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題名 跳躍相關風險下狀態轉換模型之選擇權定價：股價指數選擇權實證分析
Option pricing of a stock index under regime switching model with dependent jump size risks: empirical analysis of the stock index option作者 林琮偉
Lin, Tsung Wei貢獻者 劉惠美<br>林士貴
Liu, Hui Mei<br>Lin, Shih Kuei
林琮偉
Lin, Tsung Wei關鍵詞 Esscher轉換
跳躍相關風險下狀態轉換模型
EM演算法
概似比檢定
敏感度分析
定價誤差
Esscher transformation
regime switching model with dependent jump model
EM algorithm
likelihood ratio test
sensitivity analysis
pricing error日期 2011 上傳時間 30-Oct-2012 14:36:13 (UTC+8) 摘要 本文使用Esscher轉換法推導狀態轉換模型、跳躍獨立風險下狀狀態轉換模型及跳躍相關風險下狀態轉換模型的選擇權定價公式。藉由1999年至2011年道瓊工業指數真實市場資料使用EM演算法估計模型參數並使用概似比檢定得到跳躍相關風險下狀態轉換模型最適合描述報酬率資料。接著進行敏感度分析得知，高波動狀態的機率、報酬率的整體波動度及跳躍頻率三者與買權呈現正相關。最後由市場驗證可知，跳躍相關風險下狀態轉換模型在價平及價外的定價誤差皆是最小，在價平的定價誤差則略高於跳躍獨立風險下狀態轉換模型。
In this paper, we derive regime switching model, regime switching model with independent jump and regime switching model with dependent jump by Esscher transformation. We use the data from 1999 to 2011 Dow-Jones industrial average index market price to estimate the parameter by EM algorithm. Then we use likelihood ratio test to obtain that regime switching model with dependent jump is the best model to depict return data. Moreover, we do sensitivity analysis and find the result that the probability of the higher volatility state , the overall volatility of rate of return , and the jump frequency are positively correlated with call option value. Finally, we enhance the empirical value of regime switching model with dependent jump by means of calculating the price error.參考文獻 中文文獻 [1] 汪昱頡，(2008)。跳躍風險下馬可夫轉換模型之實證分析，高雄大學統計研究所碩士論文。 [2] 徐于琇，(2008)。跳躍風險下狀態轉換模型下SEM演算法及Gibbs Sampling之參數變異數估計，高雄大學統計研究所碩士論文。 [3] 黃慈慧，(2011)。跳躍相關風險下狀態轉換模型之股價指數實證分析，國立政治大學統計學系碩士論文。 英文文獻 [4] Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). “Maximum likelihood from incomplete data via the EM algorithm,” Journal of the Royal Statistical Society, Vol. 39, 1-38. [5] Duan, J. C., Popova, I., and Ritchken, P. (2002). “Option pricing under regime switching,” Quantitative Finance, Vol. 2, 116-132. [6] Elliott, R. J., Chan, L., and Siu, T. K., (2005). “Option pricing and Esscher transform under regime switching,” Annals of Finance, Vol. 1, 423-432. [7] Elliott, R. J., and Siu, T. K., (2012). “Option pricing and filtering with hidden Markov-modulated pure-jump processes,” Applied Mathematical Finance, iFirst, 1-25. [8] Gerber, H., and Shiu, E., (1994). “Option pricing by Esscher transforms,” Transactions of the Society of Actuaries, Vol. 46, 140. [9] Hamilton, J. D., (1989). “A new approach to the economic analysis of nonstationary time series and the business cycle,” Econometrica, Vol. 57, 357-384. [10] Hardy, M. R., (2001). “A regime-switching model of long-term stock returns,” North American Actuarial Journal, Vol. 5, 41-53. [11] Lange, K. A, (1995). “Gradient algorithm locally equivalent to the EM algorithm,” Journal of the Royal Statistical Society, Vol. 57, 425-437. [12] Liao, S. L., Chang, C. K., Lin, S. K., 2008, "A recursive formula of a participating contract embedding a surrender option," Journal of Financial Studies, Vol. 16, 107-147. [13] Liew, C. C., and Siu, T. K., (2010). “A hidden Markov regime-switching model for