固定收益证券风险对冲研究
|
摘要
固定收益市场是金融市场的重要组成部分。在固定收益市场快速发展并且风险加剧的背景下，对固定收益证券的风险管理问题进行研究，建立科学的风险对冲模型，对各类投资者乃至市场监管机构都具有重要的理论和实际意义。
本文对静态利率期限结构模型和动态利率期限结构模型下的国债利率风险度量和对冲，以及基于风险因子的可违约债券（信用组合）的风险对冲及损失分解进行了系统而深入的研究。
首先，在介绍静态利率期限结构模型下的利率风险度量工具的基础上，引入一个额外的曲度因子将Nelson-Siegel久期向量模型扩展，得到了Svensson久期向量模型和四形状因子久期向量模型。基于上交所国债数据进行实证研究，发现第二曲度因子只能解释上交所国债收益率变化方差的很小一部分，然而将其引入后可显著减小利率风险对冲误差。此外，四形状因子久期向量模型的待估参数更少并且利率风险免疫效果略好于Svensson久期向量模型，是更好的利率风险对冲模型。
其次，在介绍利率期限结构预测的动态Nelson-Siegel类模型的基础上，将四形状因子模型扩展为动态四形状因子类模型，并对这两类利率期限结构预测模型进行一阶差分修正。基于上交所国债数据进行实证研究，发现引入额外的曲度因子可显著提升利率期限结构预测的效果，并且对这两类模型进行一阶差分修正可显著减小其利率期限结构预测误差。
在利率期限结构预测的基础上，将债券价格及收益率的预测信息引入利率风险对冲模型。在四形状因子久期向量模型下，基于上交所国债数据进行实证研究，发现将利率期限结构的预测信息引入后，可进一步减小利率风险对冲误差。
再次，在介绍动态利率期限结构模型下随机久期的基础上，推导了仿射模型下的随机久期向量，并说明Vasicek模型和CIR模型下的随机久期均为随机久期向量退化为一维的特例。基于上交所国债数据进行实证研究，发现四因子非高斯仿射模型和四因子高斯仿射下随机久期向量的利率风险对冲效果分别显著优于CIR模型和Vasicek模型下的随机久期，并且四因子非高斯仿射模型下随机久期向量的利率风险对冲效果优于四因子高斯仿射模型下的随机久期向量。
此外，对静态利率期限结构模型和动态利率期限结构模型下的国债利率风险对冲结果进行对比，发现引入利率期限结构预测信息的四形状因子久期向量模型的利率风险对冲效果最好，而四因子非高斯仿射模型下随机久期向量的利率风险对冲效果甚至劣于四形状因子久期向量模型。
最后，在对信用组合的因子模型以及违约传染模型进行介绍的基础上，将违约传染效应引入信用组合的因子模型，构建了违约传染情形下信用组合的因子模型，获得了信用组合的系统性损失及其对冲和Hoeffding分解的解析结果。发现对于同质组合，引入违约传染效应后，由于其系统性损失的期望增大，最优对冲组合中无风险债券的头寸亦增大；当同质组合中各债券的违约概率较低（较高）时，引入违约传染效应后，最优对冲组合中各系统风险因子的头寸增大（减小）。对含有两个系统因子情形下信用组合系统性损失的Hoeffding分解进行数值模拟，发现随着置信水平的提高，同质组合系统性损失的CVaR增大，其中预期项的贡献率减小，而两因子的联合贡献率增大；同质组合的违约比例增大也即违约传染效应增强时，同质组合系统性损失的CVaR亦增大，并且主要源于两因子的联合贡献。
The fixed income market is an important part of the financial markets. Under thebackground of rapid growth and severe fluctu ation of the fixed income market, it’s ofcritical significance to research on the risk hedging of fixed income securities so as tobuild more accurate immunization models, wh ich can be u seful for the investors andeven the regulators.
In this dissertation, a syst ematic and intensive research is m ade on hedging ofinterest rates risk of treasury bonds based on both statistic and dynamic interest ratesterm structure models and on hedging of defaultable bonds based on the factor modelsof credit portfolio.
