基于SVJD动态扩展模型的中国固定收益证券定价研究
|
摘要
自上世纪九十年代以来,中国的市场利率以及固定收益证券市场发生了以下几个显著的变化:第一,中国的利率市场化改革已经取得了显著的成效,市场利率的动态行为特征发生了显著的变化;第二,利率成为央行调节宏观经济的重要工具变量之一,宏观经济状况对利率的影响越来越重要;第三,中国固定收益证券市场取得了长足的发展;第四,投资者和金融机构所面临的利率风险加剧了。
上述变化引出了以下既有理论意义、又有现实应用价值、且紧密联系的三个问题。第一,中国市场利率的动态行为特征及宏观经济状况对利率行为的影响;第二,固定收益证券的定价,尤其是宏观经济变量对固定收益证券价格的影响;第三,收益率曲线的形状及其变动特征,即利率期限结构问题。
论文在分析关于这三个问题现有研究不足的基础上,进一步对它们进行了深入的研究,得到以下主要结果:
1.中国市场利率的动态行为特征
中国市场利率不仅具有均值回复和时变波动率特征,还具有跳跃行为。通货膨胀率以及利率水平偏离其长期趋势水平的幅度是决定利率跳跃强度的重要因素,偏离幅度越大,利率发生跳跃的可能性越大。
2.固定收益证券定价
以中国市场利率动态行为特征为依据,论文构建了扩展SVJD动态利率期限结构模型,并给出了扩展模型下零息债券及其欧式看涨期权的封闭定价公式,以及抵押贷款支持证券的蒙特卡罗模拟数值定价方法。在研究这些固定收益证券价格的性质时,论文尤其关注通货膨胀率以及利率的跳跃行为对证券价格的影响。
零息债券价格具有如下性质:第一,零息债券价格关于通货膨胀率z的单调性随着短期利率跳跃幅度均值μ_J符号的变化而变化,μ_J为负(正)数时,零息债券价格是z的增(减)函数;第二,零息债券价格关于z长期趋势水平(?)的单调性也取决于μ_J的符号,μ_J小(大)于零时,零息债券价格是(?)的减(增)函数;第三,零息债券价格是宏观经济波动率σ_z的增函数,而它关于z均值回复速度κ_z的单调性不仅取决于z与(?)的相对大小关系,还取决于μ_J的符号;第四,当σ_z比较小时,零息债券价格是μ_J的减函数;但当σ_z比较大时,随着μ_J的增加,零息债券价格先下降后上升;零息债券价格总是短期利率跳跃幅度标准差σ_J的增函数、凸函数;第五,零息债券价格波动率是z、σ_z以及σ_J的增函数。
零息债券欧式看涨期权价格具有如下性质:第一,μ_J大(小)于零时,期权价格是z的减(增)函数;第二,期权价格是σ_z的增函数;第三,期权价格是μ_J的减函数,是σ_J的增函数。
抵押贷款支持证券价格具有如下性质:第一,抵押贷款支持证券价格是z的减函数,当μ_J小于零(足够大)时,它是宏观经济波动率σ_z的增(先增后减)函数;第二,抵押贷款支持证券价格是房产价格h的增函数,是h波动率σ_h的减函数;第三,σ_z较小(大)时,抵押贷款支持证券的价格是μ_J的增(减)函数;抵押贷款支持证券价格是σ_J的减函数。
3.收益率曲线的形状及其变动特征
基于零息债券的定价公式,论文推导了扩展模型生成的收益率曲线,研究了收益率曲线的形状及其变动特征。
就收益率曲线形状而言,扩展模型能够生成递增、递减、先递增后递减以及先递减后递增等多种复杂形状的收益率曲线。当短期利率r与其长期趋势水平(?)比较接近时,收益率曲线的单调性与μ_J的符号密切相关,μ_J大于零时,收益率曲线往往会先递增、后递减;反之,收益率曲线就递减。
就收益率曲线的变动特征而言,扩展模型能够生成向上移动、向下移动以及扭曲变动等多种形式的收益率曲线变动方式。但是,只有通货膨胀率状态变量z的增加能够使得收益率曲线发生扭曲变动。
z主要对收益率曲线的前端部分产生影响,而利率的跳跃行为对收益率曲线前端部分的影响强于其对收益率曲线尾端部分的影响。
z、z的波动率σ_z以及σ_J增加时,收益率的波动率也增加。
In the last 20 years,several significant changes have taken place in the market interest rate and the fixed income security market of China.First,great progress has been made in the interest rate reform,and the dynamics of the market interest rate has changed significantly.Second,interest rate has been an important policy instrument of the central bank to adjust the macro economy,so the condition of the macro economy has great impact on the behavior of the interest rate.Third,extensive development has achieved in the fixed income security markets.Fourth,interest rate risk that the investors and financial institutions are faced with has been enlarged.
Such changes result in the following three theoretically meaningful,practically valuable problems which are related with each other closely.First,the dynamics of Chinese market interest rate and the impact on the behavior of the interest rate imposed by the macro economy.Second,pricing of the fixed income securities and the influence on the prices that the macro economic variables have.Third,shape and shift of the yield curve,that is to say,the problem of the term structure of interest rate.
Based on the analysis of the shortcomings of the existing research about the previous three problems,this dissertation studies them to a deeper extent.The results are as follows:
1.Dynamics of Chinese market interest rate
There are not only mean reversion and time-varying volatility features in the dynamics of Chinese market rate,but also jump behavior in it.Deviations from the level of the inflation and interest rate to their respective long term level are important determinants of the jump intensity of the interest rate.The bigger of the deviations, the larger of the probability that the interest rate will jump.
2.Fixed income securities pricing
Based on the dynamics of Chinese market interest rate,the dissertation constructed an extended SVJD dynamic interest rate model.Closed form pricing formulas of zero-coupon bond and its option are derived under the extended model, and the Monte Carlo numerical pricing methods of the mortgage-backed security (MBS) are also performed.When studying the properties of the prices of these securities,the dissertation focuses on the impacts imposed by inflation and the jump behavior of the interest rate.
Properties of the zero-coupon bond price are as follows:(1) the monotony of the zero-coupon bond price as a function of inflation z alters according to the sign of the mean of the jump size of the short rateμ_J whenμ_J is negative(positive),the price is an increasing(a decreasing) function of z;(2) whenμ_J is smaller(bigger) than zero, zero-coupon bond price is a decreasing(an increasing) function of the long term level of inflation,(?);(3) zero-coupon bond price is an increasing function of the volatility of the macro economy,σ_z;its monotony as a function ofκ_z,the mean reversion rate of z,depends not only on the relative size between z and(?),but also on the sign ofμ_J;(4) whenσ_z is small,the price is a decreasing function ofμ_J,but whenσ_z is large, zero-coupon bond price is first decreasing then increasing asμ_J increases;the price is a increasing and convex function of the standard deviation of the jump size aσ_J;(5) the volatility of the zero-coupon price is a increasing function of z,σ_z andσ_J.
Properties of the price of the European call option on the zero-coupon bond are as follows:(1) asμ_J is bigger(smaller) than zero,option price is a decreasing(an increasing) function of z;(2) option price is an increasing function ofσ_z;(3) option price is a decreasing function ofμ_J,and an increasing function ofσ_J.
Properties of the price of MBS are as follows:(1) it is a decreasing function of z; whenμ_J is smaller than zero(large enough),it is an increasing(a first increasing then decreasing) function ofσ_z;(2) the price of MBS is an increasing function of house price,h,a decreasing function of the volatility of house priceσ_h;(3) whenσ_z is small (large),the price of MBS is an increasing(a decreasing) function ofμ_J,it is also a decreasing function ofσ_J.
