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博碩士論文 etd-0717110-064416 詳細資訊
Title page for etd-0717110-064416
論文名稱
Title
隨機波動之Levy過程下選擇權評價之研究-以台灣加權股價指數選擇權為例
Option Pricing under Stochastic Volatility for Levy Processes: An Empirical Analysis of TAIEX Index Options
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
52
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2010-06-16
繳交日期
Date of Submission
2010-07-17
關鍵字
Keywords
傅立葉轉換、Levy過程、隨機波動度
Levy Processes, Fourier Transform, Stochastic Volatility
統計
Statistics
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中文摘要
許多文獻實證指出,實際股價報酬呈現厚尾、高峰之分配,且具有微笑波動度與波動叢聚的情形,而模型中同時包含隨機波動與跳躍的捕捉能有較優的評價績效,故本文採用Carr, Geman, Madan, Yor(2001)所提出結合CIR之隨機波動度與單純跳躍Levy過程之隨機波動Levy模型,以台灣加權股價指數選擇權為實證對象,欲探討此種複雜的模型是否能夠有較精確的評價,並與一般常見之選擇權評價模型做比較。
本文所採用之模型總共分為三大類,一為一般的對照比較模型(B-S模型與Merton跳躍擴散模型);二為單純跳躍之Levy模型(NIG、VG、CGMY),最後則為隨機波動之Levy模型,其中隨機波動之Levy模型又因股價過程之設定不同分為一般指數股價過程與隨機指數股價過程,以上股價模型皆可利用快速傅立葉轉換而得到選擇權價格。本文實證結果顯示,無論樣本內與樣本外,考慮了隨機波動之Levy模型皆有較小之訂價誤差,其中又以隨機波動之CGMY過程之訂價誤差為最小;就誤差結構而言,價性程度與距到期日皆為顯著影響誤差之因素。
Abstract
none
目次 Table of Contents
第一章 緒論 1
第一節 研究背景與動機 1
第二節 研究目的 3
第三節 研究架構 4
第二章 文獻探討 6
第一節 股價隨機過程之文獻探討 6
第二節 波動率模型之相關文獻探討 8
第三章 研究方法 10
第一節 選擇權評價方法 10
第二節 股價隨機過程 12
第三節 參數估計方法 23
第四節 訂價模型績效衡量與誤差分析 25
第四章 實證結果與分析 26
第一節 資料來源與描述 26
第二節 各模型之參數估計結果 30
第三節 各模型之樣本內與樣本外誤差分析 31
第四節 訂價誤差之結構分析 37
第五章 結論與建議 41
第一節 研究結論 41
第二節 後續研究之建議 42
參考文獻 44
參考文獻 References
一、 英文文獻
1. Akigiray, V. and Booth G., ( 1998) “Mixed Diffusion-Jump Process Modeling of Exchange Rate Movements,” The Review of Economics and Statistics, Vol. 70, No. 4, pp. 631-637.
2. Amin, Kaushik and Robert Jarrow. (1992) “Pricing Options on Risky Assets in a Stochastic Interest Rate Economy,” Mathematical Finance Vol. 2, pp. 217-237.
3. Barndoff-Nielsen, O. E., (1995) “Normal Inverse Gaussian Distributions and the Modeling of Stock Returns,” Research Report No. 300, Department of Theoretical Statistics, Aarhus University,
4. Bakshi, G, Cao, C. and Chen, Z. ( 1997)“ Empirical Performance of Alternative Option Pricing Models,” The Journal of Finance ,vol. 52, pp.2003-2049
5. Ball, C. A., and Roma, A., (1994) ” Stochastic Volatility Option Pricing,” Journal of Financial and Quantitative Analysis ,vol. 29, pp. 589-607.
6. Bates, D. (1996) “Jump and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options,” Review of Financial Studies, Vol. 9, pp. 69-107.
7. Britten-Jones, M., & Neuberger, A. (1999) “Option Prices, Implied Price Processes, Stochastic Volatility,” Journal of Finance, Vol. 55, No. 2, pp.839-866.
8. Carr, P. and Madan, D., (1999) “Option Valuation Using the Fast Fourier Transform,” Journal of Computational Finance, Vol. 2, No. 4, pp. 61-73.
9. Carr, P., Geman, H., Madan, D. B., and Yor, M., (2002) “The Fine Structure of Asset Returns: An Empirical Investigation,” Journal of Business, Vol. 75, No. 2, pp. 305-332.