First, based on a concise introduction of risk hedging tools under statistic interestrates term structure m odels, another curv ature factor is introduced to extend theNelson-Siegel duration vector m odel to the Svensson duration vector model and theFour-Shape-Factor duration vector m odel. Empirical te sts base d on the data ofShanghai Security Exchange (hereafter SSE) show that although the second curvaturefactor explains little part of the variance of interest rates term structure, interest ratesrisk hedging errors can be reduced sign ificantly by introduci ng it. Besides, theFour-Shape-Factor duration vector model has less param eter to be estim ated andperforms better than the Svensson duration vector model, which m akes it the b ettermodel for interest rates risk hedging.
Second, after a brief introduc tion of dynamic Nelson-Siegel-style models whichare proved to be effective in interest rates term structure forecasting, another curvaturefactor is introduced to extend the dynamic Nelson-Siegel-style models to the dynamicFour-Shape-Factor-style models. Besides, bo th of these two cla sses of models aremodified by m odeling their first-dif ferenced parameter series. Em pirical tests basedon the data of SSE show that the incorpor ation of the seco nd curvature factor canimprove the performance of interest rates term structure forecasting significantly andthe firs t-differenced modification of thes e tw o class es o f m odels can also y ieldsmaller and more stable forecasting errors.
On the basis of forecasting of interest rates term structure, bonds’ prices ar eforecasted by discounting their future cash flows, which are introd uced to theFour-Shape-Factor duration vector model. Empirical tests based on the SSE data show that the in corporation of the f orecasting inf ormation about the inte rest rates ter mstructure can im prove the interest ra tes risk hedging perform ance of theFour-Shape-Factor duration vector model significantly.
Third, based on a system atic introduction of t he stochastic duration under thedynamic interest rates term structure m odels, the stochastic duration vector of theAffine T erm S tructure Model is derive d, whereas the stochastic duration underVasicek&CIR Model is in terpreted as the degra dation in the f orm ofone-dimensional stochastic duration vector. Empirical tests ba sed on the SSE datashow that the four-factor stochastic duration vector performs significantly better thanstochastic duration when hedging the intere st rate risk of treasure bonds. Besides,stochastic duration vector of the four-factor Non-Gaussian Af fine Term S tructureModel yields sm aller hedging errors than th at of four-factor Gaussian Af fine TermStructure Model.
Besides, the interest rates risk hedgi ng errors under both the statistic interestrates term structure m odels and dynam ic in terest rates term structure m odels arecompared. It shows that Four-Shape-Factor duration vector model with the forecastinginformation of the intere st rates term structure incorporated performs best, whereasthe stochastic duration vector of the four-factor Non-Gaussian Affine Term StructureModel perf orms even worse than the F our-Shape-Factor duration vector m odelwithout the forecasting information of the interest rates term structure incorporated.
Finally, based on a laconic introduction of the default contagion m odel and thefactor models of credit portf olio, default contagion effect is introduced to the factormodels of credit portfolio, under w hich the analytical results for hedging the creditrisk of portfolio with linear combinations of systematic risk factors and for Hoeffdingdecomposition of the portfolio systematic loss into a sum terms depending on the riskfactors are presented. For hom ogenous cr edit portfolio, the expectation of itssystematic loss as well as the position of the risk-free bond in the hedging portfolioincreases after th e default contagion effect is in troduced. Besides, when the d efaultprobability of the counterparty in the homogenous portfolio is relatively low (h igh),the position in the systematic risk factors increases (decreases) after the incorporationof default contagion ef fect. Simulation results under the two system atic risk factorscondition show that when the confidence level increases, the CVaR of systematic lossincreases too, which is m ainly attributed to not the expectation term but the factorco-movements term. Besides, if the fraction o f default in creases, which m eans the default contagion ef fect strengthens, the CV aR of systematic loss increases, whichmainly results from the factor co-movements term too.
