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題名 兩段迴歸結合蒙地卡羅模擬對可轉債定價之研究
Pricing Convertible Bonds by Piecewise Regression and Monte Carlo Simulation作者 董恆元
Tung, Heng Yuan貢獻者 陳麗霞
董恆元
Tung, Heng Yuan關鍵詞 可轉換公司債
定價
蒙地卡羅模擬
最小平方迴歸法
繼續持有價值
兩段迴歸
定價偏差比
價性
擔保狀況
Convertible bonds
pricing
Monte Carlo simulation
Least-squares regression
continuation value
piecewise regression
mispricing rate
moneyness
guaranteed condition日期 2012 上傳時間 2-九月-2013 15:37:06 (UTC+8) 摘要 可轉換公司債兼具了選擇權以及債券的性質，價值又會受到股價之影響，以傳統的方法定價十分不易。由於蒙地卡羅模擬能解決定價問題上狀態變數或許為多維度及路徑相依的問題，Kind 與Wilde 在2004 年提出以蒙地卡羅模擬對可轉債定價，且以最小平方迴歸法估計繼續持有價值，並在僅考慮轉換及還本兩種選擇權及沒有違約風險之下，以數值範例呈現單一迴歸模式無法適當估計繼續持有價值。然而，他們並未進行實證。本研究乃以民國99 年台灣發行的可轉債為研究對象，除考慮發行時的合約條件外，另加上信用評等的考量以將違約機率透過現金流量套入定價過程中，並分別以兩段迴歸及單一迴歸估計繼續持有價值以結合蒙地卡羅模擬，實證結果顯示就可轉債之起始定價的偏差比而言，兩段迴歸得到的結果優於單一迴歸。惟在兩段迴歸之下，超過八成的可轉債其模擬價格依然高於市場價格。實證結果也顯示價性(moneyness)及擔保狀況與定價的偏差有關。
Convertible bonds (CBs) possess features of both bonds and options, and their prices are affected by the underlying stocks, which make the pricing problem an uneasy task for traditional methods. Since Monte Carlo simulation can handle the problems of path-dependence and multivariate dimensions faced by pricing, Kind and Wilde (2004) suggested to price CBs via least-squares Monte Carlo simulations (LSM), which estimate the continuation values by least squares regression. They also demonstrated that a single regression line could not appropriately estimate the continuation value even only conversion and redemption were allowed and the CB was free of default. So the idea of piecewise regression was recommended to improve the estimation process. However, they didn’t apply piecewise regression to real data. Therefore, piecewise regression together with Monte Carlo simulation were employed to investigate the pricing issue of Taiwan’s CBs. CBs issued on 2010 were selected, besides reviewing the contents of CB’s contracts, default risks based on credit ratings were taken into account to evaluate the discounted cash flows in the pricing procedure. Comparing the estimated model prices of LSM with initial selling prices, the mispricing rates of single regression model and piecewise regression model were obtained for further analysis. Result shows that the modified piecewise regression method performs better in mispricing rate. However, similar to previous findings, 80% of the estimated model prices based on piecewise regressions are still higher than market prices. It also shows that moneyness and guaranteed condition will relate to mispricing rate.參考文獻 國外：Ammann, M., Kind, A. & Wilde, C. (2008). Simulation-based pricing of convertible bonds. Journal of Empirical Finance, 15, 310-331. Ammann, M., Kind, A. & Wilde, C. (2003). Are convertible bonds underpriced? An analysis of the French market. Journal of Banking and Finance, 27(4), 635-653. Ayache, E., Forsyth, P.A. & Vetzal, K.R. (2003). Valuation of convertible bonds with credit risk. Journal of Derivatives, 11(1), 9-29. Black, F. & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637-654. Brennan, M. J. & Schwartz, E.S. (1980). Analyzing convertible bonds. Journal of Financial and Quantitative