利率衍生产品定价的影响因素研究
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摘要
利率衍生品占全球金融衍生产品的大部分,我国2005年起也逐渐推出了一些银行间利率衍生品,3年多来发展迅速。研究利率衍生品的定价是金融研究中最具有挑战性的课题之一,利率具有复杂的随机行为,均值回复且不可直接交易,这意味着利率衍生品的定价复杂程度远远超过其他种类的衍生产品。利率衍生品定价的基本方法有数值法和偏微分方程法两种,数值法分为树图法、蒙特卡罗模拟法和差分法三种。偏微分方程法根据标的资产和衍生品各自的特点建立不同的偏微分方程,根据不同的边界条件求解,当然很多偏微分方程求解析解有相当的难度,可以求助于数值方法。
传统的利率衍生品定价是基于BLACK-SCHOLES公式,但是这个公式把利率和资产价格波动率设为常数,不符合利率的运动特征。由此发展出了一系列关于利率期限结构的模型和波动率模型。目前有众多类型的期限结构模型来解释利率的动态过程,大体上分为均衡模型和无套利定价模型两类。均衡模型中,初始期限结构是模型的一个输入,在无套利模型中,它是模型的一个输出。期限结构模型是从特定的经济条件假设下的均衡的动态结果,但因为其参数是用历史数据估计得出的,可能与实际中的真实期限结构不匹配;无套利模型的优点是能精确地与现实期限结构相符合。这两大类模型中的单因素模型容易分析以及使用方便,但其缺陷是很难拟合观测到的收益曲线以及利率波动。多因素模型能够较好的弥补单因素模型的缺陷,但通常很难求解。各模型均有优缺点,可根据实际情况选择模型。波动率是B-S公式中唯一不能直接观察到的变量,一般通过历史波动率或隐含波动率求取。针对B-S公式波动率为常数的不足,有两个办法改善:一是开发更复杂的模型比如随机波动率模型,二是交易人员在B-S公式上开发出来的一些校正波动率的技巧,利用波动率与执行价格和有效期限的关系进行校正。
本文介绍了我国几种已有的利率衍生品的定价公式,包括可转换债券、利率互换、远期利率协议、远期债券。分析了我国这几种利率衍生品的市场发展情况,指出了它们在市场交易中都存在价格失准的现象。针对基准利率在利率衍生品定价中的重要作用,本文比较了我国的几种主要利率:一年期定期存款利率、国债现货和国债回购利率、Shibor利率是否符合基准利率的要求。最后总结了我国利率衍生品定价存在基准利率建设有缺陷、交易主体同质性强、信用体系缺失、市场机制存在弊端等市场方面的影响因素。
Interest rate derivatives in the global financial derivatives account for most of our country since 2005 has gradually introduced a number of inter-bank interest rate derivatives, 3 years developed rapidly. Research interest rate derivatives pricing is a financial study of the most challenging one of the topics that interest rates have a complex random acts of mean-reversion and can not deal directly, which means that the interest rate derivatives pricing complexity than other types of derivatives Products. Interest rate derivatives pricing the basic methods of partial differential equations and numerical method are divided into numerical methods tree method, Monte Carlo simulation and difference of three. According to the Law on the subject of partial differential equations assets and derivatives to build their own different characteristics of partial differential equations, according to the different conditions for solving the border, of course, a lot of partial differential equations analytical solution for a considerable degree of difficulty, you can resort to numerical methods.
Traditional interest rate derivatives pricing is based on the BLACK-SCHOLES formula, but the formula to interest rates and asset price volatility as constant, interest rates do not meet the characteristics of the movement. This leads to a series of interest rate on the term structure of volatility models and model. There are many types of models to explain the term structure of interest rates, dynamic process, is divided into general equilibrium model and two types of arbitrage pricing model. Equilibrium model, the initial term structure is a model of input in the no-arbitrage model, it is a model of the output. No-arbitrage model has the advantage of reality and be able to accurately match the term structure. These two types of single-factor model of the model analysis, and easy to use, but its defect is very difficult to fit the observed yield curve, as well as fluctuations in interest rates. Multi-factor model better able to make up for the single-factor model of the defect, but is often difficult to solve. The model has advantages and disadvantages, according to the actual situation may choose to model. Volatility of B-S formula can not be directly observed , through the general history of volatility or implied volatility strike. B-S formula for fluctuations in the rate constant for the lack of improvement in two ways: First, the development of more sophisticated models such as stochastic volatility model, and the other is trading in the B-S formula developed on some of the volatility of the correction techniques, the use of volatility And the implementation of the price and duration of the relationship between the correction.
