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題名 考慮信用風險及Lévy過程之可轉換公司債評價
Valuation of Convertible Bond under Lévy process with Default Risk作者 李嘉晃
Li, Chia Huang貢獻者 廖四郎
Liao, Szu Lang
李嘉晃
Li, Chia Huang關鍵詞 Lévy過程
信用風險
可轉換公司債
最小平方蒙地卡羅法
Lévy process
credit risk
convertible bond
least squares Monte Carlo Simulation日期 2012 上傳時間 3-Jun-2013 17:52:38 (UTC+8) 摘要 由於違約事件不斷發生以及在財務實證上顯示證券的報酬率有厚尾與高狹峰的現象，本文使用縮減式模型與Lévy過程來評價有信用風險下的可轉換公司債。在Lévy過程中，本研究假設股價服從NIG及VG模型，發現此兩種模型比傳統的GBM模型更符合厚尾現象。此外，在Lévy過程參數估計方面，本文使用最大概似法估計參數，在評價可轉換公司債方面，本研究採用最小平方蒙地卡羅法。本文之實證結果顯示，Lévy模型的績效比傳統GBM模型佳。
Due to the reason that the default events occurred constantly and still continue taking place, empirical log return distributions exhibit fat tail and excess kurtosis, this paper evaluates convertible bonds under Lévy process with default risk using the reduced-form approach. Under the Lévy process, the underlying stock prices are set to be normal inverse Gaussian (NIG) and variance Gamma (VG) model to capture the jump components. In the empirical analysis, we use the maximum likelihood method to estimate the parameters of Lévy distributions, and apply the least squares Monte Carlo Simulation to price convertible bonds. Five examples are shown in pricing convertible bonds using the traditional model and Lévy model. The empirical results show that the performance of Lévy model is better than the traditional one.參考文獻 Albrecher, H. and Predota, M. (2004). On Asian option pricing for NIG Levy processes, Journal of Computational and Applied Mathmatic,172, 153-168. Ammann, M., Kind, A. and Wilde, C. (2007). Simulation-based pricing of convertible bonds. Journal of Empirical Finance, 15, 310-331. Ammann, M. and Seiz, R. (2006). Pricing and hedging mandatory convertible bonds. Journal of Derivatives,13, 30-46. Ayache, E., Forsyth, P. A. and Vetzal, K. R. (2004). The valuation of convertible bonds with default risk. Journal of Derivatives, 1, 9-29. Barndorff-Nielsen, O. E. (1995). Normal inverse Gaussian distributions and modeling of stock returns. Technical report, Aarhus University. Black, F. and Cox, J. C. (1976). Valuing corporate securities: some effects on the bonds indenture provisions. Journal of Finance, 31, 351-367. Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637-654. Brennan, M. J. and Schwartz, E.S. (1977). Convertible bond: valuation and optimal strategies for call and conversion. Journal of Finance, 32, 1699-1715. Brennan, M. J. and Schwartz, E.S. (1980). Analyzing convertible bonds. Journal of Financial and Quantitative Analysis, 15, 907-929. Caeeiere, J. F. (1996), Valuation of the early-exercise price for options using simulations and nonparametric regression, Mathematics and Economics, 19, 19-30. Cariboni, J. and Schoutens, W. (2007). Pricing credit default swaps under Lévy models. Journal of Computational Finance, 10, 1-21. Carr, P., Wu, L. (2004). Time-changed Lévy process and option pricing. Journal of Financial Economics, 71,113-141. Carayannopoulos, P. (1996). Valuation convertible bonds under the assumption of stochastic interest rate: An Empirical investigation. Quarterly Journal of Business and Economics, 6, 17-31. Duffie, D. and Singleton, K. (1997). An econometric model of the term structure of interest rate swap yields. Journal of Finance, 52, 1287-1321. Duffie, D. and Singleton, K. J. (1999). Modelling term structures of defaultable bonds. The Review of Financial Studies, 12, 687-720. Goldman, S. (1994). Valuing convertible bonds as derivatives. Quantitative Strategies Research Notes. Hirsa, A. and Madan, D. B. (2004). Pricing American option under variance Gamma. Journal of Computational Finance, 7, 63-80. Ingersoll, J. E. (1977). A contingent claims valuation of convertible