本文对静态利率期限结构模型和动态利率期限结构模型下的国债利率风险度量和对冲，以及基于风险因子的可违约债券（信用组合）的风险对冲及损失分解进行了系统而深入的研究。
首先，在介绍静态利率期限结构模型下的利率风险度量工具的基础上，引入一个额外的曲度因子将Nelson-Siegel久期向量模型扩展，得到了Svensson久期向量模型和四形状因子久期向量模型。基于上交所国债数据进行实证研究，发现第二曲度因子只能解释上交所国债收益率变化方差的很小一部分，然而将其引入后可显著减小利率风险对冲误差。此外，四形状因子久期向量模型的待估参数更少并且利率风险免疫效果略好于Svensson久期向量模型，是更好的利率风险对冲模型。
其次，在介绍利率期限结构预测的动态Nelson-Siegel类模型的基础上，将四形状因子模型扩展为动态四形状因子类模型，并对这两类利率期限结构预测模型进行一阶差分修正。基于上交所国债数据进行实证研究，发现引入额外的曲度因子可显著提升利率期限结构预测的效果，并且对这两类模型进行一阶差分修正可显著减小其利率期限结构预测误差。
在利率期限结构预测的基础上，将债券价格及收益率的预测信息引入利率风险对冲模型。在四形状因子久期向量模型下，基于上交所国债数据进行实证研究，发现将利率期限结构的预测信息引入后，可进一步减小利率风险对冲误差。
再次，在介绍动态利率期限结构模型下随机久期的基础上，推导了仿射模型下的随机久期向量，并说明Vasicek模型和CIR模型下的随机久期均为随机久期向量退化为一维的特例。基于上交所国债数据进行实证研究，发现四因子非高斯仿射模型和四因子高斯仿射下随机久期向量的利率风险对冲效果分别显著优于CIR模型和Vasicek模型下的随机久期，并且四因子非高斯仿射模型下随机久期向量的利率风险对冲效果优于四因子高斯仿射模型下的随机久期向量。
此外，对静态利率期限结构模型和动态利率期限结构模型下的国债利率风险对冲结果进行对比，发现引入利率期限结构预测信息的四形状因子久期向量模型的利率风险对冲效果最好，而四因子非高斯仿射模型下随机久期向量的利率风险对冲效果甚至劣于四形状因子久期向量模型。
最后，在对信用组合的因子模型以及违约传染模型进行介绍的基础上，将违约传染效应引入信用组合的因子模型，构建了违约传染情形下信用组合的因子模型，获得了信用组合的系统性损失及其对冲和Hoeffding分解的解析结果。发现对于同质组合，引入违约传染效应后，由于其系统性损失的期望增大，最优对冲组合中无风险债券的头寸亦增大；当同质组合中各债券的违约概率较低（较高）时，引入违约传染效应后，最优对冲组合中各系统风险因子的头寸增大（减小）。对含有两个系统因子情形下信用组合系统性损失的Hoeffding分解进行数值模拟，发现随着置信水平的提高，同质组合系统性损失的CVaR增大，其中预期项的贡献率减小，而两因子的联合贡献率增大；同质组合的违约比例增大也即违约传染效应增强时，同质组合系统性损失的CVaR亦增大，并且主要源于两因子的联合贡献。
The fixed income market is an important part of the financial markets. Under thebackground of rapid growth and severe fluctu ation of the fixed income market, it’s ofcritical significance to research on the risk hedging of fixed income securities so as tobuild more accurate immunization models, wh ich can be u seful for the investors andeven the regulators.
In this dissertation, a syst ematic and intensive research is m ade on hedging ofinterest rates risk of treasury bonds based on both statistic and dynamic interest ratesterm structure models and on hedging of defaultable bonds based on the factor modelsof credit portfolio.
First, based on a concise introduction of risk hedging tools under statistic interestrates term structure m odels, another curv ature factor is introduced to extend theNelson-Siegel duration vector m odel to the Svensson duration vector model and theFour-Shape-Factor duration vector m odel. Empirical te sts base d on the data ofShanghai Security Exchange (hereafter SSE) show that although the second curvaturefactor explains little part of the variance of interest rates term structure, interest ratesrisk hedging errors can be reduced sign ificantly by introduci ng it. Besides, theFour-Shape-Factor duration vector model has less param eter to be estim ated andperforms better than the Svensson duration vector model, which m akes it the b ettermodel for interest rates risk hedging.