3.Shape and shift of the yield curve
From the zero-coupon bond pricing formula,the dissertation derives the yield curve generated by the extended model,and then investigates the shape and shift of the yield curve.
As to the shape of the yield curve,the extended model can generate decreasing, increasing,first increasing then decreasing and first decreasing then increasing types of shape.When short rate r is close to its long term level(?),the monotony of the yield curve is closely related with the sign ofμ_J,asμ_J is bigger than zero,the yield curve will first increase,and then decrease;conversely,the yield curve will decrease.
As to the shift of the yield curve,the extended model can generate upward, downward and twisted shifts.But only the changes of the inflation can generate twisted shift of the yield curve.
z mainly impacts the short end of the yield,and the impact that the jump behavior has on the short end is more influential than on the long end of the yield curve. As z,σ_z andσ_J increase respectively,yield volatility increases accordingly
上述变化引出了以下既有理论意义、又有现实应用价值、且紧密联系的三个问题。第一,中国市场利率的动态行为特征及宏观经济状况对利率行为的影响;第二,固定收益证券的定价,尤其是宏观经济变量对固定收益证券价格的影响;第三,收益率曲线的形状及其变动特征,即利率期限结构问题。
论文在分析关于这三个问题现有研究不足的基础上,进一步对它们进行了深入的研究,得到以下主要结果:
1.中国市场利率的动态行为特征
中国市场利率不仅具有均值回复和时变波动率特征,还具有跳跃行为。通货膨胀率以及利率水平偏离其长期趋势水平的幅度是决定利率跳跃强度的重要因素,偏离幅度越大,利率发生跳跃的可能性越大。
2.固定收益证券定价
以中国市场利率动态行为特征为依据,论文构建了扩展SVJD动态利率期限结构模型,并给出了扩展模型下零息债券及其欧式看涨期权的封闭定价公式,以及抵押贷款支持证券的蒙特卡罗模拟数值定价方法。在研究这些固定收益证券价格的性质时,论文尤其关注通货膨胀率以及利率的跳跃行为对证券价格的影响。
零息债券价格具有如下性质:第一,零息债券价格关于通货膨胀率z的单调性随着短期利率跳跃幅度均值μ_J符号的变化而变化,μ_J为负(正)数时,零息债券价格是z的增(减)函数;第二,零息债券价格关于z长期趋势水平(?)的单调性也取决于μ_J的符号,μ_J小(大)于零时,零息债券价格是(?)的减(增)函数;第三,零息债券价格是宏观经济波动率σ_z的增函数,而它关于z均值回复速度κ_z的单调性不仅取决于z与(?)的相对大小关系,还取决于μ_J的符号;第四,当σ_z比较小时,零息债券价格是μ_J的减函数;但当σ_z比较大时,随着μ_J的增加,零息债券价格先下降后上升;零息债券价格总是短期利率跳跃幅度标准差σ_J的增函数、凸函数;第五,零息债券价格波动率是z、σ_z以及σ_J的增函数。
零息债券欧式看涨期权价格具有如下性质:第一,μ_J大(小)于零时,期权价格是z的减(增)函数;第二,期权价格是σ_z的增函数;第三,期权价格是μ_J的减函数,是σ_J的增函数。
抵押贷款支持证券价格具有如下性质:第一,抵押贷款支持证券价格是z的减函数,当μ_J小于零(足够大)时,它是宏观经济波动率σ_z的增(先增后减)函数;第二,抵押贷款支持证券价格是房产价格h的增函数,是h波动率σ_h的减函数;第三,σ_z较小(大)时,抵押贷款支持证券的价格是μ_J的增(减)函数;抵押贷款支持证券价格是σ_J的减函数。
3.收益率曲线的形状及其变动特征
基于零息债券的定价公式,论文推导了扩展模型生成的收益率曲线,研究了收益率曲线的形状及其变动特征。
就收益率曲线形状而言,扩展模型能够生成递增、递减、先递增后递减以及先递减后递增等多种复杂形状的收益率曲线。当短期利率r与其长期趋势水平(?)比较接近时,收益率曲线的单调性与μ_J的符号密切相关,μ_J大于零时,收益率曲线往往会先递增、后递减;反之,收益率曲线就递减。
就收益率曲线的变动特征而言,扩展模型能够生成向上移动、向下移动以及扭曲变动等多种形式的收益率曲线变动方式。但是,只有通货膨胀率状态变量z的增加能够使得收益率曲线发生扭曲变动。
z主要对收益率曲线的前端部分产生影响,而利率的跳跃行为对收益率曲线前端部分的影响强于其对收益率曲线尾端部分的影响。
z、z的波动率σ_z以及σ_J增加时,收益率的波动率也增加。
In the last 20 years,several significant changes have taken place in the market interest rate and the fixed income security market of China.First,great progress has been made in the interest rate reform,and the dynamics of the market interest rate has changed significantly.Second,interest rate has been an important policy instrument of the central bank to adjust the macro economy,so the condition of the macro economy has great impact on the behavior of the interest rate.Third,extensive development has achieved in the fixed income security markets.Fourth,interest rate risk that the investors and financial institutions are faced with has been enlarged.
Such changes result in the following three theoretically meaningful,practically valuable problems which are related with each other closely.First,the dynamics of Chinese market interest rate and the impact on the behavior of the interest rate imposed by the macro economy.Second,pricing of the fixed income securities and the influence on the prices that the macro economic variables have.Third,shape and shift of the yield curve,that is to say,the problem of the term structure of interest rate.
Based on the analysis of the shortcomings of the existing research about the previous three problems,this dissertation studies them to a deeper extent.The results are as follows:
1.Dynamics of Chinese market interest rate
There are not only mean reversion and time-varying volatility features in the dynamics of Chinese market rate,but also jump behavior in it.Deviations from the level of the inflation and interest rate to their respective long term level are important determinants of the jump intensity of the interest rate.The bigger of the deviations, the larger of the probability that the interest rate will jump.
2.Fixed income securities pricing
Based on the dynamics of Chinese market interest rate,the dissertation constructed an extended SVJD dynamic interest rate model.Closed form pricing formulas of zero-coupon bond and its option are derived under the extended model, and the Monte Carlo numerical pricing methods of the mortgage-backed security (MBS) are also performed.When studying the properties of the prices of these securities,the dissertation focuses on the impacts imposed by inflation and the jump behavior of the interest rate.
Properties of the zero-coupon bond price are as follows:(1) the monotony of the zero-coupon bond price as a function of inflation z alters according to the sign of the mean of the jump size of the short rateμ_J whenμ_J is negative(positive),the price is an increasing(a decreasing) function of z;(2) whenμ_J is smaller(bigger) than zero, zero-coupon bond price is a decreasing(an increasing) function of the long term level of inflation,(?);(3) zero-coupon bond price is an increasing function of the volatility of the macro economy,σ_z;its monotony as a function ofκ_z,the mean reversion rate of z,depends not only on the relative size between z and(?),but also on the sign ofμ_J;(4) whenσ_z is small,the price is a decreasing function ofμ_J,but whenσ_z is large, zero-coupon bond price is first decreasing then increasing asμ_J increases;the price is a increasing and convex function of the standard deviation of the jump size aσ_J;(5) the volatility of the zero-coupon price is a increasing function of z,σ_z andσ_J.