securities. Journal of Financial Economics, 4, 289-322. Jarrow, R. A. and Turnbull S. M. (1995). Pricing options on financial securities subject to default risk. Journal of Finance, 50, 481-523. Jarrow, R. A., Lando, D., and Turnbull, S. M. (1997). A Markov model for the term structure of credit risk spreads. Review of Financial Studies, 10, 481-523. Kalemanova, A., Schmid, B. and Werner R. (2007). The normal inverse Gaussian distribution for synthetic CDO pricing. Journal of Derivatives, 14, 80-93. Lando, D. (1998). On Cox process and credit risky securities. Review of Derivatives Research, 2, 99-120. Liao, S. L. and Huang, H. H. (2006). Valuation and optimal strategies of convertible bonds. Journal of Future Markets, 26, 895-922. Longstaff, F. A. and Schwartz, E. S. (2001). Valuing American option by simulation: a simple least squares approach. The Review of Financial Studies, 14, 113-147. Madan, D. B., Carr, P. and Chang, E. C. (1998). The variance Gamma process and option pricing. European Finance Review, 2, 79-105. Mandelbrot, B. (1963). The variation of certain speculative prices. Journal of Business, 45, 542-543. McConnell, J. J. and Schwartz, E. S. (1986). LYON taming. Journal of Finance, 41, 564-575. Merton, R. C. (1974). “On the pricing of corporate debt: The risk structure of interest rate.” Journal of Finance, 29, 449-470. Muromachi, Y. (1999). The growing recognition of credit risk in corporate and financial bond markets. NLI Research Institute. Ribeiro, C. and Webber, N. (2002). Valuing path dependent options in variance Gamma model by Monte Carlo with Gamma bridge. Working Paper Series, Financial Econometrics Research Centre, Coventry. Stentoft, L. (2008). American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution. Journal of Financial Econometrics, 6, 540-582. Takahashi, A., Kobayashi, T. and Nakagawa, N. (2001). Pricing convertible bonds with default risk: A Duffie-Singleton approach. Journal of Fixed Income ,11, 20-29. Tilley, J. A. (1993). Valuing American options in a path simulation model. Transactions of the Society of Actuaries, 45, 83-104. Tsiveriotis, K. and Fernandes, C. (1998). Valuing convertible bonds with credit risks. Journal of Fixed Income, 8, 95-102. Vascieck, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177-188. 描述 博士
國立政治大學
金融研究所
95352510
101資料來源 http://thesis.lib.nccu.edu.tw/record/#G0953525106 資料類型 thesis dc.contributor.advisor 廖四郎 zh_TW dc.contributor.advisor Liao, Szu Lang en_US dc.contributor.author (Authors) 李嘉晃 zh_TW dc.contributor.author (Authors) Li, Chia Huang en_US dc.creator (作者) 李嘉晃 zh_TW dc.creator (作者) Li, Chia Huang en_US dc.date (日期) 2012 en_US dc.date.accessioned 3-Jun-2013 17:52:38 (UTC+8) - dc.date.available 3-Jun-2013 17:52:38 (UTC+8) - dc.date.issued (上傳時間) 3-Jun-2013 17:52:38 (UTC+8) - dc.identifier (Other Identifiers) G0953525106 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/58335 - dc.description (描述) 博士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 金融研究所 zh_TW dc.description (描述) 95352510 zh_TW dc.description (描述) 101 zh_TW dc.description.abstract (摘要) 由於違約事件不斷發生以及在財務實證上顯示證券的報酬率有厚尾與高狹峰的現象，本文使用縮減式模型與Lévy過程來評價有信用風險下的可轉換公司債。在Lévy過程中，本研究假設股價服從NIG及VG模型，發現此兩種模型比傳統的GBM模型更符合厚尾現象。此外，在Lévy過程參數估計方面，本文使用最大概似法估計參數，在評價可轉換公司債方面，本研究採用最小平方蒙地卡羅法。本文之實證結果顯示，Lévy模型的績效比傳統GBM模型佳。 