Second, after a brief introduc tion of dynamic Nelson-Siegel-style models whichare proved to be effective in interest rates term structure forecasting, another curvaturefactor is introduced to extend the dynamic Nelson-Siegel-style models to the dynamicFour-Shape-Factor-style models. Besides, bo th of these two cla sses of models aremodified by m odeling their first-dif ferenced parameter series. Em pirical tests basedon the data of SSE show that the incorpor ation of the seco nd curvature factor canimprove the performance of interest rates term structure forecasting significantly andthe firs t-differenced modification of thes e tw o class es o f m odels can also y ieldsmaller and more stable forecasting errors.
On the basis of forecasting of interest rates term structure, bonds’ prices ar eforecasted by discounting their future cash flows, which are introd uced to theFour-Shape-Factor duration vector model. Empirical tests based on the SSE data show that the in corporation of the f orecasting inf ormation about the inte rest rates ter mstructure can im prove the interest ra tes risk hedging perform ance of theFour-Shape-Factor duration vector model significantly.
Third, based on a system atic introduction of t he stochastic duration under thedynamic interest rates term structure m odels, the stochastic duration vector of theAffine T erm S tructure Model is derive d, whereas the stochastic duration underVasicek&CIR Model is in terpreted as the degra dation in the f orm ofone-dimensional stochastic duration vector. Empirical tests ba sed on the SSE datashow that the four-factor stochastic duration vector performs significantly better thanstochastic duration when hedging the intere st rate risk of treasure bonds. Besides,stochastic duration vector of the four-factor Non-Gaussian Af fine Term S tructureModel yields sm aller hedging errors than th at of four-factor Gaussian Af fine TermStructure Model.
Besides, the interest rates risk hedgi ng errors under both the statistic interestrates term structure m odels and dynam ic in terest rates term structure m odels arecompared. It shows that Four-Shape-Factor duration vector model with the forecastinginformation of the intere st rates term structure incorporated performs best, whereasthe stochastic duration vector of the four-factor Non-Gaussian Affine Term StructureModel perf orms even worse than the F our-Shape-Factor duration vector m odelwithout the forecasting information of the interest rates term structure incorporated.
Finally, based on a laconic introduction of the default contagion m odel and thefactor models of credit portf olio, default contagion effect is introduced to the factormodels of credit portfolio, under w hich the analytical results for hedging the creditrisk of portfolio with linear combinations of systematic risk factors and for Hoeffdingdecomposition of the portfolio systematic loss into a sum terms depending on the riskfactors are presented. For hom ogenous cr edit portfolio, the expectation of itssystematic loss as well as the position of the risk-free bond in the hedging portfolioincreases after th e default contagion effect is in troduced. Besides, when the d efaultprobability of the counterparty in the homogenous portfolio is relatively low (h igh),the position in the systematic risk factors increases (decreases) after the incorporationof default contagion ef fect. Simulation results under the two system atic risk factorscondition show that when the confidence level increases, the CVaR of systematic lossincreases too, which is m ainly attributed to not the expectation term but the factorco-movements term. Besides, if the fraction o f default in creases, which m eans the default contagion ef fect strengthens, the CV aR of systematic loss increases, whichmainly results from the factor co-movements term too.
引文
[1] Gupton G., Finger C., Bhatia M. CreditMetrics technical document [R]. TechnicalReport, J.P. Morgan&Co,1997.
[2] Crosbie P. Modeling default risk [R]. Technical Report, KMV Corporation,1999.
[3] Credite S uisse Finan cial Produ cts, Cr editRisk+: a credit risk managem entframework [R],1997.
[4] Macaulay F. Some theoretical problems suggested by the move ment of interestrates, bond yields and stock prices in the United States Since1856[M], New York:Columbia University Press,1938.
