考虑展期风险的可赎回CoCo债券定价
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摘要
始于2007年的次贷危机结束之后,CoCo债券(contingent convertible bond)因为其能够在金融危机时迅速提高银行资本充足率而受到关注.本文考虑了展期风险对CoCo债券价格的影响,用Copula函数刻画股票价格与核心一级资本比率(Core Tier 1 Ratio,CTR)的相关性,用CIR模型刻画利率期限结构,并对CoCo债券的赎回进行判定,采用蒙特卡罗模拟法为带有可赎回条款的CoCo债券定价.将此模型应用于巴克莱银行发行的可赎回CoCo债券验证模型的有效性.最后,结合国际上已发行的CoCo债券的相关条款和我国银监会对于减记债(中国版CoCo债券)的基本要求,设计了中国版的CoCo债券,并在数值计算的基础上进行了股价冲击和银行业监管要求对CoCo债券价格影响的敏感性分析.
The financial crisis since 2007 has highlighted the fragility of the banking system. CoCo bonds have been a hot topic as both a solution to the "too big to fail"problem and a measure by which financial institutions can raise the capital adequacy ratio and save themselves during crises. In this paper,CoCo bonds with extension risk are analyzed. Stock price and Core Tier 1 Ratio are simultaneously simulated and copula functions are introduced to measure the correlation between stock price and Core Tier 1 Ratio. CIR model is used to describe the term structure of interest rates,and Monte-Carlo simulation method is employed to price callable CoCo bonds. Further,callable CoCo bonds issued by Barclays bank are applied to test the performance of our model. Finally,the paper designs the Chinese version of CoCo bonds,and gives the numerical calculation and scenario analysis.
The financial crisis since 2007 has highlighted the fragility of the banking system. CoCo bonds have been a hot topic as both a solution to the "too big to fail"problem and a measure by which financial institutions can raise the capital adequacy ratio and save themselves during crises. In this paper,CoCo bonds with extension risk are analyzed. Stock price and Core Tier 1 Ratio are simultaneously simulated and copula functions are introduced to measure the correlation between stock price and Core Tier 1 Ratio. CIR model is used to describe the term structure of interest rates,and Monte-Carlo simulation method is employed to price callable CoCo bonds. Further,callable CoCo bonds issued by Barclays bank are applied to test the performance of our model. Finally,the paper designs the Chinese version of CoCo bonds,and gives the numerical calculation and scenario analysis.
引文
[1]Spiegeleer J D,Schoutens W. Pricing contingent convertibles:A derivatives approach[J]. The Journal of Derivatives,2012,20(2):27-36.
[2]Barucci E,Del V L. Countercyclical contingent capital[J]. Journal of Banking&Finance,2012,36(6):1688-1709.
[3]French K,Baily M,Campbell J,et al. The squam lake report:Fixing the financial system[J]. Journal of Applied Corporate Finance,2010,22(3):8-21.
[4]McDonald R L. Contingent capital with a dual price trigger[J]. Journal of Financial Stability,2013,9(2):230-241.
[5]Corcuera J M,Spiegeleer J D,Fajardo J,et al. Close form pricing formulas for coupon cancellable Co Cos[J]. Journal of Banking and Finance,2014,42(3):339-351.
[6]Lou P,Yang Z. Real options and contingent convertibles with regime switching[J]. Journal of Economic Dynamics&Control,2017,75:122-135.
[7]Li P,Meng H,Yu H. Chinese write-down bonds and bank capital structure[J]. Quantitative Finance,2018,18(9):1-16.
[8]Ammann M,Blickle K,Ehmann C. Announcement effects of contingent convertible securities:Evidence from the global banking industry[J]. European Financial Management,2017,23(1):127-152.
[9]秦学志,胡友群,尚勤,等.基于转换点生存概率的或有可转债定价研究[J].管理工程学报,2015,29(2):182-189.Qin Xuezhi,Hu Youqun,Shang Qin,et al. Research on pricing contingent convertible bonds with survival probability-based trigger[J]. Journal of Industrial Engineering/Engineering Management,2015,29(2):182-189.(in Chinese)
[10]赵志明,杨招军.或有可转换债券的定价和公司资本结构[J].管理科学学报,2015,18(12):27-35.Zhao Zhiming,Yang Zhaojun. Pricing of contingent convertible bonds and capital structure[J]. Journal of Management Sciences in China,2015,18(12):27-35.(in Chinese)
[11]李平,尹菁华,来娜,等.基于Copula双变量模拟的Co Co债券定价[J].系统工程学报,2016,31(6):772-782.Li Ping,Yin Jinghua,Lai Na,et al. Co Co bond pricing based on copulas bivariate simulation[J]. Journal of Systems Engineering,2016,31(6):772-782.(in Chinese)
[12]秦学志,胡友群,石玉山.含有股权回售与赎回条款的或有可转债定价研究[J].管理科学学报,2016,19(7):102-114.Qin Xuezhi,Hu Youqun,Shi Yushan. Pricing of share-puttable&callable Co Cos[J]. Journal of Management Sciences in China,2016,19(7):102-114.(in Chinese)
[13]De Spiegeleer J,Schoutens W. Coco bonds with extension risk[J]. Wilmott,2014,(71):78-91.
[14]Vasicek O. An equilibrium characterization of the term structure[J]. Journal of Financial Economics,1977,5(2):177-188.