Properties of the price of the European call option on the zero-coupon bond are as follows:(1) asμ_J is bigger(smaller) than zero,option price is a decreasing(an increasing) function of z;(2) option price is an increasing function ofσ_z;(3) option price is a decreasing function ofμ_J,and an increasing function ofσ_J.
Properties of the price of MBS are as follows:(1) it is a decreasing function of z; whenμ_J is smaller than zero(large enough),it is an increasing(a first increasing then decreasing) function ofσ_z;(2) the price of MBS is an increasing function of house price,h,a decreasing function of the volatility of house priceσ_h;(3) whenσ_z is small (large),the price of MBS is an increasing(a decreasing) function ofμ_J,it is also a decreasing function ofσ_J.
3.Shape and shift of the yield curve
From the zero-coupon bond pricing formula,the dissertation derives the yield curve generated by the extended model,and then investigates the shape and shift of the yield curve.
As to the shape of the yield curve,the extended model can generate decreasing, increasing,first increasing then decreasing and first decreasing then increasing types of shape.When short rate r is close to its long term level(?),the monotony of the yield curve is closely related with the sign ofμ_J,asμ_J is bigger than zero,the yield curve will first increase,and then decrease;conversely,the yield curve will decrease.
As to the shift of the yield curve,the extended model can generate upward, downward and twisted shifts.But only the changes of the inflation can generate twisted shift of the yield curve.
z mainly impacts the short end of the yield,and the impact that the jump behavior has on the short end is more influential than on the long end of the yield curve. As z,σ_z andσ_J increase respectively,yield volatility increases accordingly
引文
[1]范龙振.上交所债券利率期限结构与两因子Vasicek模型[J].复旦学报(自然科学版),2003,5:773-778.
[2]范龙振,王晓丽.上交所国债市场利率期限结构及其信息价值[J].管理工程学报,2004,1:72-75.
[3]林海,郑振龙.中国利率期限结构:理论及应用[M].北京:中国财经出版社,2004.
[4]梁福涛.我国利率调整的通货膨胀因素模型估计[J].国际商务研究,2005,4:17-24.
[5]刘金全,王勇,张鹤.利率期限结构与宏观经济因素的动态相依性--基于VAR模型的经验研究[J].财经研究,2007,33(5):126-133.
[6]刘康兵,申朴,李达.利率与通货膨胀:一个费雪效应的经验分析[J].财经研究,2003,29(2):24-29.
[7]李和金,郑兴山,李湛.非参数利率期限结构模型的实证检验[J].上海交通大学学报,2003,4:607-609.
[8]潘冠中,邵斌.单因子利率模型的极大似然估计--对中国利率的实证分析[J].财经研究,2004,10:62-69.
[9]石晶莹.我国的利率市场化改革实践综述[J].绥化学院学报,2007,27(1):19-23.
[10]孙继国,伍海华.同业拆借利率与宏观经济变量之关系研究[J].广东金融学院学报,2004,19(5):13-18.
[11]孙丽瑶.同业拆借利率与宏观经济变量协整关系的实证分析[J].沿海企业与科技,2006,10:32-34.
[12]王国刚,何旭强.债券市场发展:2005年回顾与2006年创新[J].福建论坛(人文社会科学版),2006,5:13-16.
[13]王国刚,何旭强.债券市场:创新发展与市场走势--2006年回顾与2007年展望[J].国际经济评沦,2007,2:35-39.
[14]吴艳.我国国债收益率曲线的实证分析[J].内蒙古财经学院学报,2004,3:44-47.
[15]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,2002,3:22-25.
[16]颜炬,石磊.我国银行间债券市场的发展[J].中国金融,2007,8:31-33.
[17]洪永淼,林海.中国市场利率动态研究-基于短期国债回购利率的实证分析[J].经济学季刊,2006,1:511-532。
[18]阎衍.2008年固定收益产品发行规模有望破万亿[N].http://finance.cctv.com/20080306/101784.shtml,2008.
[19]Ahn,C.M.,Thompson,H.E.Jump-Diffusion Processes and the Term Structure of Interest Rates [J].Journal of Finance,1988,43(1):155-174.
[20]A(l|")t-Sahalia,Y.Estimating Continuous-Time Models with Discretely Sampled Data[J].Working Paper,http://www.princeton.edu/-yacine/eswc2005.pdf,2002.
[21]A(l|")t-Sahalia,Y.,Kimmel,R.Maximum Likelihood Estimation of Stochastic Volatility Models[J].Journal of Financial Economics,2007,No.83:413-452.
[22]Akesson,F.,Lehoczky,J.P.Path Generation for Quasi-Monte Carlo Simulation of Mortgage-Backed Securities[J].Management Science,2000,46(9):1171-1187.
[23]Andersen,L.A Simple Approach to the Pricing of Bermudan Swaptions in the Multi-Factor Libor Market Model[J].Journal of Computational Finance,2000,3(2):1-32.
[24]Andersen,T.G.,Benzoni,L.,and Lund J.Stochastic Volatility,Mean Drift,and Jumps in the Short-Term Interest Rate[J].Working Paper,http://www.jesperlund.com/papers/abl2.pdf,2004.
[25]Ang,A.,Piazzesi,Mo A No-Arbitrage Vector Autoregression of Term Structure Dynamics with Macroeconomic and Latent Variables[J].Journal of Monetary Economics,2003,50:745-787.
[26]Ames,W.F.Numerical Methods for Partial Differential Equations(Second Edition)[M].Academic Press,1977.
[27]Asgharian,H.,Bengtsson,C.Jump Spillover in International Equity Markets[J].Journal of Financial Econometrics,2006,4(2):167-203.
[28]Askin,D,J.,Curtin,W.J.and Lowell,L.Forecasting Prepayment Rates for Mortgage-Backed Securities[A].In The Handbook of Mortgage-Backed Securities[M].1988.
[29]Bakshi,G.,Cao,C.,Chen,Z.W.Empirical Performance of Alternative Option Pricing Models[J].Journal of Finance,1997,No.52:2003-2049.
[30]Balduzzi,P.,Das,S.R.,Foresi,S.and Sundaram,R.A Simple Approach to Three-Factor Affine Term Structure Models[J].The Journal of Fixed Income,1996,6(3):43-53.
[31]Bali,T.G.Testing the Empirical Performance of Stochastic Volatility Models of the Short-Term Interest Rate[J].The Journal of Financial and Quantitative Analysis,2000,35(2):191-215.
[32]Ball,C.,Torous,W.N.A Simplified Jump Process for Common Stock Returns[J].Journal of Financial and Quantitative Analysis,1983,18(1):53-65.
[33]Barraquand,J.Numerical Valuation of High Dimensional Multivariate European Securities[J].Management Science,1995,No.41:1882-1891.
[34]Beaglehole,D.R.,Tenney,M.S.Corrections and Additions to "A Nonlinear Equilibrium Model of the Term Structure of Interest Rates"[J].Journal of Financial Economics,1992,32(3):345-353.
[35]Beaglehole,D.R.,Tenney,M.S.General Solutions of Some Interest Rate-Contingent Claim Pricing Equations[J].The Journal of Fixed Income,1991,No.1:69-83.
[36]Black,E,Derman,E.and Toy,W.A One-Factor Model of Interest Rates and Its Application to Treasury Bond Options[J].Financial Analysts Journal,1990,46(1):33-39.
[37]Broadie,M.,Glasserman,P.Pricing American-Style Securities Using Simulation[J].Journal of Economic Dynamics and Control,1997b,21(8-9):1323-1352.