[5] Fisher L., Weil R. Coping with th e risk of interest-rate fluc tuations: Returns tobondholders from naive and optim al strategies [J], Journal of Business,1971,44(4):408-431.
[6] Cooper I.A. Asset value, interest-rate ch ange, and duration [J], Journal ofFinancial and QuantitativeAnalysis,1977,12(5):701-723.
[7] Kaffky T.E., Ma Y.Y., Nozari A. Ma naging yield curve exposure: introducingreshaping durations [J], Journal of Fixed Income,1992,2(3):39-45.
[8] Rogers L., Tehranchi M. Can the implied volatility surface move by parallel shifts[J], Finance&Stochastics,2010,14(2):235-248.
[9] Fong G. and O. Vasicek, A risk minimization strategy for portfolio immunization[J], Journal of Finance,1984,39(5):1541-1546.
[10] Nawalkha S.K., Cham bers D. R. An i mproved immunization strategy:M-Absolute [J], FinancialAnalysts Journal,1996,52(5):69-76.
[11] Balbas A., Ibanez A. When can you immunize a bond portfolio?[J], Journal ofBanking&Finance,1998,22(12):1571-1595.
[12] Nawalkha S.K., Chambers D.R. The M-Vector Model: Derivation and Testing ofExtensions to the M-Square Model [J], Journal of Portfolio Managem ent,1997,23(2):92-98.
[13] Nawalkha S.K., Soto G.M., Zhang J. Generalized M-vector m odels for hedginginterest rate risk [J], Journal of Banking&Finance,2003,27(8):1582-1604.
[14] Navarro E., Nave G. M. The structur e of spot rates and immunization: Somefurther results [J]. Spanish Economic Review,2001,3(4):273-294.
[15] Ho T.S.Y. Key rate durations: Measures of interest rate risk [J], Journal of FixedIncome,1992,2(2):29-44.
[16] Ho T.S.Y., Chen M.Z. H., Eng F.H.T. VAR Analytics: Portfolio S tructure, KeyRate Convexities, and VAR Betas [J], Journal of Portfolio Managem ent,1996,23(1):89-98.
[17] Litterman R., Scheinkman J. Common factors affecting bond returns [J], Journalof Fixed Income,1991,1(1):54-61.
[18] Barber J.R., Cooper M.L. I mmunization Using Principal Com ponent Analysis[J], Journal of Portfolio Management,1996,23(1):99-105.
[19] Bliss R.R. Movem ents in the term st ructure of interest rates [J], Econom icReview,1997,82(4):16-33.
[20] Nawalkha S.K., Soto G.M., Beliaeva N.A. Interest Rate Risk Modeling: TheFixed Income Valuation Course [M], Hoboken: John Wiley&Sons,2005.
[21] Granito M. Bond Portfolio Immunization [M], Green-wich: JAI Press,1984.
[22] Chambers D.R., Carleton W.T., McEnally R.W. Immunizing Default-Free BondPortfolios with a Duration V ector [J], Journal of Financial and QuantitativeAnalysis,1988,23(1):89-104.
[23] Nawalkha S.K. The Duration Vector: Acontinuous-time extension to default-freeinterest rate contingent claims [J], J ournal of Banking&Finance,1995,19(8):1359-1378.
[24] Merton R.C. The theory of rational option pricing [J], Bell Journal of Economics,1973,4(1):142-183.
[25] Willner R. A New T ool for Portfolio Managers: Level, Slope, and CurvatureDurations [J], Journal of Fixed Income,1996,6(1):48-59.
[26] Diebold F.X., Ji L., Li C. A Thre e-Factor Y ield Curve Model: Non-Af fineStructure, System atic Risk Sources, and Generalized Duration [R], WorkingPaper, PIER,2006.
[27] Kondratiuk-Janyska A., Kaluszka M. On new imm unization strategies underrandom shocks on the term structure of in terest rates [J], Operations Researchand Decisions,2009,1:91-101.
[28] Llano-Ferro F. Modelling bond duration and convexity under interest rate andtime to m aturity variations [J], International Research Journal of Finance andEconomics,2009,26:144-147.
