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題名 偏斜常態分配的隨機誤差與隱藏馬可夫鏈建構選擇權定價模型——以標準普爾500指數為例
Option Pricing Model with Skew Normal Random Error and Hidden Markov Chain: Evidence from the S&P500作者 王楷文
Wang, Kai-Wen貢獻者 劉惠美
王楷文
Wang, Kai-Wen關鍵詞 選擇權評價
偏斜常態分配
隱藏馬可夫模型
Option Pricing
Skew Normal Distribution
Hidden Markov Model日期 2020 上傳時間 1-Apr-2021 11:21:17 (UTC+8) 摘要 本文根據以往研究經驗及觀察標準普爾 500 指數 (S&P500) 價格的變動趨勢，發現大部分選擇權的標的商品的價格並非總是很好地符合常態分配，並且常常具有偏斜及高峰、厚尾的特性，故本研究旨在放寬 B-S 模型背後的嚴謹假設，考慮服從偏斜常態分配的隨機誤差建構一個全新的選擇權評價模型，本研究將其稱為 Skew Normal 模型。並且選擇權的標的商品價格的波動率也並非始終為一個常數，因此又根據隱藏馬克夫模型推導出了另一個全新的選擇權評價模型，本研究將其稱為 Skew-Odmm 模型。並且以 2018 至 2019 年 S&P500 的價格走勢為實證對象，驗證了相較於傳統的 B-S 模型，兩個新模型都會因為負偏度適當低估選擇權的權利金。且考慮了波動率的兩種狀態的 Skew-Odmm 模型相較於Skew Normal 模型獲得結果也有所差異。
According to the previous research experience and the price trend of the S&P 500 index, we find that the price of most target product of the options are not always well-aligned with the normal distribution, and often have the characteristics such as skew, peak and thick tail, so this study aims to relax the rigorous assumptions behind the B-S model and consider the random errors subject to skew normal distribution to construct a new option pricing model. This study calls it the Skew Normal model. And the volatility of the target product price of the options is not always a constant, so another new option pricing model is derived based on the hidden markov model, which is called Skew-Odmm model in this study. And with the price trend of S&P500 from 2018 to 2019 as an empirical object, it is verified that compared with the traditional B-S model, the two new models will appropriately underestimate the premium of the option due to negative skewness. And the Skew-Odmm model, which takes into account the two states of volatility, has different results compared with the Skew Normal model.參考文獻 陳松男， (2002) 。金融工程學：金融商品創新選擇權理論。出版地：華泰文化。黃怡佳 (2006) ，選擇權評價模型之實證分析——以台指選擇權及 S&P500 選擇權為例，國立高雄應用科技大學陳峙儒 (2004) S&P500 股價指數期貨與現貨間價格預測效果的探討 ---根據時間序列與人工智慧模型，國立成功大學馬毓駿 (1999) ，馬克夫轉換模型在投資策略上的應用，國立政治大學Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian journal of statistics, 2, 171-178.Andersen, T. G., & Bollerslev, T. (1998). Answering the skeptics: Yes, standard volatility models do provide accurate forecasts. Internationaleconomic review, 885-905.Harvey, C. R., & Whaley, R. E. (1991). S&P 100 index option volatility. The Journal of Finance, 46(4), 1551-1561.Chan, K., Chan, K. C., & Karolyi, G. A. (1991). Intraday volatility in the stock index and stock index futures markets. The Review of Financial Studies, 4(4), 657-684.Chiras, D. P., & Manaster, S. (1978). The information content of option prices and a test of market efficiency. Journal of Financial Economics, 6(2-3), 213-234.Lee, J. H., & Linn, S. C. (1994). College of Business Administration University of Oklahoma. The Review of Futures Markets, 13, 1.Owen, D. B. (1956). Tables for computing bivariate normal probabilities. The Annals of Mathematical Statistics, 27(4), 1075-1090.Goodwin, T. H. (1993). Business-cycle analysis with a Markov-switching model. Journal of Business & Economic Statistics, 11(3), 331-339.Chen, S. N., Hsu, P. P., & Liang, K. Y. (2019). Option pricing and hedging in different cyclical structures: a two dimensional Markov-modulated model. The European Journal of Finance, 25(8), 762-779.Neely, C., Weller, P., & Dittmar, R. (1997). Is technical analysis in the foreign exchange market profitable? A genetic programming approach. Journal of financial and Quantitative Analysis, 405-426.Bakshi, G., Cao, C., & Chen, Z. (1997). Empirical performance of alternative option pricing models. The Journal of finance, 52(5), 2003-2049.Corrado, C., & Su, T. (1998). An empirical test of the Hull‐White option pricing model. Journal of Futures Markets: Futures, Options, and Other Derivative Products, 18(4), 363-378. 描述 碩士
國立政治大學
統計學系