In this paper, several of our existing interest rate derivatives pricing formula, including convertible bonds, the interest rate swap, forward rate agreements, long-term bonds. Analysis of China's these types of interest rate derivatives market developments, pointing out that their transactions are in the market price of the existence of inaccuracy. Benchmark interest rates in response to interest rate derivatives pricing in the important role of this article compared the number of China's main interest rate: one-year time deposit interest rates, government bonds and treasury stock repurchase rate, Shibor interest rates in line with the benchmark interest rate. Finally, summed up China's interest rate derivatives pricing benchmark interest rates there are construction defects, the strong homogeneity of the trading parts, and lack of credit system, market mechanisms, such as the existence of the defects of market factors.
传统的利率衍生品定价是基于BLACK-SCHOLES公式,但是这个公式把利率和资产价格波动率设为常数,不符合利率的运动特征。由此发展出了一系列关于利率期限结构的模型和波动率模型。目前有众多类型的期限结构模型来解释利率的动态过程,大体上分为均衡模型和无套利定价模型两类。均衡模型中,初始期限结构是模型的一个输入,在无套利模型中,它是模型的一个输出。期限结构模型是从特定的经济条件假设下的均衡的动态结果,但因为其参数是用历史数据估计得出的,可能与实际中的真实期限结构不匹配;无套利模型的优点是能精确地与现实期限结构相符合。这两大类模型中的单因素模型容易分析以及使用方便,但其缺陷是很难拟合观测到的收益曲线以及利率波动。多因素模型能够较好的弥补单因素模型的缺陷,但通常很难求解。各模型均有优缺点,可根据实际情况选择模型。波动率是B-S公式中唯一不能直接观察到的变量,一般通过历史波动率或隐含波动率求取。针对B-S公式波动率为常数的不足,有两个办法改善:一是开发更复杂的模型比如随机波动率模型,二是交易人员在B-S公式上开发出来的一些校正波动率的技巧,利用波动率与执行价格和有效期限的关系进行校正。
本文介绍了我国几种已有的利率衍生品的定价公式,包括可转换债券、利率互换、远期利率协议、远期债券。分析了我国这几种利率衍生品的市场发展情况,指出了它们在市场交易中都存在价格失准的现象。针对基准利率在利率衍生品定价中的重要作用,本文比较了我国的几种主要利率:一年期定期存款利率、国债现货和国债回购利率、Shibor利率是否符合基准利率的要求。最后总结了我国利率衍生品定价存在基准利率建设有缺陷、交易主体同质性强、信用体系缺失、市场机制存在弊端等市场方面的影响因素。
Interest rate derivatives in the global financial derivatives account for most of our country since 2005 has gradually introduced a number of inter-bank interest rate derivatives, 3 years developed rapidly. Research interest rate derivatives pricing is a financial study of the most challenging one of the topics that interest rates have a complex random acts of mean-reversion and can not deal directly, which means that the interest rate derivatives pricing complexity than other types of derivatives Products. Interest rate derivatives pricing the basic methods of partial differential equations and numerical method are divided into numerical methods tree method, Monte Carlo simulation and difference of three. According to the Law on the subject of partial differential equations assets and derivatives to build their own different characteristics of partial differential equations, according to the different conditions for solving the border, of course, a lot of partial differential equations analytical solution for a considerable degree of difficulty, you can resort to numerical methods.
Traditional interest rate derivatives pricing is based on the BLACK-SCHOLES formula, but the formula to interest rates and asset price volatility as constant, interest rates do not meet the characteristics of the movement. This leads to a series of interest rate on the term structure of volatility models and model. There are many types of models to explain the term structure of interest rates, dynamic process, is divided into general equilibrium model and two types of arbitrage pricing model. Equilibrium model, the initial term structure is a model of input in the no-arbitrage model, it is a model of the output. No-arbitrage model has the advantage of reality and be able to accurately match the term structure. These two types of single-factor model of the model analysis, and easy to use, but its defect is very difficult to fit the observed yield curve, as well as fluctuations in interest rates. Multi-factor model better able to make up for the single-factor model of the defect, but is often difficult to solve. The model has advantages and disadvantages, according to the actual situation may choose to model. Volatility of B-S formula can not be directly observed , through the general history of volatility or implied volatility strike. B-S formula for fluctuations in the rate constant for the lack of improvement in two ways: First, the development of more sophisticated models such as stochastic volatility model, and the other is trading in the B-S formula developed on some of the volatility of the correction techniques, the use of volatility And the implementation of the price and duration of the relationship between the correction.