[29] Ki m S.H. Interest rate risk of bond investm ent [J], Journal of internationalbusiness and economics,2011,11(3):123-127.
[30]薛一飞，张维，刘豹.我国债券投资中一种利率风险最小化模型的分析[J]，系统工程理论方法与应用，1999,8(1)：2-10.
[31]张继强.债券利率风险管理的三因子模型[J]，数量经济技术经济研究，2004,1:62-67.
[32]文忠桥.国债投资的利率风险免疫研究[J]，数量经济技术经济研究，2005，8：93-101.
[33]龚朴，何旭彪.非平移收益曲线的风险免疫策略[J]，管理科学学报,2005，8(4)：60-67.
[34]王宗军，冯娟.利率风险管理的三因子久期模型[J]，系统管理学报，2007，16(6)：698-700.
[35]刘艳萍，巩玉芳，迟国泰.基于利率非平行移动风险控制的资产负债组合优化模型[J]，管理学报，2009，6(9)：1215-1225.
[36]刘艳萍，王婷婷，迟国泰.基于方向久期利率风险免疫的资产负债组合优化模型[J]，管理评论，2009，21(4)：12-33.
[37]李正红.中国债券投资的利率风险研究[D]，西北工业大学博士学位论文，2006.
[38]焦志常.固定收益证券组合投资于风险管理研究[D]，吉林大学博士学位论文，2006.
[39]朱峰.国债利率风险免疫策略研究[D]，厦门大学博士学位论文，2004.
[40] Vasicek O.A. An equilibrium characterization of the term structure [J], Journalof Financial Economics,1977,5(2):177-188.
[41] Cox J.C., Ingersoll J.E., Ross S.A. An intertemporal general equilibrium modelof asset prices [J], Econometrica,1985,53(2):363-384.
[42] Cox J.C., Ingersoll J.E., Ross S.A. A theory of the term structure of interest rates[J], Econometrica,1985,53(2):385-407.
[43] Brennan M.J., Schwartz E.S. An equilibrium model of bond pricing and a test ofmarket efficiency [J], Jo urnal of Fin ancial and Quantitative Analysis,1982,17(3):307-329.
[44] Fong H.G., Vasicek O.A. Interest rate volatility as a stoc hastic factor [R],Working Paper, GiffordAssociates,1992.
[45] Longstaff F.A., Schwartz E.S. Interest-rate volatility and the term structure: Atwo-factor general equilib rium model [J], Journal of Finance,1992,47(4):1259-1282.
[46] Duffie D., Kan R. A yield-factor m odel of inte rest ra tes [J], Mathem aticalFinance,1996,6(4):379-406.
[47] Ho T.S.Y., Lee S.B. T erm structur e m ovement and pricing interest ratecontingent claims [J], Journal of Finance,1986,41(5):1012-1029.
[48] Hull J., W hite A. Pricing inte rest-rate derivative securities [J], Review ofFinancial Studies,1990,3(4):573-592.
[49] Heath D., Jarrow R., Mort on A. Bond pricing and the te rm structure of interestrates: a dis crete time approximation [J], Journal of Financial and Quantita tiveAnalysis,1990,25(4):419-440.
[50] Heath D., Jarrow R., Morton A. Con tingent claim valuat ion with a randomevolution of interest rates [J], Review of Futures Markets,1990,9:54-82.
[51] Heath D., Jarrow R., Mort on A. Bond pricing and the te rm structure of interestrates: A new m ethodology for contingent claims valuation [J], Econom etrica,1992,60(1):77-105.
[52] Heath D., Jarrow R., Morton A. Easier done than said [J], risk,1992,5(9):77-80.
[53] Diebold F., Li C. For ecasting the term structure of government bond yields [J],Journal of Econometrics,2006,130(2):337-364.
[54] Duffee G. R. Term premia and interest rate forecasts in affine models [J], Journalof Finance,2002,57(1):405-443.