[38]Bodie,Z.,Merton,R.C.金融学[M].北京:中国人民大学出版社,2000:189.
[39]Boyle,P.,Broadie,M.and Glasserman,P.Monte Carlo Methods for Security Pricing[J].Journal of Economic Dynamics and Control,1997,21(8-9):1267-1321.
[40]Brandimarte,P.Numerical Methods in Finance[M].New York:John Wiley & Sons,Inc,2002:Chapter 4 and 7.
[41]Brennan,M.J.,Schwartz,E.S.A Continuous Time Approach to the Pricing of Bonds[J].Journal of Banking and Finance,1979,No.3:133-155.
[42]Brennan,M.J.,Schwartz,E.S.The Valuation of American Put Options[J].Journal of Finance,1977,32(2):449-462.
[43]Black,F.,Karasinski,P.Bond and Option Pricing when Short Rates are Lognormal[J].Financial Analysts Journal,1991,47(4):52-59.
[44]Caflisch,R.E.,Morokoff,W.and Owen,A.Valuation of Mortgage Backed Securities Using Brownian Bridges to Reduce Effective Dimension[J].Journal of Computational Finance,1997,1(1):27-46.
[45]Carr,P.,Yang,G.Simulating Bermudan lnterest Rate Derivatives[J].Working Paper,Morgan Stanley and Open Link Financial,1997,December.
[46]Chacko,G.,Das,S.Pricing Interest Rate Derivatives." A General Approach[J].The Review of Financial Studies,2002,15(1):195-241.
[47]Chan,K.C.,Karolyi,G.A.,Longstaff,F.A.and Sanders,A.B.An Empirical Comparison of Alternative Models oft he Short Term Interest Rate[J].Journal of Finance,1992,47(3):1209-1227.
[48]Chen,L.Stochastic Mean and Stochastic Volatility----A Three-Factor Model of the Term Structure of Interest Rates and Its Applications in Derivatives Pricing and Risk Management[J].Financial Markets,Institutions & Instruments,1996,5(1):1-88.
[49]Chen,L.Interest Rate Dynamics,Derivatives Pricing,and Risk Management[M].Springer,1996.
[50]Chert,R.R.,Scott,L.Stochastic Volatility and Jumps in Interest Rates:An Empirical Analysis[J].Working Paper,http://www.rci.rutgers.edu/-rchen/JumpsStochVolPaper.pdf,2004.
[51]Claus Munk.Fixed Income Analysis:Securities,Pricing,and Risk Management[M].http://www.sam.sdu.dk/-cmu/noter/FIAjan05.pdf,2004.
[52]Cont,R.and Tankov,P.Financial Modelling With Jump Processes[M].Chapman & Hall,CRC Financial Mathematics Series,2004:274-275.
[53]Cox,J.C.,Ingersoll,J.E.and Ross,S.A.A Theory of the Term Structure of Interest Rates[J].Econometrica,1985b,53(2):385-407.
[54]Cox,J.C.,Ross,S.A.and Rubinstein,M.Option Pricing:A Simplified Approach[J].Journal of Financial Economics,1979,No.7:229-263.
[55]Dai,Q.,Singleton,K.J.Specification Analysis of Affine Term Structure Models[J].The Journal of Finance,2000,55(5):1943-1978.
[56]Das,S.R.The Surprise Element:Jumps in Interest Rates[J].Journal of Econometrics,2002,No.106:27-65.
[57]Das,S.R.,Foresi,S.Exact Solutions for Bond and Options Prices with Systematic Jump Risk[J].Review of Derivatives Research,1996,No.1:7-24.
[58]Diebold,F.X.,Rudebusch,G.D.and Aruoba,S.B.The Macro Economy and the Yield Curve:A Dynamic Latent Factor Approach[J].Journal of Econometrics,2006,No.131:309-338.
[59]Duan,J.C.Augmented GARCH(p,q) Process and Its Diffusion Limit[J].Journal of Econometrics,1997,No.79:97-127.
[60]Duffle,D.Dynamic Asset Pricing Theory(Third Edition)[M].Princeton:Princeton University Press,2001:101-131.
[61]Duffle,D.,Kan,R.A Yield-Factor Model of Interest Rates[J].Mathematical Finance,1996,6(4): 379-406.
[62]Duffle,D.,Pan,J.,and Singleton,K.Transform Analysis and Asset Pricing for Affine Jump-Diffusions[J].Econometrica,2000,68(6):1343-1376.
[63]Durham,J.B.Jump-Diffusion Processes and Affine Term Structure Models:Additional Closed-Form Approximate Solutions,Distributional Assumptions for Jumps,and Parameter Estimates[J].Finance and Economics Discussion Series 2005-53,Board of Governors of the Federal Reserve System(U.S.),2005.
[64]Elerian,O.,Chib,S.,and Shephard,N.Likelihood Inference for Discretely Observed Nonlinear Diffusions[J].Econometrica,2001,No.69:959-994.
[65]Engle,R.F.Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of UK Inflation[J].Econometrica,1982,No.50:987-1008.
[66]Eraker,B.MCMC Analysis of Diffusion Models with Applications to Finance[J].Journal of Econometrics,2001,No.19:177-191.
[67]Estrella,A.,Hardouvelis,G.A.The Term Structure as A Predictor of Real Economic Activity[J].Journal of Finance,1991,46:555-576.
[68]Estrella,A.,Mishkin,F.S.Predicting US Recessions:Financial Variables as Leading Indicators [J].Review of Economics and Statistics,1998,80:45-61.
[69]Faria,J.R.,Carneiro,F.G.Does High Inflation Affect Growth the Long and Short Run?[J].Journal of Applied Economics,2001,4(1):89-105.
[70]Finnerty,J.D.Exact Formulas for Pricing Bonds and Options When Interest Rate Diffusions Contain Jumps[J].The Journal of Financial Research,2005,ⅩⅩⅧ(3):319-341.
[71]Gallant,A.R.,Tanchen,G.Testing Continuous-Time Models of the Spot Interest Rate[J].Review of Financial Studies,1996,No.3:197-215.
[72]Hamilton,J.Time Series Analysis[M].Princeton:Princeton University Press,1994:Chapter 5.
[73]He,H.Convergence from Discrete - to Continuous - Time Contingent Claims Prices[J].The Review of Financial Studies,1990,3(4):523-546.
[74]Heston.A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options[J].Review of Financial Studies,1993,No.6:327-343.
[75]Ho,T.S.Y.,Lee,S.B.Term Structure Movements and Pricing Interest Rate Contingent Claims[J].Journal of Finance,1986,41(5):1011-1029.
[76]Hong,Y.M.,Li,H.Nonparametric Specification Testing for Continuous-Time Models with Applications to Term Structure of Interest Rates[J].Review of Financial Studies,2004,18(1): 37-84.
[77]Hong,Y.,Li,H.and Zhao,F.Out-of-Sample Performance of Discrete-Time Spot Interest Rate Models[J].Journal of Business and Economics Statistics,2004,22(4):457-473.
[78]Hull,J.Options,Futures,and Other Derivatives(Fifth Edition)[M].Prentice-Hall,Inc,2003.
[79]Hull,J.,White,A.Numerical Procedures for Implementing Term Structure Models I:Single-Factor Models[J].The Journal of Derivatives,1994a,Fall:7-16.
[80]Hull,J.,White,A.Numerical Procedures for Implementing Term Structure Models Ⅱ:Two-Factor Models[J].The Journal of Derivatives,1994b,Winter:37-48.