In this paper, several of our existing interest rate derivatives pricing formula, including convertible bonds, the interest rate swap, forward rate agreements, long-term bonds. Analysis of China's these types of interest rate derivatives market developments, pointing out that their transactions are in the market price of the existence of inaccuracy. Benchmark interest rates in response to interest rate derivatives pricing in the important role of this article compared the number of China's main interest rate: one-year time deposit interest rates, government bonds and treasury stock repurchase rate, Shibor interest rates in line with the benchmark interest rate. Finally, summed up China's interest rate derivatives pricing benchmark interest rates there are construction defects, the strong homogeneity of the trading parts, and lack of credit system, market mechanisms, such as the existence of the defects of market factors.
引文
1约翰.赫尔,期权、期货和衍生证券(第三版),张陶伟译,北京:华夏大学出版社,2000
2郑振龙,林海.中国可转换债券定价研究.厦门大学学报(哲学社会科学版),2004(2):93-99.
3郑小迎,陈军,陈金贤.可转换债券定价模型探讨系统工程理论与实践,2000(8):24-28.
4于瑾.利率期限结构研究.中国国家图书馆:对外经济贸易大学,2002
5李和金.非参数利率期限结构模型与混合债券的定价研究.中国国家图书馆上海交通大学,2002
6郑振龙,林海.中国市场利率期限结构的静态估计武汉金融,2003(3):33-36.
7郑振龙,林海中国利率期限结构理论与应用厦门大学出版社2004
8滋维.博迪,亚历克斯.凯恩,艾伦J.马库斯等著,朱宝宪,吴洪,赵冬青等译,投资学,北京:机械工业出版社,2004
9宋逢明,金融工程原理-无套利均衡分析,北京:清华大学出版社,1999
10罗伯特.L.麦克唐纳衍生产品市场钱立译,北京中国人民大学出版社2006
11金冶明,随机分析基础及其应用,国防工业出版社,2003
12唐纳德.R. ,今井贤志,马克.梅斯勒高级金融风险管理朱世武译北京中国人民出版社2006
13 Salih Neftci金融衍生工具中的数学(第2版)朱波译成都西南财经大学出版社2008
14 2008年上半年银行间市场运行报告中国人民银行2008
15王兴安利率模型上海上海财经大学出版社2007
1 Black, F. and P. Karasinski, 1991 Bond and Option Pricing When Short Rates are Lognormal , Financial Analysis Journal, July-August, 52-59
2 Ingersoll J E , A contingent--claims valuation of convertible securities,Journal of Financial Economics,1977,4(2):289-322
3 Merton,R.C,Theory of rational option pricing,Bell Journal of Economics and Management Science,1973(4):367-382
4 Duffie,D.and K.Singleton,Modeling Term Structures of Defaultable Bonds,Review of Financial Studies,1999(12):687-720
5 Heath,D,R.A.Jarrow,and A.Morton,Bond Pricing and the Term Structure of Interest Rates:A New Methodology for Contingent Claims Valuation,Econometrica,1992(60):77-105
6 Jessica James and Nick Webber,《Interest Rate Modeling》, Wiley. Corporate Use of Interest Rate Swaps: Theory and Evidence,Haitao Li.,Connie X. Mao,J Journal of Banking and Finance
7 Breeden, D. and R. Litzenberger 1978 , Prices of state-contingent claims implicit in options prices, Journal of Business 51, 621-652
8 Duffie, Darrell, and Chi-fu Huang, 1985, Implementing Arrow-Debreu equilibria by continuous trading of long-lived securities, Econometrica 53, 1337-1356.
9 Grossman, S. 1988 , An analysis of the implications for stock and futures price volatility of program trading and dynamic hedging strategies, Journal of Business 61, pp. 275-298
10 Merton, R. C. 1990 , The financial system and economic performance, Journal of Financial S ervices Research 4, pp. 263-300
11 Rubinstein, Mark, 1994 , Implied binominal trees, Journal of Finance 49, pp. 771-818.
12 Ho,T.and Lee,S.B.Term structure movements and the pricing of interest rate contingent claims.Journal of Finance,1986.(41):1011-1030
13 Litterman,R.and Scheinkman,J.Common Factors Affecting Bond Returns.Journal of Fixed Income,1991.(1):54-61
14 Stanton,R.A nonparametric model of term structure dynamics and the market price of interest rate risk.Journal of Finance,1997.(52):1973-2002
15 Longstaff,F.A.and Schwartz.E.S.Interest rate volatility and the term structure:a two-factor general equilibrium model.Journal of Finance.1992,(47):1259-1282
16 Vetzal,K .An improved finite difference approach to fitting the initial term structure.The Journal of Fixed Income,1998.pp.62-81
17 Jamshidian.Libor and swap market models and measures,Finance and Stochastics,1997.(1):291-328
18 Brennan M.J. ,Schwartz E.S.Convertible bonds:Valuation and optimal strategies for all and conversion.The Journal of Finance,1997.32(5):1699-1715
19 Kent T.Saunders.The interest rate swap:Theory and evidence.Journal of Corporate Finance, 1999:55-78
20 Ravi Jagannathan,Andrew Kaplin and Steve Sun. An evaluation of multi-factor CIR models using LIBOR,swap rates,and cap and swaption prices.Journal of Economics,2003.(116):113~146
2郑振龙,林海.中国可转换债券定价研究.厦门大学学报(哲学社会科学版),2004(2):93-99.
