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題名 基於最小平方蒙地卡羅模擬法評價可轉債：以中國大陸市場為例
Evaluation of Convertible Bonds Based on the Least Square Monte Carlo Simulation: Take Mainland China Market as an Example作者 崔璨
Cui, Can貢獻者 林士貴<br>張興華
Lin, Shih-Kuei<br>Chang, Hsing-Hua
崔璨
Cui, Can關鍵詞 可轉債
蒙地卡羅模擬
二項樹模擬
Convertible Bond
Monte Carlo Simulation
Binomial Tree Simulation日期 2020 上傳時間 1-Dec-2020 14:58:32 (UTC+8) 摘要 可轉債是一種可以按照約定的價格轉換成股票的公司債券，融合了股票及債券特性，是中國資本市場的重要組成部分。目前，隨著越來越多的機構及個人投資者加入可轉債的市場，需要一個合理的評價模型，讓市場參與者可以有一個公允的參考價值。本文首先介紹了可轉債的定義，以及可轉債定價理論的研究現狀，然後圍繞可轉債定價存在的問題進行研究，主要內容包括分析影響可轉債的因素、各可轉債條款的影響。接著，介紹了BS 定價模型、二項樹模型（BT）以及最小平方蒙地卡羅模型（LSM）在評價可轉債時的理論及優缺點。本文選擇對仍上市流通、交易量較高、條款設置合理的39 只可轉債進行分析。選取了各可轉債在2019 年的12 個節點進行了模擬，比較2019 年的交易價格和模擬出的理論價格差異。通過實證分析，可以看出無論是單個時間節點，還是整體的誤差率，LSM 模型都比BT 模型更貼近可轉債的實際價格，但仍與實際價格有一些偏差，並且中國可轉債價值存在被市場低估的現象。
Convertible bond is a kind of corporate bond that can be converted into stock according to the agreed price. It integrates the characteristics of stock and bond, and is an important part of China`s capital market. At present, with more and more institutional and individual investors joining the convertible bond market, a reasonable evaluation model is needed so that market participants can have a fair reference value.This paper first introduces the definition of convertible bonds, and the research status of the pricing theory of convertible bonds, and then studies the problems existing in the pricing of convertible bonds. The main content includes the analysis of the factors affecting convertible bonds and the impact of the terms of convertible bonds. Then, it introduces the theory, advantages and disadvantages of BS pricing model, binomial tree model (BT) and least square Monte Carlo model (LSM) in evaluating convertible bonds.This paper chooses 39 convertible bonds in China which are still on the market, with high trading volume and reasonable terms. The paper selects 12 nodes of each convertible bond in 2019 to simulate, and compares the trading price in 2019 with the theoretical price. Through the empirical analysis, it can be seen that the LSM model is closer to the actual price of convertible bonds than the BT model, whether it is a single time node or the overall error rate, but there are still some deviations from the actual price, and the value of convertible bonds in China is underestimated by the market.參考文獻 Bhattacharya, M., & Zhu, Y. (1997). Valuation and analysis of convertible securities. The Handbook of Fixed Income Securities, 5, 791-817.Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 81(3), 637-654.Boyle, P. P. (1977). Options: A monte carlo approach. Journal of financial economics, 4(3), 323-338.Boyle, P. P. (1986). Option valuation using a tree-jump process. International Options Journal, 3, 7-12.Brennan, M. J., & Schwartz, E. S. (1980). Analyzing convertible bonds. Journal of Financial and Quantitative analysis, 907-929.Chan, A. W., & Chen, N. F. (2007). Convertible bond underpricing: Renegotiable covenants, seasoning, and convergence. Management Science, 53(11), 1793-1814.Cheung, W., and Nelken, I. (1994). Costing the converts. Risk, 7(7),47-49.Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of financial Economics, 7(3), 229-263.Ho, T. S., & Lee, S. B. (1986). Term structure movements and pricing interest rate contingent claims. the Journal of Finance, 41(5), 1011-1029.Ingersoll Jr, J. E. (1977). A contingent-claims valuation of convertible securities. Journal of Financial Economics, 4(3), 289-321.Longstaff, F. A., & Schwartz, E. S. (2001). Valuing American options by simulation: a simple least-squares approach. The review of financial studies, 14(1), 113-147.Lvov, D., Yigitbasioglu, A. B., & El Bachir, N. (2004, December). Pricing convertible bonds by simulation. In Second IASTED international conference (pp. 259-264).Moreno, M., & Navas, J. F. (2003). On the robustness of least-squares Monte Carlo (LSM) for pricing American derivatives. Review of Derivatives Research, 6(2), 107-128.Nyborg, K. G. (1996). The use and pricing of convertible bonds. Applied Mathematical Finance, 3(3), 167-190.Poensgen, O. H. (1965). The valuation of convertible bonds.Tsiveriotis, K., & Fernandes, C. (1998). Valuing convertible bonds with credit risk. The Journal of Fixed Income, 8(2), 95.