[15]Ball C A,Torous W N. A simplified jump process for common stock returns[J]. Journal of Financial and Quantitative Analysis,1983,18(01):53-65.
[16]Merton R C. Option pricing when underlying stock returns are discontinuous[J]. Journal of Financial Economics,1976,3(1):125-144.
[17]谢赤,吴雄伟.基于Vasicek和CIR模型中的中国货币市场利率行为实证分析[J].中国管理科学,2002,10(3):22-25.Xie Chi,Wu Xiongwei. An empirical analysis of the interest rate behavior in China’s monetary market using the Vasicek and CIR models[J]. Chinese Journal of Management Science,2002,10(3):22-25.(in Chinese)
[18]谢为安,蔡益润.我国可回售债券的定价——基于同期限国债收益率曲线的模拟[J].复旦学报:自然科学版,2011,50(1):103-108.Xie Weian,Cai Yirun. The pricing of puttable bond in Chinese bond market:A simulation based on the yield curve of government bonds with the same term[J]. Journal of Fudan University(Natural Science),2011,50(1):103-108.(in Chinese)
[19]Overbeck L,Rydén T. Estimation in the Cox-Ingersoll-Ross model[J]. Econometric Theory,1997,13(3):430-461.
[2]Barucci E,Del V L. Countercyclical contingent capital[J]. Journal of Banking&Finance,2012,36(6):1688-1709.
[3]French K,Baily M,Campbell J,et al. The squam lake report:Fixing the financial system[J]. Journal of Applied Corporate Finance,2010,22(3):8-21.
[4]McDonald R L. Contingent capital with a dual price trigger[J]. Journal of Financial Stability,2013,9(2):230-241.
[5]Corcuera J M,Spiegeleer J D,Fajardo J,et al. Close form pricing formulas for coupon cancellable Co Cos[J]. Journal of Banking and Finance,2014,42(3):339-351.
[6]Lou P,Yang Z. Real options and contingent convertibles with regime switching[J]. Journal of Economic Dynamics&Control,2017,75:122-135.
[7]Li P,Meng H,Yu H. Chinese write-down bonds and bank capital structure[J]. Quantitative Finance,2018,18(9):1-16.
[8]Ammann M,Blickle K,Ehmann C. Announcement effects of contingent convertible securities:Evidence from the global banking industry[J]. European Financial Management,2017,23(1):127-152.
[9]秦学志,胡友群,尚勤,等.基于转换点生存概率的或有可转债定价研究[J].管理工程学报,2015,29(2):182-189.Qin Xuezhi,Hu Youqun,Shang Qin,et al. Research on pricing contingent convertible bonds with survival probability-based trigger[J]. Journal of Industrial Engineering/Engineering Management,2015,29(2):182-189.(in Chinese)
[10]赵志明,杨招军.或有可转换债券的定价和公司资本结构[J].管理科学学报,2015,18(12):27-35.Zhao Zhiming,Yang Zhaojun. Pricing of contingent convertible bonds and capital structure[J]. Journal of Management Sciences in China,2015,18(12):27-35.(in Chinese)
[11]李平,尹菁华,来娜,等.基于Copula双变量模拟的Co Co债券定价[J].系统工程学报,2016,31(6):772-782.Li Ping,Yin Jinghua,Lai Na,et al. Co Co bond pricing based on copulas bivariate simulation[J]. Journal of Systems Engineering,2016,31(6):772-782.(in Chinese)
[12]秦学志,胡友群,石玉山.含有股权回售与赎回条款的或有可转债定价研究[J].管理科学学报,2016,19(7):102-114.Qin Xuezhi,Hu Youqun,Shi Yushan. Pricing of share-puttable&callable Co Cos[J]. Journal of Management Sciences in China,2016,19(7):102-114.(in Chinese)
[13]De Spiegeleer J,Schoutens W. Coco bonds with extension risk[J]. Wilmott,2014,(71):78-91.
[14]Vasicek O. An equilibrium characterization of the term structure[J]. Journal of Financial Economics,1977,5(2):177-188.
[15]Ball C A,Torous W N. A simplified jump process for common stock returns[J]. Journal of Financial and Quantitative Analysis,1983,18(01):53-65.
[16]Merton R C. Option pricing when underlying stock returns are discontinuous[J]. Journal of Financial Economics,1976,3(1):125-144.
[17]谢赤,吴雄伟.基于Vasicek和CIR模型中的中国货币市场利率行为实证分析[J].中国管理科学,2002,10(3):22-25.Xie Chi,Wu Xiongwei. An empirical analysis of the interest rate behavior in China’s monetary market using the Vasicek and CIR models[J]. Chinese Journal of Management Science,2002,10(3):22-25.(in Chinese)
[18]谢为安,蔡益润.我国可回售债券的定价——基于同期限国债收益率曲线的模拟[J].复旦学报:自然科学版,2011,50(1):103-108.Xie Weian,Cai Yirun. The pricing of puttable bond in Chinese bond market:A simulation based on the yield curve of government bonds with the same term[J]. Journal of Fudan University(Natural Science),2011,50(1):103-108.(in Chinese)
[19]Overbeck L,Rydén T. Estimation in the Cox-Ingersoll-Ross model[J]. Econometric Theory,1997,13(3):430-461.