3郑小迎,陈军,陈金贤.可转换债券定价模型探讨系统工程理论与实践,2000(8):24-28.
4于瑾.利率期限结构研究.中国国家图书馆:对外经济贸易大学,2002
5李和金.非参数利率期限结构模型与混合债券的定价研究.中国国家图书馆上海交通大学,2002
6郑振龙,林海.中国市场利率期限结构的静态估计武汉金融,2003(3):33-36.
7郑振龙,林海中国利率期限结构理论与应用厦门大学出版社2004
8滋维.博迪,亚历克斯.凯恩,艾伦J.马库斯等著,朱宝宪,吴洪,赵冬青等译,投资学,北京:机械工业出版社,2004
9宋逢明,金融工程原理-无套利均衡分析,北京:清华大学出版社,1999
10罗伯特.L.麦克唐纳衍生产品市场钱立译,北京中国人民大学出版社2006
11金冶明,随机分析基础及其应用,国防工业出版社,2003
12唐纳德.R. ,今井贤志,马克.梅斯勒高级金融风险管理朱世武译北京中国人民出版社2006
13 Salih Neftci金融衍生工具中的数学(第2版)朱波译成都西南财经大学出版社2008
14 2008年上半年银行间市场运行报告中国人民银行2008
15王兴安利率模型上海上海财经大学出版社2007
1 Black, F. and P. Karasinski, 1991 Bond and Option Pricing When Short Rates are Lognormal , Financial Analysis Journal, July-August, 52-59
2 Ingersoll J E , A contingent--claims valuation of convertible securities,Journal of Financial Economics,1977,4(2):289-322
3 Merton,R.C,Theory of rational option pricing,Bell Journal of Economics and Management Science,1973(4):367-382
4 Duffie,D.and K.Singleton,Modeling Term Structures of Defaultable Bonds,Review of Financial Studies,1999(12):687-720
5 Heath,D,R.A.Jarrow,and A.Morton,Bond Pricing and the Term Structure of Interest Rates:A New Methodology for Contingent Claims Valuation,Econometrica,1992(60):77-105
6 Jessica James and Nick Webber,《Interest Rate Modeling》, Wiley. Corporate Use of Interest Rate Swaps: Theory and Evidence,Haitao Li.,Connie X. Mao,J Journal of Banking and Finance
7 Breeden, D. and R. Litzenberger 1978 , Prices of state-contingent claims implicit in options prices, Journal of Business 51, 621-652
8 Duffie, Darrell, and Chi-fu Huang, 1985, Implementing Arrow-Debreu equilibria by continuous trading of long-lived securities, Econometrica 53, 1337-1356.
9 Grossman, S. 1988 , An analysis of the implications for stock and futures price volatility of program trading and dynamic hedging strategies, Journal of Business 61, pp. 275-298
10 Merton, R. C. 1990 , The financial system and economic performance, Journal of Financial S ervices Research 4, pp. 263-300
11 Rubinstein, Mark, 1994 , Implied binominal trees, Journal of Finance 49, pp. 771-818.
12 Ho,T.and Lee,S.B.Term structure movements and the pricing of interest rate contingent claims.Journal of Finance,1986.(41):1011-1030
13 Litterman,R.and Scheinkman,J.Common Factors Affecting Bond Returns.Journal of Fixed Income,1991.(1):54-61
14 Stanton,R.A nonparametric model of term structure dynamics and the market price of interest rate risk.Journal of Finance,1997.(52):1973-2002
15 Longstaff,F.A.and Schwartz.E.S.Interest rate volatility and the term structure:a two-factor general equilibrium model.Journal of Finance.1992,(47):1259-1282
16 Vetzal,K .An improved finite difference approach to fitting the initial term structure.The Journal of Fixed Income,1998.pp.62-81
17 Jamshidian.Libor and swap market models and measures,Finance and Stochastics,1997.(1):291-328
18 Brennan M.J. ,Schwartz E.S.Convertible bonds:Valuation and optimal strategies for all and conversion.The Journal of Finance,1997.32(5):1699-1715
19 Kent T.Saunders.The interest rate swap:Theory and evidence.Journal of Corporate Finance, 1999:55-78
20 Ravi Jagannathan,Andrew Kaplin and Steve Sun. An evaluation of multi-factor CIR models using LIBOR,swap rates,and cap and swaption prices.Journal of Economics,2003.(116):113~146