[81]Hull,J.,White,A.Numerical Procedures for Implementing Term Structure Models Ⅱ:Two-Factor Models[J].The Journal of Derivatives,1994b,Winter:37-48.
[82]Hull,J.,White,A.Valuing Derivative Securities Using the Explicit Finite Difference Method[J].Journal of Financial and Quantitative Analysis,1990b,25(1):87-100.
[83]Hull,J.,White,A.Using Hull-White lnterest Rate Trees[J].The Journal of Derivatives,1996,Spring:26-36.
[84]Hull,J.,White,A.One-Factor Interest-Rate Models and the Valuation of Interest Rate Derivative Securities[J].Journal of Financial and Quantitative Analysis,1993,28(2):235-254.
[85]Jamshidian,F.An Exact Bond Option Formula[J].Journal of Finance,1989,44(1):205-209.
[86]Jamshidian,F.Bond,Futures and Option Valuation in the Quadratic Interest Rate Model[J].Applied Mathematical Finance,1996,No.3:93-115.
[87]Johannes,M.The Statistical and Economic Role of Jumps in Interest Rates[J].Journal of Finance,2004,No.59:227-260.
[88]Johannes,M.S.A Nonparametric View of the Role of Jumps to Interest Rates[J].Working Paper,Graduate school of Business,Columbia University,2000.
[89]Joy,C.,Boyle,P.and Tan,K.S.Quasi-Monte Carlo Methods in Numerical Finance[J].Management Science,1996,42(6):926-938.
[90]Johnson,C.Numerical Solution of Partial Differential Equations by the Finite Element Method [M].Cambridge University Press,1990.
[91]Kan,R.Shape of the Yield Curve under CIR Single Factor Model:A Note[J].Working paper,University of Chicago,1992.
[92]Kariya,T.,Kobayashi,M.Pricing Mortgage-Backed Securities(MBS):A Model Describing The Burnout Effect[J].Asia-Pacific Financial Markets,2000,No.7:189-204.
[93]Kariya,T.,Ushiyama,F.and Pliska,S.R.A 3-Factor Valuation Model for Mortgage-Backed Securities(MBS)[J].Working Paper,http://tigger.uic.edu/-srpliska/papers/MBS.pdf,2002.
[94]Kau,J.B.,Keenan,D.C.,Muller,W.J.and Epperson,J.E A Generalized Valuation Model for Fixed-Rate Residential Mortgages[J].Journal of Money,Credit and Banking,1992,24(3):279-299.
[95]Knez,P.,Litterman,R.,and Scheinkman,J.A.Explorations into Factors Explaining Money Market Returns[J].Journal of Finance,1994,No.49:1861-1882.
[96]Leippold,M.,Wu L.Asset Pricing Under the Quadratic Class[J].Journal of Financial and Quantitative Analysis,2002,37(2):271-295.
[97]Longstaff,F.A.A Nonlinear General EquilibriumModel of the Term Structure of Interest Rates [J].Journal of Financial Economics,1989,No.23:195-224.
[98]Longstaff,F.A.The Valuation of Options on Coupon Bonds[J].Journal of Banking and Finance,1993,No.17:27-42.
[99]Longstaff,F.A.,Schwartz,E.S.lnterest Rate Volatility and the Term Structure:A Two-Factor General Equilibrium Model[J].The Journal of Finance,1992a,47(4):1259-1282.
[100]Longstaff,F.A.,Schwartz E.S.Valuing American Options By Simulation:A Simple Least-Squares Approach[J].Review of Financial Studies,2001,14(1):113-147.
[101]Macaulay,F.R.Some Theoretical Problems Suggested by the Movements of Interest Rates,Bond Yields,and Stock Prices in the United States since 1856[M].New York:Columbia University Press,1938.
[102]Merton,R.C.A Dynamic General Equilibrium Model of the Asset Market and Its Application to the Pricing of the Capital Structure of the Firm[J].Working Paper 497-70,Sloan School of Management,MIT,1970.
[103]Merton,R.C.Option Pricing When the Underlying Stock Returns Are Discontinuous[J].Journal of Financial Economics,1976,3(1-2):125-144.
[104]Mikkelsen,P.MCMC Based Estimation of Term Structure Models[J].University of Aarhus,Center for Analytical Finance,Working Paper,2001,No.9.
[105]Miroslav Verbic.Income,Employment and Distribution Effects of Inflation[J].University of Maribor,Working Paper,http://129.3.20.41/eps/mac/papers/0012/0012017.pdf,2000.
[106]Morokff,W.,Caflisch R.E.A Quasi-Monte Carlo Approach to Particle Simulation of the Heat Equation[J].SIAM J.Numer.Anal.,1993,30(6):1558-1573.
[107]Morokff,W.,Caflisch R.E.Quasi-Monte Carlo Integration[J].J.Comput.Phys,1995,122(2):218-230.
[108]Morokff,W.,Caflisch R.E.Quasi-random Sequences and Their Discrepancies[J].SIAM J.Sci.Statist.Comput,1994,15:1251-1279.
[109]Morokoff,W.Generating Quasi-Random Paths for Stochastic Processes[J].SIAM Review,1998,40(4):765-788.
[110]Nelson,C.R.,Siegel,A.F.Parsimonious Modeling of Yield Curves[J].Journal of Business,1987,60(4):473-489.
[111]Ninomiya,S.,Tezuka,S.Toward Real-Time Pricing of Complex Financial Derivatives[J].Applied Mathematical Finance,1996,3(1):1-20.
[112]Nowman,B.Gaussian Estimation of Single-Factor Continuous Time Models of the Term Structure of Interest Rates[J].Journal of Finance,1997,No.52:1695-1706.
[113]Paskov,S.H.New Methodologies for Valuing Derivatives[A].In Dempster,M.,Pliska,S.Mathematics of Derivative Securities[M].Isaac Newton Institute:Cambridge University Press,1997:545-582.
[114]Paskov,S.H.,Traub,J.F.Faster Valuation of Financial Derivatives[J].Journal of Portfolio Management,1995,No.22:113-120.
[115]Pedersen,H.W.,Shiu,E.S.W.and Thorlacius,A.E.Arbitrage-Free Pricing of Interest Rate Contingent Claims[J].Transactions of Society of Actuaries,1989,No.41:231-279.
[116]Piazzesi,M.Bond Yields and the Federal Reserve[J].Journal of Political Economy,2005,113(2):311-344.
[117]Rendleman,R.,Bartter,B.The Pricing of Options on Debt Securities[J].Journal of Financial and Quantitative Analysis,1980,No.15:11-24.
[118]Richard,S.E,Roll,R.Prepayments on Fixed-Rate Mortgage-Backed Securities[J].Journal of Portfolio Management,1989,Spring:73-82.
[119]Ross,S.A.Neoclassical Finance[M].Princeton:Princeton University Press,2004:Chapter 1.
[120]Schwartz,E.S.The Valuation of Warrants:Implementing a New Approach[J].Journal of Financial Economics,1977,No.4:79-93.
[121]Schwartz,E.S.,Torous,W.N.Prepayment and The Valuation of Mortgage-Backed Securities [J].Journal of Finance,1989,44:375-392.
[122]Singleton,K.Estimation of Affine Asset Pricing Models Using The Empirical Characteristic Function[J].Journal of Econometrics,2001,No.102:111-141.
[123]Tian,Y.A Simplified Approach to the Pricing of Interest-Rate Contingent Claims[J].Journal of Financial Engineering,1993,No.1:285-314.