[55]郑振龙，柯鸿，莫天瑜.利率仿射模型下的利率风险价格形式实证研究[J]，管理科学学报，2010，13(9):4-15.
[56] Ang A., Piazzesi M. A no-arbitrage vector autoregr ession of term struc turedynamics with m acroeconomic and latent variables [J], Journal of MonetaryEconomics,2003,50(4):745-787.
[57] Hordahl P., Tristani O., Vestin D. A joint econometric model of macroeconomicand term-structure dynam ics [J], Journal of Econom etrics,2006,131(1):405-444.
[58] Moench E. Forecasting the y ield curve in a data-rich environ ment: Ano-arbitrage factor-augmented VAR approach [J]. Journal of Econometrics,2008,146(1):26-43.
[59] Carriero A. Forecasting the Yield Curve Using Priors from No Arbitrage AffineTerm S tructure Mode ls [J], Intern ational Econom ic Review,2011,52(2):425-459.
[60] Pooter M., Ravazzolo F., Dijk D. T erm S tructure Forecasting Usin g MacroFactors and forecast combination [R], Working Paper, Norges Bank,2010.
[61] Nelson R., Siegel F. Parsim onious m odeling of yield curves [J], Journal ofBusiness,1987,60(4):473-489.
[62] Christensen J., Diebold F.X., Rudebusch G.D. The Affine Arbitrage-Free Classof Nelson-Siegel Term Structure Models [R], Working Paper, National Bureau ofEconomic Research,2007.
[63] Diebold F.X., Rudebusch G.D., Aruoba S.B. The Macroeconom y and the Y ieldCurve: A Dynamic Latent Factor Appro ach [J], Journal of Econom etrics,2006,131(1):309-338.
[64] Yu W.C., Zivot E. Fo recasting the term structures of T reasury and corporateyields using dyna mic Nelson-Siegel m odels [J], International Journal ofForecasting,2011,27(2):579-591.
[65] Cochrane J., Piazzesi M. Bond risk premia [J], Am erican Economic Review,2005,95(1):138-160.
[66] Almeida C., Gomes R., Leite A., et al. Does Curvature Enhance Forecasting [J],International Journal of Theoretical&Applied Finance,2009,12(8):1172-1196.
[67] Svensson L. Estim ating and Interpre ting F orward In terest Ra tes: Sweden1992-1994[R], Working Paper, National Bureau of Economic Research,1994.
[68] Ludvigson S.C., Ng S. Macro Factors in Bond Risk Prem ia [J], Review ofFinancial Studies,2009,22(12):5027-5067.
[69] Laurini M., Hotta L., Bayesian extensions to Diebold-Li term structure model [J],International Review of FinancialAnalysis,2010,19(5):342-350.
[70]叶振军，张庆翠，王春峰.时变参数N-S利率期限结构模型的主微分分析及其实证研究[J].预测,2009，28(4)：62-65.
[71]胡志强，王婷.基于Nelson-Siegel模型的国债利率期限结构预测[J]，经济评论，2009，6:57-66.
[72]王志强，康书隆. Nelson-Siegel久期配比免疫模型的改进与完善[J]，数量经济技术经济研究，2010，12:133-147.
[73] Cox J.C., Ingersoll J.E., Ross S.A. Du ration and the Measurement of Basis Risk[J], Journal of Business,1979,52(1):51-61.
[74] Boyle P.P. I mmunization under stochastic models of the term structure [J],Journal of the Institute ofActuaries,1978,105:177-187.
[75] Wu X.P. A New S tochastic Dura tion Based on the V asicek and CIR T ermStructure Theories [J], Journal of Bu siness Finance&Accounting,2000,27(7):912-932.
[76] Kwon O. On the equivalence of a cla ss of af fine term s tructure models [J],Annals of Finance,2009,5(2):263-279.
[77] Munk C. Stochastic duration and fast coupon bond option pricing in multi-factor[J]. Review of Derivatives Research,1999,3(2):157-181.
[78] Bjork T., Svensson L. On the existen ce of finite dim ensional realizations fornonlinear forward rate models [J], Mathematical Finance,2001,11(2):205-243.