莊新田, & 周玲春. (2006). 基於雙因素的可轉換債券定價模型. 東北大學學報 (自然科學版), 27(3), 320-323.袁新熠. (2008). 基於最小二乘蒙特卡洛方法對中國可轉債市場價格的偏差分析(Master`s thesis, 電子科技大學).唐文彬, & 張小勇. (2008). LSM 可轉債定價模型及其應用研究. 財經理論與實踐, 29(4), 50-53.陳盛業, & 王義克. (2007). 奇異期權與中國可轉債定價. 清華大學學報(自然科學版)(06), 127-130.張江紅, & 楊善朝. (2007). 可轉換債券定價的三叉樹方法. 太原師範學院學報: 自然科學版, 6(2), 8-11.張德華, & 陶融. (1999). 布萊克—斯科爾斯期權定價模型在可轉換債券定價中的應用. 財經理論與實踐, 20(6), 52-54.鄭振龍, & 林海. (2004). 中國可轉換債券定價研究(Doctoral dissertation).賴其男, 姚長輝, & 王志誠. (2005). 關於我國可轉換債券定價的實證研究. 金融研究, (9), 105-121. 描述 碩士
國立政治大學
金融學系
107352046資料來源 http://thesis.lib.nccu.edu.tw/record/#G0107352046 資料類型 thesis dc.contributor.advisor 林士貴<br>張興華 zh_TW dc.contributor.advisor Lin, Shih-Kuei<br>Chang, Hsing-Hua en_US dc.contributor.author (Authors) 崔璨 zh_TW dc.contributor.author (Authors) Cui, Can en_US dc.creator (作者) 崔璨 zh_TW dc.creator (作者) Cui, Can en_US dc.date (日期) 2020 en_US dc.date.accessioned 1-Dec-2020 14:58:32 (UTC+8) - dc.date.available 1-Dec-2020 14:58:32 (UTC+8) - dc.date.issued (上傳時間) 1-Dec-2020 14:58:32 (UTC+8) - dc.identifier (Other Identifiers) G0107352046 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/132883 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 金融學系 zh_TW dc.description (描述) 107352046 zh_TW dc.description.abstract (摘要) 可轉債是一種可以按照約定的價格轉換成股票的公司債券，融合了股票及債券特性，是中國資本市場的重要組成部分。目前，隨著越來越多的機構及個人投資者加入可轉債的市場，需要一個合理的評價模型，讓市場參與者可以有一個公允的參考價值。本文首先介紹了可轉債的定義，以及可轉債定價理論的研究現狀，然後圍繞可轉債定價存在的問題進行研究，主要內容包括分析影響可轉債的因素、各可轉債條款的影響。接著，介紹了BS 定價模型、二項樹模型（BT）以及最小平方蒙地卡羅模型（LSM）在評價可轉債時的理論及優缺點。本文選擇對仍上市流通、交易量較高、條款設置合理的39 只可轉債進行分析。選取了各可轉債在2019 年的12 個節點進行了模擬，比較2019 年的交易價格和模擬出的理論價格差異。通過實證分析，可以看出無論是單個時間節點，還是整體的誤差率，LSM 模型都比BT 模型更貼近可轉債的實際價格，但仍與實際價格有一些偏差，並且中國可轉債價值存在被市場低估的現象。 zh_TW dc.description.abstract (摘要) Convertible bond is a kind of corporate bond that can be converted into stock according to the agreed price. It integrates the characteristics of stock and bond, and is an important part of China`s capital market. At present, with more and more institutional and individual investors joining the convertible bond market, a reasonable evaluation model is needed so that market participants can have a fair reference value.This paper first introduces the definition of convertible bonds, and the research status of the pricing theory of convertible bonds, and then studies the problems existing in the pricing of convertible bonds. The main content includes the analysis of the factors affecting convertible bonds and the impact of the terms of convertible bonds. Then, it introduces the theory, advantages and disadvantages of BS pricing model, binomial tree model (BT) and least square Monte Carlo model (LSM) in evaluating convertible bonds.This paper chooses 39 convertible bonds in China which are still on the market, with high trading volume and reasonable terms. The paper selects 12 nodes of each convertible bond in 2019 to simulate, and compares the trading price in 2019 with the theoretical price. Through the empirical analysis, it can be seen that the LSM model is closer to the actual price of convertible bonds than the BT model, whether it is a single time node or the overall error rate, but there are still some deviations from the actual price, and the value