[124]Vasicek,O.An Equilibrium Characterization of the Term Structure[J].Journal of Financial Economics,1977,No.5:177-188.
[125]Vetzal,K.R.Stochastic Volatility,Movements in the Short Term lnterest Rates,and Bond Option Values[J].Journal of Banking and Finance,1997,21:169-196.
[126]Wilmott,P.,Dewynne,J.and Howison,S.Option Pricing:Mathematical Models and Computation[M].Oxford Financial Press,1993.
[127]Wu,T.Monetary Policy and the Slope Factors in Empirical Term Structure Estimations[J].Federal Reserve Bank of San Francisco Working Paper,2002:2-7.
[128]Zhou,H.Jump-Diffusion Term Structure and Ito Conditional Moment Generator[J].Working Paper,Federal Reserve Board,2001,FEDS Working Paper No.2001-28.
[2]范龙振,王晓丽.上交所国债市场利率期限结构及其信息价值[J].管理工程学报,2004,1:72-75.
[3]林海,郑振龙.中国利率期限结构:理论及应用[M].北京:中国财经出版社,2004.
[4]梁福涛.我国利率调整的通货膨胀因素模型估计[J].国际商务研究,2005,4:17-24.
[5]刘金全,王勇,张鹤.利率期限结构与宏观经济因素的动态相依性--基于VAR模型的经验研究[J].财经研究,2007,33(5):126-133.
[6]刘康兵,申朴,李达.利率与通货膨胀:一个费雪效应的经验分析[J].财经研究,2003,29(2):24-29.
[7]李和金,郑兴山,李湛.非参数利率期限结构模型的实证检验[J].上海交通大学学报,2003,4:607-609.
[8]潘冠中,邵斌.单因子利率模型的极大似然估计--对中国利率的实证分析[J].财经研究,2004,10:62-69.
[9]石晶莹.我国的利率市场化改革实践综述[J].绥化学院学报,2007,27(1):19-23.
[10]孙继国,伍海华.同业拆借利率与宏观经济变量之关系研究[J].广东金融学院学报,2004,19(5):13-18.
[11]孙丽瑶.同业拆借利率与宏观经济变量协整关系的实证分析[J].沿海企业与科技,2006,10:32-34.
[12]王国刚,何旭强.债券市场发展:2005年回顾与2006年创新[J].福建论坛(人文社会科学版),2006,5:13-16.
[13]王国刚,何旭强.债券市场:创新发展与市场走势--2006年回顾与2007年展望[J].国际经济评沦,2007,2:35-39.
[14]吴艳.我国国债收益率曲线的实证分析[J].内蒙古财经学院学报,2004,3:44-47.
[15]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,2002,3:22-25.
[16]颜炬,石磊.我国银行间债券市场的发展[J].中国金融,2007,8:31-33.
[17]洪永淼,林海.中国市场利率动态研究-基于短期国债回购利率的实证分析[J].经济学季刊,2006,1:511-532。
[18]阎衍.2008年固定收益产品发行规模有望破万亿[N].http://finance.cctv.com/20080306/101784.shtml,2008.
[19]Ahn,C.M.,Thompson,H.E.Jump-Diffusion Processes and the Term Structure of Interest Rates [J].Journal of Finance,1988,43(1):155-174.
[20]A(l|")t-Sahalia,Y.Estimating Continuous-Time Models with Discretely Sampled Data[J].Working Paper,http://www.princeton.edu/-yacine/eswc2005.pdf,2002.
[21]A(l|")t-Sahalia,Y.,Kimmel,R.Maximum Likelihood Estimation of Stochastic Volatility Models[J].Journal of Financial Economics,2007,No.83:413-452.
[22]Akesson,F.,Lehoczky,J.P.Path Generation for Quasi-Monte Carlo Simulation of Mortgage-Backed Securities[J].Management Science,2000,46(9):1171-1187.
[23]Andersen,L.A Simple Approach to the Pricing of Bermudan Swaptions in the Multi-Factor Libor Market Model[J].Journal of Computational Finance,2000,3(2):1-32.
[24]Andersen,T.G.,Benzoni,L.,and Lund J.Stochastic Volatility,Mean Drift,and Jumps in the Short-Term Interest Rate[J].Working Paper,http://www.jesperlund.com/papers/abl2.pdf,2004.
[25]Ang,A.,Piazzesi,Mo A No-Arbitrage Vector Autoregression of Term Structure Dynamics with Macroeconomic and Latent Variables[J].Journal of Monetary Economics,2003,50:745-787.
[26]Ames,W.F.Numerical Methods for Partial Differential Equations(Second Edition)[M].Academic Press,1977.
[27]Asgharian,H.,Bengtsson,C.Jump Spillover in International Equity Markets[J].Journal of Financial Econometrics,2006,4(2):167-203.
[28]Askin,D,J.,Curtin,W.J.and Lowell,L.Forecasting Prepayment Rates for Mortgage-Backed Securities[A].In The Handbook of Mortgage-Backed Securities[M].1988.
[29]Bakshi,G.,Cao,C.,Chen,Z.W.Empirical Performance of Alternative Option Pricing Models[J].Journal of Finance,1997,No.52:2003-2049.
[30]Balduzzi,P.,Das,S.R.,Foresi,S.and Sundaram,R.A Simple Approach to Three-Factor Affine Term Structure Models[J].The Journal of Fixed Income,1996,6(3):43-53.
[31]Bali,T.G.Testing the Empirical Performance of Stochastic Volatility Models of the Short-Term Interest Rate[J].The Journal of Financial and Quantitative Analysis,2000,35(2):191-215.
[32]Ball,C.,Torous,W.N.A Simplified Jump Process for Common Stock Returns[J].Journal of Financial and Quantitative Analysis,1983,18(1):53-65.
[33]Barraquand,J.Numerical Valuation of High Dimensional Multivariate European Securities[J].Management Science,1995,No.41:1882-1891.
[34]Beaglehole,D.R.,Tenney,M.S.Corrections and Additions to "A Nonlinear Equilibrium Model of the Term Structure of Interest Rates"[J].Journal of Financial Economics,1992,32(3):345-353.
[35]Beaglehole,D.R.,Tenney,M.S.General Solutions of Some Interest Rate-Contingent Claim Pricing Equations[J].The Journal of Fixed Income,1991,No.1:69-83.
[36]Black,E,Derman,E.and Toy,W.A One-Factor Model of Interest Rates and Its Application to Treasury Bond Options[J].Financial Analysts Journal,1990,46(1):33-39.
[37]Broadie,M.,Glasserman,P.Pricing American-Style Securities Using Simulation[J].Journal of Economic Dynamics and Control,1997b,21(8-9):1323-1352.
[38]Bodie,Z.,Merton,R.C.金融学[M].北京:中国人民大学出版社,2000:189.
[39]Boyle,P.,Broadie,M.and Glasserman,P.Monte Carlo Methods for Security Pricing[J].Journal of Economic Dynamics and Control,1997,21(8-9):1267-1321.
[40]Brandimarte,P.Numerical Methods in Finance[M].New York:John Wiley & Sons,Inc,2002:Chapter 4 and 7.
[41]Brennan,M.J.,Schwartz,E.S.A Continuous Time Approach to the Pricing of Bonds[J].Journal of Banking and Finance,1979,No.3:133-155.
[42]Brennan,M.J.,Schwartz,E.S.The Valuation of American Put Options[J].Journal of Finance,1977,32(2):449-462.
