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| Title: | 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 |
| Authors: | 董恆元
Tung, Heng Yuan |
| Contributors: | 陳麗霞
董恆元
Tung, Heng Yuan |
| Keywords: | 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 |
| Date: | 2012 |
| Issue Date: | 2013-09-02 15:37:06 (UTC+8) |
| Abstract: | 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. |
| Reference: | 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.
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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.
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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.
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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。 |
| Description: | 碩士
國立政治大學
統計研究所
100354026
101 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0100354026 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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