of convertible bonds in China is underestimated by the market. en_US dc.description.tableofcontents 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 研究內容與架構 2第二章 文獻回顧 5第一節 國際上可轉債定價的相關研究 5二、樹圖定價法 6三、模擬定價法 6第二節 中國大陸可轉債定價的相關研究 7一、偏微分方程定價法 7二、樹圖定價法 7三、模擬定價法 7第三章 中國可轉債特性 9第一節 中國可轉債市場 9一、起始階段 9二、探索階段 9三、蓬勃發展階段 10第二節 可轉債的基本要素 11一、債權性 11二、股權性 11三、期權性 12第三節 影響定價的因素 12一、利率 12二、標的股票 13三、存續期間及轉股期限 13四、轉股價格和轉股數量 13第四節 中國可轉債條款 14一、可轉債條款特性 14二、路徑依賴性 17三、條款的影響 17第五節 与台灣可轉債的差異 18第四章 研究方法及步驟 20第一節 Black-Scholes選擇權定價法 20第二節 二項樹定價法 21第三節 最小平方法蒙地卡羅模擬定價法 22第四節 比較及總結 24第五節 定價模型參數介紹 25第五章 實證研究 27第一節 樣本可轉債 27第二節 參數設定 30第三節 評價結果 33第四節 誤差分析 39一、模型因素 39二、市場因素 39三、其他因素 39第六章 結論與未來展望 40參考文獻 41附錄 43 zh_TW dc.format.extent 1039213 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0107352046 en_US dc.subject (關鍵詞) 可轉債 zh_TW dc.subject (關鍵詞) 蒙地卡羅模擬 zh_TW dc.subject (關鍵詞) 二項樹模擬 zh_TW dc.subject (關鍵詞) Convertible Bond en_US dc.subject (關鍵詞) Monte Carlo Simulation en_US dc.subject (關鍵詞) Binomial Tree Simulation en_US dc.title (題名) 基於最小平方蒙地卡羅模擬法評價可轉債：以中國大陸市場為例 zh_TW dc.title (題名) Evaluation of Convertible Bonds Based on the Least Square Monte Carlo Simulation: Take Mainland China Market as an Example en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) Bhattacharya, M., & Zhu, Y. (1997). Valuation and analysis of convertible securities. The Handbook of Fixed Income Securities, 5, 791-817.Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 81(3), 637-654.Boyle, P. P. (1977). Options: A monte carlo approach. Journal of financial economics, 4(3), 323-338.Boyle, P. P. (1986). Option valuation using a tree-jump process. International Options Journal, 3, 7-12.Brennan, M. J., & Schwartz, E. S. (1980). Analyzing convertible bonds. Journal of Financial and Quantitative analysis, 907-929.Chan, A. W., & Chen, N. F. (2007). Convertible bond underpricing: Renegotiable covenants, seasoning, and convergence. Management Science, 53(11), 1793-1814.Cheung, W., and Nelken, I. (1994). Costing the converts. Risk, 7(7),47-49.Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of financial Economics, 7(3), 229-263.Ho, T. S., & Lee, S. B. (1986). Term structure movements and pricing interest rate contingent claims. the Journal of Finance, 41(5), 1011-1029.Ingersoll Jr, J. E. (1977). A contingent-claims valuation of convertible securities. Journal of Financial Economics, 4(3), 289-321.Longstaff, F. A., & Schwartz, E. S. (2001). Valuing American options by simulation: a simple least-squares approach. The review of financial studies, 14(1), 113-147.Lvov, D., Yigitbasioglu, A. B., & El Bachir, N. (2004, December). Pricing convertible bonds by simulation. In Second IASTED international conference (pp. 259-264).Moreno, M., & Navas, J. F. (2003). On the robustness of least-squares Monte Carlo (LSM) for pricing American derivatives. Review of Derivatives Research, 6(2), 107-128.Nyborg, K. G. (1996). The use and pricing of convertible bonds. Applied Mathematical Finance, 3(3), 167-190.Poensgen, O. H. (1965). The valuation of convertible bonds.Tsiveriotis, K., & Fernandes, C. (1998). Valuing convertible bonds with credit risk. The Journal of Fixed Income, 8(2), 95.莊新田, & 周玲春. (2006). 基於雙因素的可轉換債券定價模型. 東北大學學報 (自然科學版), 27(3), 320-323.袁新熠. (2008). 基於最小二乘蒙特卡洛方法對中國可轉債市場價格的偏差分析(Master`s thesis, 電子科技大學).唐文彬, & 張小勇. (2008). LSM 可轉債定價模型及其應用研究. 財經理論與實踐, 29(4), 50-53.陳盛業, & 王義克. (2007). 奇異期權與中國可轉債定價. 清華大學學報(自然科學版)(06), 127-130.張江紅, & 楊善朝. (2007). 可轉換債券定價的三叉樹方法. 太原師範學院學報: 自然科學版, 6(2), 8-11.張德華, & 陶融. (1999). 布萊克—斯科爾斯期權定價模型在可轉換債券定價中的應用. 財經理論與實踐, 20(6), 52-54.鄭振龍, & 林海. (2004). 中國可轉換債券定價研究(Doctoral dissertation).賴其男, 姚長輝, & 王志誠. (2005). 關於我國可轉換債券定價的實證研究. 金融研究, (9), 105-121. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU202001794 en_US
