parameters of volatility model are usually assumed to be constant during the empirical study period, which implies that market structure has not been changed over the time. In practice, we can see the structure change easily happen in financial (options) market. This phenomena intrigue our interesting. In conventional approaches we usually remedy the models to improve the performances, therefore, there are many complexity models has been developed. But in practice their improvements are often restricted.
This article focuses on the structure change point and provides an alternative thinking to enhance the performance. From the empirical study, we can see even the simple Black-Scholes model we can improve its performance radically.
This research applies Black-Scholes and Hull-White models on TAIEX Options. In which the historical volatility model and GARCH model are used for estimation. In Black-Scholes model (applied with historical volatility), we find three structure change points during 1 July 2004 to 31 July 2005. The performance of the model is significantly better than the model that has not been considered with structure change, especially for the deep-out-the-money pricing of the call options. The reason could be that the buyers are more sensibility than the others. In the GARCH model we find one change point, similar to the historical volatility model, these models has been considered with structure change are significantly better than the others.
第一章 研究動機、目的與本文架構 1
第一節 研究動機與目的 1
第二節 本文架構 1
第二章 文獻回顧 3
第三章 研究方法 4
第一節 選擇權評價模型 4
第二節 波動估計模型 10
第三節 定價模型績效評估之方法 11
第四節 波動結構性改變之檢定方法 11
第四章 實證研究 13
第一節 資料來源與處理 13
第二節 GARCH(p ,q)的認定及估計GARCH參數 14
第三節 不考慮結構性改變下之訂價誤差 14
第四節 Structure Change 16
第五節 考慮結構性改變後之訂價誤差 17
第五章 結論與建議 19
第一節 研究結論 19
第二節 對後續研究之建議 20
參考文獻 21
附錄一 23
附錄二 27
附錄三 29
附圖 30
1.石村貞夫、石村園子 (2004),細說Black-Scholes微分方程式,鼎茂圖書,李詩政、吳文峰 譯。
2.黃昭元(2003),台灣、美國、日本、香港、中國大陸股價報酬與波動性外溢效果之研究-多變量BEKK-GARCH模型之應用,東海大學經濟學系研究所碩士論文。
3.黃健喬(2004),選擇權定價與行為分析之探討-Black and Schoels模型、隨機波動模型之應用,東海大學經濟學系研究所碩士論文。
4.陳浚宏(2003),B-S模式與隨機波動性定價模式之比較-台灣股價指數選擇權之實證,成功大學企業管理研究所碩士論文。
5.陳昶均(2004),不同波動性估計模型下台指選擇權評價績效之比較,東吳大學商學院企業管理學系碩士班碩士論文。
6.關旭東(2004),隨機波動度下選擇權評價之實證-以台灣股價指數選擇權為例,輔仁大學金融學系研究所碩士論文。
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10.Black, F. and Scholes, M. (1973), “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, Vol. 81, pp. 637-659.
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13.Garman, M. B. “A General Theory of Asset Valuation under Diffusion State Processes.” Working Paper No. 50, University of California, Berkeley, 1976.
14.Greene, W. H. (2003), Econometric Analysis, 5th ed., N. J.: Prentice-Hall.
15.Heston, S. L. (1993), “A Closed-Form Solution for Options with Stochastic Volatility with Application to Bond and currency Options,” Review of Financial Studies, Vol.6, pp.327-343.
16.Hull, J. (2003), Options, Futures, and Other Derivatives, 5th ed., N. J.: Prentice-Hall.
17.Hull, J. and White, A. (1987), “The pricing of Options on Assets with Stochastic Volatilities,” Journal of Finance, Vol. 42, pp.281-300.
18.Merton, R. C. (1973), “Theory of Rational Option Pricing,” Bell Journal of Economics and Management Science, vol. 4, No. 1, pp.141-183.
19.Scott, L. O. (1987), “Option Pricing when the Variance Changes randomly: Theory, Estimation and Testing,” Journal of Financial and Quantitative Analysis, Vol. 22, pp.419-438.
20.Scott, L. O. (1997), “Pricing Stock Options in a Jump-diffusion Model with Stochastic Volatility and Interest Rates: Applications of Fourier Inversion Methods,” Mathematical Finance, Vol. 7, pp.345-358.
21.Wiggins, J. B. (1987), “Option Values under Stochastic Volatility: Theory and Empirical Evidence,” Journal of Financial Economics, Vol. 19, pp.351-372.
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