Analysis, 15(4), 907-929. Broadie, M. & Glassermam, P. (1997). Pricing American-Style Securities by Simulation. Journal of Economic Dynamics and Control, 21, 1323-1352. Buchan, M. J. (1997). Convertible bond pricing: Theory and evidence. Harvard University. Buchan, M. J. (1998). The pricing of convertible bonds with stochastic term structures and corporate default risk. Amos Tuck School of Business, Dartmouth College. Carrière, J. F. (1996). Valuation of early-exercise price of options using simulations and nonparametric regression. Insurance Mathematics and Economics, 19, 19-30. Garcia, D. (2003). Convergence and Biases of Monte Carlo estimates of American option prices using a parametric exercise rule. Journal of Economic Dynamics & Control, 27(10), 1855-1879. Grant, D., Vora, G. & Weeks, D. (1997). Path-Dependent Options: Extending the Monte Carlo Simulation Approach. Management Science, 43(11), 1589-1602. Ingersoll, J. E. (1977). A contingent claim valuation of convertible securities. Journal of Financial Economics, 4(3), 289-321. Kind, A. (2005). Pricing American-Style Options by Simulation. Swiss Society for Financial Market Research, 109-116. Kind, A. & Wilde, C. (2004). Princing Convertible Bonds with Monte Carlo Simulation. Working Paper.King, R. (1986). Convertible bond valuation: An empirical test. Journal of Financial Research, 9(1), 53-59. Lewis, C. M. (1991). Convertible debt: Valuation and conversion in complex capital structures. Journal of Banking & Finance, 15(3), 665-682. 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. Merton, R. C. (1973). Theory of Rational Option Pricing. Bell Journal of Economics and Management Science, 4(1), 141-183. Metropolis, N. & Ulam, S. (1949). The Monte Carlo Method. Journal of the American Statistical Association, 44(247), 335-341. Nyborg, K. G. (1996). The use and pricing of convertible bonds. Applied Mathematical Finance, 3(3), 167-190. Tsiveriotis, K. & Fernandes, C. (1998). Valuing convertible bonds with credit risk. Journal of Fixed Income, 8(3), 95-102. 國內：林政緯(2005)。重設型可轉換公司債價格行為之研究, 長庚大學企業管理研究所。洪舜欣(2006)。信用風險下可轉換公司債之評價-LSM法, 成功大學財務金融所碩士論文。高依暄(2006)。制度變革對國內可轉換公司債效率性之影響。中山大學財務管理所碩士論文。許芳銘(2004)。可轉換債券之定價與拆解, 中央大學財務金融所碩士論文。張益堅(2004)。可轉換公司債的評價─以久津為例, 台灣大學財務金融所碩士論文。張家福(2000)。可轉換公司的評價與實證研究 -Two Dimensional Tree Model, 臺灣大學國際企業學研究所碩士論文。 程羿(2013)。2012年TCRI效度驗證, 貨幣觀測與信用評等, 2013.03[民102.03], 56-70。劉志清(2002)。探討不同時間到期之可轉換公司債的價格交互影響效果, 政大金融所碩士論文。 描述 碩士
國立政治大學
統計研究所
100354026
101資料來源 http://thesis.lib.nccu.edu.tw/record/#G0100354026 資料類型 thesis dc.contributor.advisor 陳麗霞 zh_TW dc.contributor.author (作者) 董恆元 zh_TW dc.contributor.author (作者) Tung, Heng Yuan en_US dc.creator (作者) 董恆元 zh_TW dc.creator (作者) Tung, Heng Yuan en_US dc.date (日期) 2012 en_US dc.date.accessioned 2-九月-2013 15:37:06 (UTC+8) - dc.date.available 2-九月-2013 15:37:06 (UTC+8) - dc.date.issued (上傳時間) 2-九月-2013 15:37:06 (UTC+8) - dc.identifier (其他 識別碼) G0100354026 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/59290 - 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) 100354026 zh_TW dc.description (描述) 101 zh_TW dc.description.abstract (摘要) 可轉換公司債兼具了選擇權以及債券的性質，價值又會受到股價之影響，以傳統的方法定價十分不易。