zh_TW dc.description.abstract (摘要) Due to the reason that the default events occurred constantly and still continue taking place, empirical log return distributions exhibit fat tail and excess kurtosis, this paper evaluates convertible bonds under Lévy process with default risk using the reduced-form approach. Under the Lévy process, the underlying stock prices are set to be normal inverse Gaussian (NIG) and variance Gamma (VG) model to capture the jump components. In the empirical analysis, we use the maximum likelihood method to estimate the parameters of Lévy distributions, and apply the least squares Monte Carlo Simulation to price convertible bonds. Five examples are shown in pricing convertible bonds using the traditional model and Lévy model. The empirical results show that the performance of Lévy model is better than the traditional one. en_US dc.description.tableofcontents Chapter1 Introduction…………………………………………………………………………...……1 Chapter 2 Literature review…………………………………………………………………………..4 2.1 Convertbile bond and Lévy process ……………………………………………………………..4 2.2 Credit risk………………………………………………………...………………………………6 Chapter 3 Methodology………...………………………………………………………………….....8 3.1 Defaultable zero-coupon bond…….…………………………….…………………………….....8 3.2 Defaultable stock valuation………………….…………………………………...........................8 3.3 The dynamics of interest rate…………………………………………………………………….9 3.4 The properties of Lévy process…………...…………………………………….........................10 3.5 The estimation method………………………………………………………….........................13 3.6 The valuation of convertible bond………...…………………………………….........................15 3.7 Least squares Monte Carlo algorithm…………………………………………...........................17 Chapter 4 Empirical results…………………………………………………………………………19 4.1 Data description…………………………………………………………………………………19 4.2 The goodness of fit test……………………………………………………….............................21 4.3 Parameter estimation of stock price and calibration of intensity rate…………………………...25 4.4 The performance of convertible bond…………………………………...………………...……27 Chapter 5 Conclusion………………………………………….........................................................30 Reference…………………………………………………………………… ……………………...32 Figure 1 The returns of all samples………………………………………………………………....21 Figure 2 The QQ plot of all samples………………………………………………………………..23 Figure 3 The pricing errors of all samples………………………………………………………….29 Table 1 Convertible bond…………………………………………………………………………...20 Table 2 KS two-sample test of five samples………………………………………………………...24 Table 3 Estimated parameters in different models………………………………………………….26 Table 4 Compariative performance of five samples………………………………………………...28 zh_TW dc.format.extent 1750280 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/#G0953525106 en_US dc.subject (關鍵詞) Lévy過程 zh_TW dc.subject (關鍵詞) 信用風險 zh_TW dc.subject (關鍵詞) 可轉換公司債 zh_TW dc.subject (關鍵詞) 最小平方蒙地卡羅法 zh_TW dc.subject (關鍵詞) Lévy process en_US dc.subject (關鍵詞) credit risk en_US dc.subject (關鍵詞) convertible bond en_US dc.subject (關鍵詞) least squares Monte Carlo Simulation en_US dc.title (題名) 考慮信用風險及Lévy過程之可轉換公司債評價 zh_TW dc.title (題名) Valuation of Convertible Bond under Lévy process with Default Risk en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) Albrecher, H. and Predota, M. (2004). On Asian option pricing for NIG Levy processes, Journal of Computational and Applied Mathmatic,172, 153-168. Ammann, M., Kind, A. and Wilde, C. (2007). Simulation-based pricing of convertible bonds. Journal of Empirical Finance, 15, 310-331. Ammann, M. and Seiz, R. (2006). Pricing and hedging mandatory convertible bonds. Journal of Derivatives,13, 30-46. Ayache, E., Forsyth, P. A. and Vetzal, K. R. (2004). The valuation of convertible bonds with default risk. Journal of Derivatives, 1, 9-29. Barndorff-Nielsen, O. E. (1995). Normal inverse Gaussian distributions and modeling of stock returns. Technical report, Aarhus University. Black, F. and Cox, J. C. (1976). Valuing corporate securities: some effects on the bonds indenture provisions. Journal of Finance, 31, 351-367. Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637-654. Brennan, M. J. and Schwartz, E.S. (1977). Convertible bond: valuation and optimal strategies for call and conversion. Journal of Finance, 32, 1699-1715. Brennan, M. J. and Schwartz, E.S. (1980). Analyzing convertible bonds. Journal of Financial and Quantitative Analysis, 15, 907-929. Caeeiere, J. F. (1996), Valuation of the early-exercise price for options using simulations and nonparametric regression, Mathematics and Economics, 19, 19-30. Cariboni, J. and Schoutens, W. (2007). Pricing credit default swaps under Lévy models. Journal of Computational Finance, 10, 1-21. Carr, P., Wu, L. (2004). Time-changed Lévy process and option pricing. Journal of Financial Economics, 71,113-141. Carayannopoulos, P. (1996). Valuation convertible bonds under the assumption of stochastic interest rate: An Empirical investigation. Quarterly Journal of Business and Economics, 6, 17-31. Duffie, D. and Singleton, K. (1997). An econometric model of the term structure of interest rate swap yields. Journal of Finance, 52, 1287-1321. Duffie, D. and Singleton, K. J. (1999). Modelling term structures of defaultable bonds. The Review of Financial Studies, 12, 687-720. Goldman, S. (1994). Valuing convertible bonds as derivatives. Quantitative Strategies Research Notes. Hirsa, A. and Madan, D. B. (2004). Pricing American option under variance Gamma. Journal of Computational Finance, 7, 63-80. Ingersoll, J. E. (1977). A contingent claims valuation of convertible securities. Journal of Financial Economics, 4, 289-322. Jarrow, R. A. and Turnbull S. M. (1995). Pricing options on financial securities subject to default risk. Journal of Finance, 50, 481-523. Jarrow, R. A., Lando, D., and Turnbull, S. M. (1997). A Markov model for the term structure of credit risk spreads. Review of Financial Studies, 10, 481-523. Kalemanova, A., Schmid, B. and Werner R. (2007). The normal inverse Gaussian distribution for synthetic CDO pricing. Journal of Derivatives, 14, 80-93. Lando, D. (1998). On Cox process and credit risky securities. Review of Derivatives Research, 2, 99-120. Liao, S. L. and Huang, H. H. (2006). Valuation and optimal strategies of convertible bonds. Journal of Future Markets, 26, 895-922. Longstaff, F. A. and Schwartz, E. S. (2001). Valuing American option by simulation: a simple least squares approach. The Review of Financial Studies, 14, 113-147. Madan, D. B., Carr, P. and Chang, E. C. (1998). The variance Gamma process and option pricing. European Finance Review, 2, 79-105. Mandelbrot, B. (1963). The variation of certain speculative prices. Journal of Business, 45, 542-543. McConnell, J. J. and Schwartz, E. S. (1986). LYON taming. Journal of Finance, 41, 564-575. Merton, R. C. (1974). “On the pricing of corporate debt: The risk structure of interest rate.” Journal of Finance, 29, 449-470. Muromachi, Y. (1999). The growing recognition of credit risk in corporate and financial bond markets. NLI Research Institute. Ribeiro, C. and Webber, N. (2002). Valuing path dependent options in variance Gamma model by Monte Carlo with Gamma bridge. Working Paper Series, Financial Econometrics Research Centre, Coventry. Stentoft, L. (2008). American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution. Journal of Financial Econometrics, 6, 540-582. Takahashi, A., Kobayashi, T. and Nakagawa, N. (2001). Pricing convertible bonds with default risk: A Duffie-Singleton approach. Journal of Fixed Income ,11, 20-29. Tilley, J. A. (1993). Valuing American options in a path simulation model. Transactions of the Society of Actuaries, 45, 83-104. Tsiveriotis, K. and Fernandes, C. (1998). Valuing convertible bonds with credit risks. Journal of Fixed Income, 8, 95-102. Vascieck, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177-188. zh_TW