[43]Black,F.,Karasinski,P.Bond and Option Pricing when Short Rates are Lognormal[J].Financial Analysts Journal,1991,47(4):52-59.
[44]Caflisch,R.E.,Morokoff,W.and Owen,A.Valuation of Mortgage Backed Securities Using Brownian Bridges to Reduce Effective Dimension[J].Journal of Computational Finance,1997,1(1):27-46.
[45]Carr,P.,Yang,G.Simulating Bermudan lnterest Rate Derivatives[J].Working Paper,Morgan Stanley and Open Link Financial,1997,December.
[46]Chacko,G.,Das,S.Pricing Interest Rate Derivatives." A General Approach[J].The Review of Financial Studies,2002,15(1):195-241.
[47]Chan,K.C.,Karolyi,G.A.,Longstaff,F.A.and Sanders,A.B.An Empirical Comparison of Alternative Models oft he Short Term Interest Rate[J].Journal of Finance,1992,47(3):1209-1227.
[48]Chen,L.Stochastic Mean and Stochastic Volatility----A Three-Factor Model of the Term Structure of Interest Rates and Its Applications in Derivatives Pricing and Risk Management[J].Financial Markets,Institutions & Instruments,1996,5(1):1-88.
[49]Chen,L.Interest Rate Dynamics,Derivatives Pricing,and Risk Management[M].Springer,1996.
[50]Chert,R.R.,Scott,L.Stochastic Volatility and Jumps in Interest Rates:An Empirical Analysis[J].Working Paper,http://www.rci.rutgers.edu/-rchen/JumpsStochVolPaper.pdf,2004.
[51]Claus Munk.Fixed Income Analysis:Securities,Pricing,and Risk Management[M].http://www.sam.sdu.dk/-cmu/noter/FIAjan05.pdf,2004.
[52]Cont,R.and Tankov,P.Financial Modelling With Jump Processes[M].Chapman & Hall,CRC Financial Mathematics Series,2004:274-275.
[53]Cox,J.C.,Ingersoll,J.E.and Ross,S.A.A Theory of the Term Structure of Interest Rates[J].Econometrica,1985b,53(2):385-407.
[54]Cox,J.C.,Ross,S.A.and Rubinstein,M.Option Pricing:A Simplified Approach[J].Journal of Financial Economics,1979,No.7:229-263.
[55]Dai,Q.,Singleton,K.J.Specification Analysis of Affine Term Structure Models[J].The Journal of Finance,2000,55(5):1943-1978.
[56]Das,S.R.The Surprise Element:Jumps in Interest Rates[J].Journal of Econometrics,2002,No.106:27-65.
[57]Das,S.R.,Foresi,S.Exact Solutions for Bond and Options Prices with Systematic Jump Risk[J].Review of Derivatives Research,1996,No.1:7-24.
[58]Diebold,F.X.,Rudebusch,G.D.and Aruoba,S.B.The Macro Economy and the Yield Curve:A Dynamic Latent Factor Approach[J].Journal of Econometrics,2006,No.131:309-338.
[59]Duan,J.C.Augmented GARCH(p,q) Process and Its Diffusion Limit[J].Journal of Econometrics,1997,No.79:97-127.
[60]Duffle,D.Dynamic Asset Pricing Theory(Third Edition)[M].Princeton:Princeton University Press,2001:101-131.
[61]Duffle,D.,Kan,R.A Yield-Factor Model of Interest Rates[J].Mathematical Finance,1996,6(4): 379-406.
[62]Duffle,D.,Pan,J.,and Singleton,K.Transform Analysis and Asset Pricing for Affine Jump-Diffusions[J].Econometrica,2000,68(6):1343-1376.
[63]Durham,J.B.Jump-Diffusion Processes and Affine Term Structure Models:Additional Closed-Form Approximate Solutions,Distributional Assumptions for Jumps,and Parameter Estimates[J].Finance and Economics Discussion Series 2005-53,Board of Governors of the Federal Reserve System(U.S.),2005.
[64]Elerian,O.,Chib,S.,and Shephard,N.Likelihood Inference for Discretely Observed Nonlinear Diffusions[J].Econometrica,2001,No.69:959-994.
[65]Engle,R.F.Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of UK Inflation[J].Econometrica,1982,No.50:987-1008.
[66]Eraker,B.MCMC Analysis of Diffusion Models with Applications to Finance[J].Journal of Econometrics,2001,No.19:177-191.
[67]Estrella,A.,Hardouvelis,G.A.The Term Structure as A Predictor of Real Economic Activity[J].Journal of Finance,1991,46:555-576.
[68]Estrella,A.,Mishkin,F.S.Predicting US Recessions:Financial Variables as Leading Indicators [J].Review of Economics and Statistics,1998,80:45-61.
[69]Faria,J.R.,Carneiro,F.G.Does High Inflation Affect Growth the Long and Short Run?[J].Journal of Applied Economics,2001,4(1):89-105.
[70]Finnerty,J.D.Exact Formulas for Pricing Bonds and Options When Interest Rate Diffusions Contain Jumps[J].The Journal of Financial Research,2005,ⅩⅩⅧ(3):319-341.
[71]Gallant,A.R.,Tanchen,G.Testing Continuous-Time Models of the Spot Interest Rate[J].Review of Financial Studies,1996,No.3:197-215.
[72]Hamilton,J.Time Series Analysis[M].Princeton:Princeton University Press,1994:Chapter 5.
[73]He,H.Convergence from Discrete - to Continuous - Time Contingent Claims Prices[J].The Review of Financial Studies,1990,3(4):523-546.
[74]Heston.A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options[J].Review of Financial Studies,1993,No.6:327-343.
[75]Ho,T.S.Y.,Lee,S.B.Term Structure Movements and Pricing Interest Rate Contingent Claims[J].Journal of Finance,1986,41(5):1011-1029.
[76]Hong,Y.M.,Li,H.Nonparametric Specification Testing for Continuous-Time Models with Applications to Term Structure of Interest Rates[J].Review of Financial Studies,2004,18(1): 37-84.
[77]Hong,Y.,Li,H.and Zhao,F.Out-of-Sample Performance of Discrete-Time Spot Interest Rate Models[J].Journal of Business and Economics Statistics,2004,22(4):457-473.
[78]Hull,J.Options,Futures,and Other Derivatives(Fifth Edition)[M].Prentice-Hall,Inc,2003.
[79]Hull,J.,White,A.Numerical Procedures for Implementing Term Structure Models I:Single-Factor Models[J].The Journal of Derivatives,1994a,Fall:7-16.
[80]Hull,J.,White,A.Numerical Procedures for Implementing Term Structure Models Ⅱ:Two-Factor Models[J].The Journal of Derivatives,1994b,Winter:37-48.
[81]Hull,J.,White,A.Numerical Procedures for Implementing Term Structure Models Ⅱ:Two-Factor Models[J].The Journal of Derivatives,1994b,Winter:37-48.
[82]Hull,J.,White,A.Valuing Derivative Securities Using the Explicit Finite Difference Method[J].Journal of Financial and Quantitative Analysis,1990b,25(1):87-100.
[83]Hull,J.,White,A.Using Hull-White lnterest Rate Trees[J].The Journal of Derivatives,1996,Spring:26-36.
[84]Hull,J.,White,A.One-Factor Interest-Rate Models and the Valuation of Interest Rate Derivative Securities[J].Journal of Financial and Quantitative Analysis,1993,28(2):235-254.
[85]Jamshidian,F.An Exact Bond Option Formula[J].Journal of Finance,1989,44(1):205-209.