由於蒙地卡羅模擬能解決定價問題上狀態變數或許為多維度及路徑相依的問題，Kind 與Wilde 在2004 年提出以蒙地卡羅模擬對可轉債定價，且以最小平方迴歸法估計繼續持有價值，並在僅考慮轉換及還本兩種選擇權及沒有違約風險之下，以數值範例呈現單一迴歸模式無法適當估計繼續持有價值。然而，他們並未進行實證。本研究乃以民國99 年台灣發行的可轉債為研究對象，除考慮發行時的合約條件外，另加上信用評等的考量以將違約機率透過現金流量套入定價過程中，並分別以兩段迴歸及單一迴歸估計繼續持有價值以結合蒙地卡羅模擬，實證結果顯示就可轉債之起始定價的偏差比而言，兩段迴歸得到的結果優於單一迴歸。惟在兩段迴歸之下，超過八成的可轉債其模擬價格依然高於市場價格。實證結果也顯示價性(moneyness)及擔保狀況與定價的偏差有關。 zh_TW dc.description.abstract (摘要) Convertible bonds (CBs) possess features of both bonds and options, and their prices are affected by the underlying stocks, which make the pricing problem an uneasy task for traditional methods. Since Monte Carlo simulation can handle the problems of path-dependence and multivariate dimensions faced by pricing, Kind and Wilde (2004) suggested to price CBs via least-squares Monte Carlo simulations (LSM), which estimate the continuation values by least squares regression. They also demonstrated that a single regression line could not appropriately estimate the continuation value even only conversion and redemption were allowed and the CB was free of default. So the idea of piecewise regression was recommended to improve the estimation process. However, they didn’t apply piecewise regression to real data. Therefore, piecewise regression together with Monte Carlo simulation were employed to investigate the pricing issue of Taiwan’s CBs. CBs issued on 2010 were selected, besides reviewing the contents of CB’s contracts, default risks based on credit ratings were taken into account to evaluate the discounted cash flows in the pricing procedure. Comparing the estimated model prices of LSM with initial selling prices, the mispricing rates of single regression model and piecewise regression model were obtained for further analysis. Result shows that the modified piecewise regression method performs better in mispricing rate. However, similar to previous findings, 80% of the estimated model prices based on piecewise regressions are still higher than market prices. It also shows that moneyness and guaranteed condition will relate to mispricing rate. en_US dc.description.tableofcontents 第一章 緒論 1第一節 研究動機以及目的 1第二節 可轉換公司債簡介 3第三節 文獻回顧 6第二章 以蒙地卡羅模擬法對可轉債定價 12第一節 蒙地卡羅模擬法對美式選擇權之定價 12第二節 最小平方蒙地卡羅模擬 13第三節 數值範例 15第四節 改進的LSM 21第三章 實證研究 28第一節 規範模型及設定參數 28第二節 研究資料篩選 31第三節 結果分析 34第四章 結論與建議 49參考文獻 51 zh_TW dc.format.extent 2645734 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0100354026 en_US dc.subject (關鍵詞) 可轉換公司債 zh_TW dc.subject (關鍵詞) 定價 zh_TW dc.subject (關鍵詞) 蒙地卡羅模擬 zh_TW dc.subject (關鍵詞) 最小平方迴歸法 zh_TW dc.subject (關鍵詞) 繼續持有價值 zh_TW dc.subject (關鍵詞) 兩段迴歸 zh_TW dc.subject (關鍵詞) 定價偏差比 zh_TW dc.subject (關鍵詞) 價性 zh_TW dc.subject (關鍵詞) 擔保狀況 zh_TW dc.subject (關鍵詞) Convertible bonds en_US dc.subject (關鍵詞) pricing en_US dc.subject (關鍵詞) Monte Carlo simulation en_US dc.subject (關鍵詞) Least-squares regression en_US dc.subject (關鍵詞) continuation value en_US dc.subject (關鍵詞) piecewise regression en_US dc.subject (關鍵詞) mispricing rate en_US dc.subject (關鍵詞) moneyness en_US dc.subject (關鍵詞) guaranteed condition en_US dc.title (題名) 兩段迴歸結合蒙地卡羅模擬對可轉債定價之研究 zh_TW dc.title (題名) Pricing Convertible Bonds by Piecewise