107354030資料來源 http://thesis.lib.nccu.edu.tw/record/#G0107354030 資料類型 thesis dc.contributor.advisor 劉惠美 zh_TW dc.contributor.author (Authors) 王楷文 zh_TW dc.contributor.author (Authors) Wang, Kai-Wen en_US dc.creator (作者) 王楷文 zh_TW dc.creator (作者) Wang, Kai-Wen en_US dc.date (日期) 2020 en_US dc.date.accessioned 1-Apr-2021 11:21:17 (UTC+8) - dc.date.available 1-Apr-2021 11:21:17 (UTC+8) - dc.date.issued (上傳時間) 1-Apr-2021 11:21:17 (UTC+8) - dc.identifier (Other Identifiers) G0107354030 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/134432 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計學系 zh_TW dc.description (描述) 107354030 zh_TW dc.description.abstract (摘要) 本文根據以往研究經驗及觀察標準普爾 500 指數 (S&P500) 價格的變動趨勢，發現大部分選擇權的標的商品的價格並非總是很好地符合常態分配，並且常常具有偏斜及高峰、厚尾的特性，故本研究旨在放寬 B-S 模型背後的嚴謹假設，考慮服從偏斜常態分配的隨機誤差建構一個全新的選擇權評價模型，本研究將其稱為 Skew Normal 模型。並且選擇權的標的商品價格的波動率也並非始終為一個常數，因此又根據隱藏馬克夫模型推導出了另一個全新的選擇權評價模型，本研究將其稱為 Skew-Odmm 模型。並且以 2018 至 2019 年 S&P500 的價格走勢為實證對象，驗證了相較於傳統的 B-S 模型，兩個新模型都會因為負偏度適當低估選擇權的權利金。且考慮了波動率的兩種狀態的 Skew-Odmm 模型相較於Skew Normal 模型獲得結果也有所差異。 zh_TW dc.description.abstract (摘要) According to the previous research experience and the price trend of the S&P 500 index, we find that the price of most target product of the options are not always well-aligned with the normal distribution, and often have the characteristics such as skew, peak and thick tail, so this study aims to relax the rigorous assumptions behind the B-S model and consider the random errors subject to skew normal distribution to construct a new option pricing model. This study calls it the Skew Normal model. And the volatility of the target product price of the options is not always a constant, so another new option pricing model is derived based on the hidden markov model, which is called Skew-Odmm model in this study. And with the price trend of S&P500 from 2018 to 2019 as an empirical object, it is verified that compared with the traditional B-S model, the two new models will appropriately underestimate the premium of the option due to negative skewness. And the Skew-Odmm model, which takes into account the two states of volatility, has different results compared with the Skew Normal model. en_US dc.description.tableofcontents 第一章 绪論 1第一節 研究動機 1第二節 研究目的 2第三節 研究架構 3第二章 文獻回顧 5第一節 衍生性金融商品發展過程 5第二節 Black- Scholes 模型 7第三節 Skew Normal 函數介紹 9第四節 隱馬克夫定價模型 21第三章 研究方法 23第一節 Skew Normal 模型推導 23第二節 模型參數的估計 29第三節 Skew-Odmm 模型的推導 31第四章 實證分析 34第一節 資料來源與說明 34第二節 不考慮兩種狀態的偏斜常態分配參數的估計 34第三節 卡房適合度檢定 37第四節 模型定價 40第五節 考慮兩種狀態的偏斜常態分配參數的估計 41第五章 結論與建議 43第一節 結論 43第二節 建議 43參考文獻 45附錄 47 zh_TW dc.format.extent 3195434 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0107354030 en_US dc.subject (關鍵詞) 選擇權評價 zh_TW dc.subject (關鍵詞) 偏斜常態分配 zh_TW dc.subject (關鍵詞) 隱藏馬可夫模型 zh_TW dc.subject (關鍵詞) Option Pricing en_US dc.subject (關鍵詞) Skew Normal Distribution en_US dc.subject (關鍵詞) Hidden Markov Model en_US dc.title (題名) 偏斜常態分配的隨機誤差與隱藏馬可夫鏈建構選擇權定價模型——以標準普爾500指數為例 zh_TW dc.title (題名) Option Pricing Model with Skew Normal Random Error and Hidden Markov Chain: Evidence from the S&P500 en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 陳松男， (2002) 。金融工程學：金融商品創新選擇權理論。出版地：華泰文化。黃怡佳 (2006) ，選擇權評價模型之實證分析——以台指選擇權及 S&P500 選擇權為例，國立高雄應用科技大學陳峙儒 (2004) S&P500 股價指數期貨與現貨間價格預測效果的探討 ---根據時間序列與人工智慧模型，國立成功大學馬毓駿 (1999) ，馬克夫轉換模型在投資策略上的應用，國立政治大學Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian journal of statistics, 2, 171-178.Andersen, T. G., & Bollerslev, T. (1998). Answering the skeptics: Yes, standard volatility models do provide accurate forecasts. Internationaleconomic review, 885-905.Harvey, C. R., & Whaley, R. E. (1991). S&P 100 index option volatility. The Journal of Finance, 46(4), 1551-1561.Chan, K., Chan, K. C., & Karolyi, G. A. (1991). Intraday volatility in the stock index and stock index futures markets. The Review of Financial Studies, 4(4), 657-684.Chiras, D. P., & Manaster, S. (1978). The information content of option prices and a test of market efficiency. Journal of Financial Economics, 6(2-3), 213-234.Lee, J. H., & Linn, S. C. (1994). College of Business Administration University of Oklahoma. The Review of Futures Markets, 13, 1.Owen, D. B. (1956). Tables for computing bivariate normal probabilities. The Annals of Mathematical Statistics, 27(4), 1075-1090.Goodwin, T. H. (1993). Business-cycle analysis with a Markov-switching model. Journal of Business & Economic Statistics, 11(3), 331-339.Chen, S. N., Hsu, P. P., & Liang, K. Y. (2019). Option pricing and hedging in different cyclical structures: a two dimensional Markov-modulated model. The European Journal of Finance, 25(8), 762-779.Neely, C., Weller, P., & Dittmar, R. (1997). Is technical analysis in the foreign exchange market profitable? A genetic programming approach. Journal of financial and Quantitative Analysis, 405-426.Bakshi, G., Cao, C., & Chen, Z. (1997). Empirical performance of alternative option pricing models. The Journal of finance, 52(5), 2003-2049.Corrado, C., & Su, T. (1998). An empirical test of the Hull‐White option pricing model. Journal of Futures Markets: Futures, Options, and Other Derivative Products, 18(4), 363-378. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU202100390 en_US