[86]Jamshidian,F.Bond,Futures and Option Valuation in the Quadratic Interest Rate Model[J].Applied Mathematical Finance,1996,No.3:93-115.
[87]Johannes,M.The Statistical and Economic Role of Jumps in Interest Rates[J].Journal of Finance,2004,No.59:227-260.
[88]Johannes,M.S.A Nonparametric View of the Role of Jumps to Interest Rates[J].Working Paper,Graduate school of Business,Columbia University,2000.
[89]Joy,C.,Boyle,P.and Tan,K.S.Quasi-Monte Carlo Methods in Numerical Finance[J].Management Science,1996,42(6):926-938.
[90]Johnson,C.Numerical Solution of Partial Differential Equations by the Finite Element Method [M].Cambridge University Press,1990.
[91]Kan,R.Shape of the Yield Curve under CIR Single Factor Model:A Note[J].Working paper,University of Chicago,1992.
[92]Kariya,T.,Kobayashi,M.Pricing Mortgage-Backed Securities(MBS):A Model Describing The Burnout Effect[J].Asia-Pacific Financial Markets,2000,No.7:189-204.
[93]Kariya,T.,Ushiyama,F.and Pliska,S.R.A 3-Factor Valuation Model for Mortgage-Backed Securities(MBS)[J].Working Paper,http://tigger.uic.edu/-srpliska/papers/MBS.pdf,2002.
[94]Kau,J.B.,Keenan,D.C.,Muller,W.J.and Epperson,J.E A Generalized Valuation Model for Fixed-Rate Residential Mortgages[J].Journal of Money,Credit and Banking,1992,24(3):279-299.
[95]Knez,P.,Litterman,R.,and Scheinkman,J.A.Explorations into Factors Explaining Money Market Returns[J].Journal of Finance,1994,No.49:1861-1882.
[96]Leippold,M.,Wu L.Asset Pricing Under the Quadratic Class[J].Journal of Financial and Quantitative Analysis,2002,37(2):271-295.
[97]Longstaff,F.A.A Nonlinear General EquilibriumModel of the Term Structure of Interest Rates [J].Journal of Financial Economics,1989,No.23:195-224.
[98]Longstaff,F.A.The Valuation of Options on Coupon Bonds[J].Journal of Banking and Finance,1993,No.17:27-42.
[99]Longstaff,F.A.,Schwartz,E.S.lnterest Rate Volatility and the Term Structure:A Two-Factor General Equilibrium Model[J].The Journal of Finance,1992a,47(4):1259-1282.
[100]Longstaff,F.A.,Schwartz E.S.Valuing American Options By Simulation:A Simple Least-Squares Approach[J].Review of Financial Studies,2001,14(1):113-147.
[101]Macaulay,F.R.Some Theoretical Problems Suggested by the Movements of Interest Rates,Bond Yields,and Stock Prices in the United States since 1856[M].New York:Columbia University Press,1938.
[102]Merton,R.C.A Dynamic General Equilibrium Model of the Asset Market and Its Application to the Pricing of the Capital Structure of the Firm[J].Working Paper 497-70,Sloan School of Management,MIT,1970.
[103]Merton,R.C.Option Pricing When the Underlying Stock Returns Are Discontinuous[J].Journal of Financial Economics,1976,3(1-2):125-144.
[104]Mikkelsen,P.MCMC Based Estimation of Term Structure Models[J].University of Aarhus,Center for Analytical Finance,Working Paper,2001,No.9.
[105]Miroslav Verbic.Income,Employment and Distribution Effects of Inflation[J].University of Maribor,Working Paper,http://129.3.20.41/eps/mac/papers/0012/0012017.pdf,2000.
[106]Morokff,W.,Caflisch R.E.A Quasi-Monte Carlo Approach to Particle Simulation of the Heat Equation[J].SIAM J.Numer.Anal.,1993,30(6):1558-1573.
[107]Morokff,W.,Caflisch R.E.Quasi-Monte Carlo Integration[J].J.Comput.Phys,1995,122(2):218-230.
[108]Morokff,W.,Caflisch R.E.Quasi-random Sequences and Their Discrepancies[J].SIAM J.Sci.Statist.Comput,1994,15:1251-1279.
[109]Morokoff,W.Generating Quasi-Random Paths for Stochastic Processes[J].SIAM Review,1998,40(4):765-788.
[110]Nelson,C.R.,Siegel,A.F.Parsimonious Modeling of Yield Curves[J].Journal of Business,1987,60(4):473-489.
[111]Ninomiya,S.,Tezuka,S.Toward Real-Time Pricing of Complex Financial Derivatives[J].Applied Mathematical Finance,1996,3(1):1-20.
[112]Nowman,B.Gaussian Estimation of Single-Factor Continuous Time Models of the Term Structure of Interest Rates[J].Journal of Finance,1997,No.52:1695-1706.
[113]Paskov,S.H.New Methodologies for Valuing Derivatives[A].In Dempster,M.,Pliska,S.Mathematics of Derivative Securities[M].Isaac Newton Institute:Cambridge University Press,1997:545-582.
[114]Paskov,S.H.,Traub,J.F.Faster Valuation of Financial Derivatives[J].Journal of Portfolio Management,1995,No.22:113-120.
[115]Pedersen,H.W.,Shiu,E.S.W.and Thorlacius,A.E.Arbitrage-Free Pricing of Interest Rate Contingent Claims[J].Transactions of Society of Actuaries,1989,No.41:231-279.
[116]Piazzesi,M.Bond Yields and the Federal Reserve[J].Journal of Political Economy,2005,113(2):311-344.
[117]Rendleman,R.,Bartter,B.The Pricing of Options on Debt Securities[J].Journal of Financial and Quantitative Analysis,1980,No.15:11-24.
[118]Richard,S.E,Roll,R.Prepayments on Fixed-Rate Mortgage-Backed Securities[J].Journal of Portfolio Management,1989,Spring:73-82.
[119]Ross,S.A.Neoclassical Finance[M].Princeton:Princeton University Press,2004:Chapter 1.
[120]Schwartz,E.S.The Valuation of Warrants:Implementing a New Approach[J].Journal of Financial Economics,1977,No.4:79-93.
[121]Schwartz,E.S.,Torous,W.N.Prepayment and The Valuation of Mortgage-Backed Securities [J].Journal of Finance,1989,44:375-392.
[122]Singleton,K.Estimation of Affine Asset Pricing Models Using The Empirical Characteristic Function[J].Journal of Econometrics,2001,No.102:111-141.
[123]Tian,Y.A Simplified Approach to the Pricing of Interest-Rate Contingent Claims[J].Journal of Financial Engineering,1993,No.1:285-314.
[124]Vasicek,O.An Equilibrium Characterization of the Term Structure[J].Journal of Financial Economics,1977,No.5:177-188.
[125]Vetzal,K.R.Stochastic Volatility,Movements in the Short Term lnterest Rates,and Bond Option Values[J].Journal of Banking and Finance,1997,21:169-196.
[126]Wilmott,P.,Dewynne,J.and Howison,S.Option Pricing:Mathematical Models and Computation[M].Oxford Financial Press,1993.
[127]Wu,T.Monetary Policy and the Slope Factors in Empirical Term Structure Estimations[J].Federal Reserve Bank of San Francisco Working Paper,2002:2-7.
[128]Zhou,H.Jump-Diffusion Term Structure and Ito Conditional Moment Generator[J].Working Paper,Federal Reserve Board,2001,FEDS Working Paper No.2001-28.