Regression and Monte Carlo Simulation en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) 國外：Ammann, M., Kind, A. & Wilde, C. (2008). Simulation-based pricing of convertible bonds. Journal of Empirical Finance, 15, 310-331. Ammann, M., Kind, A. & Wilde, C. (2003). Are convertible bonds underpriced? An analysis of the French market. Journal of Banking and Finance, 27(4), 635-653. Ayache, E., Forsyth, P.A. & Vetzal, K.R. (2003). Valuation of convertible bonds with credit risk. Journal of Derivatives, 11(1), 9-29. Black, F. & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637-654. Brennan, M. J. & Schwartz, E.S. (1980). Analyzing convertible bonds. Journal of Financial and Quantitative Analysis, 15(4), 907-929. Broadie, M. & Glassermam, P. (1997). Pricing American-Style Securities by Simulation. Journal of Economic Dynamics and Control, 21, 1323-1352. Buchan, M. J. (1997). Convertible bond pricing: Theory and evidence. Harvard University. Buchan, M. J. (1998). The pricing of convertible bonds with stochastic term structures and corporate default risk. Amos Tuck School of Business, Dartmouth College. Carrière, J. F. (1996). Valuation of early-exercise price of options using simulations and nonparametric regression. Insurance Mathematics and Economics, 19, 19-30. Garcia, D. (2003). Convergence and Biases of Monte Carlo estimates of American option prices using a parametric exercise rule. Journal of Economic Dynamics & Control, 27(10), 1855-1879. Grant, D., Vora, G. & Weeks, D. (1997). Path-Dependent Options: Extending the Monte Carlo Simulation Approach. Management Science, 43(11), 1589-1602. Ingersoll, J. E. (1977). A contingent claim valuation of convertible securities. Journal of Financial Economics, 4(3), 289-321. Kind, A. (2005). Pricing American-Style Options by Simulation. Swiss Society for Financial Market Research, 109-116. Kind, A. & Wilde, C. (2004). Princing Convertible Bonds with Monte Carlo Simulation. Working Paper.King, R. (1986). Convertible bond valuation: An empirical test. Journal of Financial Research, 9(1), 53-59. Lewis, C. M. (1991). Convertible debt: Valuation and conversion in complex capital structures. Journal of Banking & Finance, 15(3), 665-682. 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. Merton, R. C. (1973). Theory of Rational Option Pricing. Bell Journal of Economics and Management Science, 4(1), 141-183. Metropolis, N. & Ulam, S. (1949). The Monte Carlo Method. Journal of the American Statistical Association, 44(247), 335-341. Nyborg, K. G. (1996). The use and pricing of convertible bonds. Applied Mathematical Finance, 3(3), 167-190. Tsiveriotis, K. & Fernandes, C. (1998). Valuing convertible bonds with credit risk. Journal of Fixed Income, 8(3), 95-102. 國內：林政緯(2005)。重設型可轉換公司債價格行為之研究, 長庚大學企業管理研究所。洪舜欣(2006)。信用風險下可轉換公司債之評價-LSM法, 成功大學財務金融所碩士論文。高依暄(2006)。制度變革對國內可轉換公司債效率性之影響。中山大學財務管理所碩士論文。許芳銘(2004)。可轉換債券之定價與拆解, 中央大學財務金融所碩士論文。張益堅(2004)。可轉換公司債的評價─以久津為例, 台灣大學財務金融所碩士論文。張家福(2000)。可轉換公司的評價與實證研究 -Two Dimensional Tree Model, 臺灣大學國際企業學研究所碩士論文。 程羿(2013)。2012年TCRI效度驗證, 貨幣觀測與信用評等, 2013.03[民102.03], 56-70。劉志清(2002)。探討不同時間到期之可轉換公司債的價格交互影響效果, 政大金融所碩士論文。 zh_TW