10. Carr, P., Geman, H., Madan, D. B., and Yor, M. (2003) “Stochastic Volatility for Lévy Processes,” Mathematical Finance, Vol. 13, No. 3, pp. 345-382.
11. Cont, R. and Tankov, P. (2003) “Financial Modeling with Jump Processes,” CHAPMAN&HALL/CRC Financial Mathematics Series, pp. 117.
12. Cox, J. C. and S. A. Ross (1976) “A Valuation of Options for Alternative Stochastic Processes,” Journal of Financial Economics, Vol.3, pp. 145-166.
13. Derman, E. I. Kani, & Zou, J. (1996) “The local volatility surface: Unlocking the information in index option prices,” Financial Analysts Journal, pp.25-36.
14. Helyette Geman. (2002) “Pure jump Levy processes for asset price modeling,” Journal of banking & finance, vol.26, pp.1297-1316
15. Heston, S. (1993), “A closed-form solution for options with stochastic volatility with applications to bond and currency options,” Review of Financial Studies, Vol. 6, pp. 327-343.
16. Huang, J. Z. and L. Wu (2004), “Specification Analysis of Option Pricing Models Based on Time-Changed Levy Processes,” Journal of Finance, Vol. 59,pp.1405-1439.
17. Hull, J., White, A. (1987) “The pricing of options on assets with stochastic volatilities,” Journal of Finance, Vol. 42, pp.281-300.
18. Kazuhisa Matsuda(2004) “Introduction to Pricing with Fourier Transform: Option Pricing with Exponential Levy Moel,” The City University of New York.
19. Kim, I. J., and Kim, S., (2003) “ Empirical comparison of alternative stochastic volatility option pricing models: Evidence from Korean KOSPI 200 index options market,” Pacific-Basin Finance Journal Vol. 12, pp. 117-142.
20. Lam, K., E. Chang and M. C. Lee (2001), “An Empirical Test of the Variance Gamma Option Pricing Model,” Pacific-Basin Finance Conference, Seoul, Korea.
21. Lin, Y. N., S, N., and Xu, X., (2001)” Pricing FTSE 100 Index Options Under
Stochastic Volatility,” The Journal of Futures Markets, vol. 21,pp.197-211.
22. Madan, D. B., Carr, P., and Chang, E. C., (1998) “The Variance Gamma Process and Option Pricing,” European Finance Review, Vol. 2, No. 1, pp. 79-105
23. Madan, D. B. and Seneta, E., (1990 )“The VG Model for Share Market Returns,” Journal of Business, Vol.63, pp. 511-524
24. Merton, R. C. (1973) “Theory of Rational Option Pricing,” Bell Journal of Economics and Management Science, Vol. 4, No. 1, pp.141-183.
25. Merton, R.(1976) ” Option pricing when underlying stock return are discontinuous,” Journal of Financial Economics, vol. 11, pp. 474-491.
26. Nandi, Saikat (1996) “Pricing and Hedging Index Options under Stochastic Volatility: An Empirical Examination,” Working Paper, 96-9, Federal Reserve Bank of Atlanta.
27. Scott, L. O. (1987). ” Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application,” Journal of Financial and Quantitative Analysis vol. 22, pp. 419-437.
28. 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. 413-424.
29. Stein, E. M., and Stein, J. C. (1991)” Stock Price Distribution with Stochastic Volatility: An Analytic Approach,” The Review of Financial Studies ,vol. 4,pp. 727-752.


二、 中文文獻

1. 吳仰哲(2009),「Lévy 與GARCH-Lévy 過程之選擇權評價與實證分析:台灣加權股價指數選擇權為例」,管理與系統,第十七卷,49-74頁
2. 王麗妙 (1999),「以跳躍-擴散模型評價單一型認購權證之實證研究」,碩士論文,高雄第一科技大學金融營運研究所。
3. 徐有順 (2000),「The Effect of Skewness and Kurtosis Adjustment for Alternative Option Pricing Models」,碩士論文,中正大學財務金融研究所。
4. 陳能靜(2003),「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」碩士論文,輔仁大學金融研究所。
5. 簡同威(2008),「運用快速傅立葉轉換於具有特徵函數之選擇權評價模型-台指選擇權之實證」,碩士論文,淡江大學金融研究所。
6. 黃昱仁(2008), 「快速傅立葉轉換下的選擇權訂價模型-以台指選擇權為例」,碩士論文,淡江大學金融研究所。
7. 陳姵樺(2007),「利用快速傅立葉轉換進行跳躍發散與隨機波動模型之選擇權評價應用—以台指選擇權為例」,碩士論文,銘傳大學財務金融研究所。
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