option valuation,” Insurance: Mathematics and Economics, Vol. 47, 374–384. [14] Lin, S. K., Lin, C. S., and Chou, C. Y., (2010). “A recursive formula of a participating contract embedding a surrender option under regime-switching model with jump risks: evidence from stock indices.” working paper. [15] Schaller, H., and Norden, S. V., (1997). “Regime switching in stock market returns,” Applied Financial Economics Vol. 7, 177-191. [16] Schwert, G. W., (1989). “Business Cycles, Financial Crises, and Stock Volatility,” Carnegie Rochester Conference Series on Public Policy, Vol. 31, 83-126. [17] Turner, C. M., Startz, R., and Nelson, C. R. (1989). “A Markov model of heteroscedasticity, risk and learning in the stock market,” Journal of Financial Economics, Vol. 25, 3-22. 描述 碩士
國立政治大學
統計研究所
99354030
100資料來源 http://thesis.lib.nccu.edu.tw/record/#G0099354030 資料類型 thesis dc.contributor.advisor 劉惠美<br>林士貴 zh_TW dc.contributor.advisor Liu, Hui Mei<br>Lin, Shih Kuei en_US dc.contributor.author (Authors) 林琮偉 zh_TW dc.contributor.author (Authors) Lin, Tsung Wei en_US dc.creator (作者) 林琮偉 zh_TW dc.creator (作者) Lin, Tsung Wei en_US dc.date (日期) 2011 en_US dc.date.accessioned 30-Oct-2012 14:36:13 (UTC+8) - dc.date.available 30-Oct-2012 14:36:13 (UTC+8) - dc.date.issued (上傳時間) 30-Oct-2012 14:36:13 (UTC+8) - dc.identifier (Other Identifiers) G0099354030 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/55000 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計研究所 zh_TW dc.description (描述) 99354030 zh_TW dc.description (描述) 100 zh_TW dc.description.abstract (摘要) 本文使用Esscher轉換法推導狀態轉換模型、跳躍獨立風險下狀狀態轉換模型及跳躍相關風險下狀態轉換模型的選擇權定價公式。藉由1999年至2011年道瓊工業指數真實市場資料使用EM演算法估計模型參數並使用概似比檢定得到跳躍相關風險下狀態轉換模型最適合描述報酬率資料。接著進行敏感度分析得知，高波動狀態的機率、報酬率的整體波動度及跳躍頻率三者與買權呈現正相關。最後由市場驗證可知，跳躍相關風險下狀態轉換模型在價平及價外的定價誤差皆是最小，在價平的定價誤差則略高於跳躍獨立風險下狀態轉換模型。 zh_TW dc.description.abstract (摘要) In this paper, we derive regime switching model, regime switching model with independent jump and regime switching model with dependent jump by Esscher transformation. We use the data from 1999 to 2011 Dow-Jones industrial average index market price to estimate the parameter by EM algorithm. Then we use likelihood ratio test to obtain that regime switching model with dependent jump is the best model to depict return data. Moreover, we do sensitivity analysis and find the result that the probability of the higher volatility state , the overall volatility of rate of return , and the jump frequency are positively correlated with call option value. Finally, we enhance the empirical value of regime switching model with dependent jump by means of calculating the price error. en_US dc.description.tableofcontents 第一章 前言 1 第二章 文獻回顧 3 2.1 股價指數報酬率模型 3 2.2 Esscher測度轉換 5 第三章 股價指數報酬率模型 7 3.1 狀態轉換模型 7 3.2 跳躍獨立風險下狀態轉換模型 7 3.3 跳躍相關風險下狀態轉換模型 8 3.4 模型參數估計與檢定 9 第四章 股價指數選擇權定價 11 4.1 Esscher測度轉換 11 4.1.1. 狀態轉換模型之Esscher測度轉換 11 4.1.2. 跳躍獨立風險下狀態轉換模型之Esscher測度轉換 12 4.1.3. 跳躍相關風險下狀態轉換模型之Esscher測度轉換 13 4.2. 股價指數選擇權定價 16 4.2.1. 狀態轉換模型之股價指數選擇權定價 16 4.2.2. 跳躍獨立風險下狀態轉換模型之股價指數選擇權定價 17 4.2.3. 跳躍相關風險下狀態轉換模型之股價指數選擇權定價 18 第五章 實證分析 20 5.1. 模型參數估計 20 5.2. 敏感度分析 22 5.3. 市場驗證 24 第六章 結論 25 中文文獻 26 附錄A：狀態轉換模型之歐式買權定價公式 28 附錄B：跳躍獨立風險下狀態轉換模型之歐式買權定價公式 34 附錄C：跳躍相關風險下狀態轉換模型之歐式買權定價公式 41 zh_TW dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0099354030 en_US dc.subject (關鍵詞) Esscher轉換 zh_TW dc.subject (關鍵詞) 跳躍相關風險下狀態轉換模型 zh_TW dc.subject (關鍵詞) EM演算法 zh_TW dc.subject (關鍵詞) 概似比檢定 zh_TW dc.subject (關鍵詞) 敏感度分析 zh_TW dc.subject (關鍵詞) 定價誤差 zh_TW dc.subject (關鍵詞) Esscher transformation en_US dc.subject (關鍵詞) regime switching model with dependent jump model en_US dc.subject (關鍵詞) EM algorithm en_US dc.subject (關鍵詞) likelihood ratio test en_US dc.subject (關鍵詞) sensitivity analysis en_US dc.subject (關鍵詞) pricing error en_US dc.title (題名) 跳躍相關風險下狀態轉換模型之選擇權定價：股價指數選擇權實證分析 zh_TW dc.title (題名) Option pricing of a stock index under regime switching model with dependent jump size risks: empirical analysis of the stock index option en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) 中文文獻 [1] 汪昱頡，(2008)。跳躍風險下馬可夫轉換模型之實證分析，高雄大學統計研究所碩士論文。 [2] 徐于琇，(2008)。跳躍風險下狀態轉換模型下SEM演算法及Gibbs Sampling之參數變異數估計，高雄大學統計研究所碩士論文。 [3] 黃慈慧，(2011)。跳躍相關風險下狀態轉換模型之股價指數實證分析，國立政治大學統計學系碩士論文。 英文文獻 [4] Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). “Maximum likelihood from incomplete data via the EM algorithm,” Journal of the Royal Statistical Society, Vol. 39, 1-38. [5] Duan, J. C., Popova, I., and Ritchken, P. (2002). “Option pricing under regime switching,” Quantitative Finance, Vol. 2, 116-132. [6] Elliott, R. J., Chan, L., and Siu, T. K., (2005). “Option pricing and Esscher transform under regime switching,” Annals of Finance, Vol. 1, 423-432. [7] Elliott, R. J., and Siu, T. K., (2012). “Option pricing and filtering with hidden Markov-modulated pure-jump processes,” Applied Mathematical Finance, iFirst, 1-25. [8] Gerber, H., and Shiu, E., (1994). “Option pricing by Esscher transforms,” Transactions of the Society of Actuaries, Vol. 46, 140. [9] Hamilton, J. D., (1989). “A new approach to the economic analysis of nonstationary time series and the business cycle,” Econometrica, Vol. 57, 357-384. [10] Hardy, M. R., (2001). “A regime-switching model of long-term stock returns,” North American Actuarial Journal, Vol. 5, 41-53. [11] Lange, K. A, (1995). “Gradient algorithm locally equivalent to the EM algorithm,” Journal of the Royal Statistical Society, Vol. 57, 425-437. [12] Liao, S. L., Chang, C. K., Lin, S. K., 2008, "A recursive formula of a participating contract embedding a surrender option," Journal of Financial Studies, Vol. 16, 107-147. [13] Liew, C. C., and Siu, T. K., (2010). “A hidden Markov regime-switching model for option valuation,” Insurance: Mathematics and Economics, Vol. 47, 374–384. [14] Lin, S. K., Lin, C. S., and Chou, C. Y., (2010). “A recursive formula of a participating contract embedding a surrender option under regime-switching model with jump risks: evidence from stock indices.” working paper. [15] Schaller, H., and Norden, S. V., (1997). “Regime switching in stock market returns,” Applied Financial Economics Vol. 7, 177-191. [16] Schwert, G. W., (1989). “Business Cycles, Financial Crises, and Stock Volatility,” Carnegie Rochester Conference Series on Public Policy, Vol. 31, 83-126. [17] Turner, C. M., Startz, R., and Nelson, C. R. (1989). “A Markov model of heteroscedasticity, risk and learning in the stock market,” Journal of Financial Economics, Vol. 25, 3-22. zh_TW