[79] Kwon O.K. Duration, factor sensitivities, and interest rate Greeks [J], Annals ofFinance,2007,3(4):472-486.
[80] Au K.T., Thurston D.C. A New Cla ss of Duration Measures [J], Econom icsLetters,1995,47(3):372-375.
[81] Fruhwirth M. The Heath-Jarrow-Morton Duration and Convexity: A GeneralizedApproach [J], International Journal of Theoretical and Applied Finance,2002,5(7):695-700.
[82] Kraft H. Elasticity approach to portfolio optimization [J], Mathematical Methodsof Operations Research,2003,58(1):159-182.
[83] Wei J.Z. A si mple approach to bond option pricing [J], Journal of FuturesMarkets,1997,17(2):132-160.
[84] Chu C.C., Kwok Y.K. Valuation of gua ranteed annuity options in af fine termstructure models [J], International Jour nal of Theoretical a nd Applied Finance,2007,10(2):363-387.
[85] Ahlgrim K.C., D’arcy S.P., Gorvett R.W. The effective duration and convexity ofliabilities for property-liabil ity insurers under stochastic interest rates [C], Thegeneva papers on risk and insurance theory,2004,29(1):75-108.
[86]刘湘云.基于动态随机优化方法的商业银行利率风险最优控制[J]，系统管理学报，2008，17(5)：509-591.
[87]曾黎.基于违约风险的Vasicek利率风险研究[J]，数学理论与应用,2010，30(1)：67-70.
[88]王克明，梁戍.基于利率期限结构的随机久期与凸度模型构建及应用[J]，统计与决策，2010,24:158-160.
[89] Black F., Scholes M. The pricing of options and corporate liabilities [J], Journalof Political Economy,1973,81(3):637-654.
[90] Merton R.C. On the pricing of corporate debt: The risk structure of interest rates[J], Journal of Finance,1974,29(2):449-470.
[91] Black F., Cox J.C. Valuing corporate securities: Some effects of bond indentureprovisions [J], Journal of Finance,1976,31(2):351-367.
[92] Geske R. The valuation of corporate li abilities as compound options [J], Journalof Financial and QuantitativeAnalysis,1977,12(4):542-552.
[93] Longstaff F.A., Schwartz E.S. A simple approach to valuing risky f ixed andfloating rate debt [J], Journal of Finance,1995,50(3):789-819.
[94] Anderson R. W., Sundaresan S. Design and valuation of debt contracts [J],Review of Financial Studies,1996,9(1):37-68.
[95] Mella-Barral P., Perraudin W. Strategic debt service [J], Journal of Finance,1997,52(2):532-556.
[96] Ericsson J., Reneby J. The valuation of corporate liabilities: Theory and tests [R],Working Paper, McGill University,2001.
[97] Lando D. Credit Risk Modeling: Theo ry and Applications [M], Princeton:Princeton University Press,2004.
[98] Chan-Lau J.A., Sy A.N.R. Distance-to-default in banking: A bridge too far?[R],Working Paper, IMF,2006.
[99] Capuano C. The option-iPoD: The pr obability of default im plied by optionprices based on entropy [R], Working Paper, IMF,2008.
[100] Jarrow R.A., Tumbull S.M. Pricing derivatives on financial securities subject tocredit risk [J], Journal of Finance,1995,50(1):53-85.
[101] Jarrow R.A., Lando D., T umbull S.M. AMarkov model for the term structureof credit risk spreads [J], The Revi ew of Financial S tudies,1997,10(2):481-523.
[102] Hurd T.R., Kuznetsov A. Af fine Ma rkov chain m odels of m ultifirm creditmigration [J], Journal of Credit Risk,2007,3(1):3-29.
[103] Duffie D., Singleton K.J. Modeling term structures of defaultable bonds [J],Review of Financial Studies,1999,12(4):687-720.
[104] Wong H. Y., W ong T.L. Reduced-form models with regim e switching: Anempirical analysis for corporate bonds [J], Asia-Pacific Financial Markets,2007,14(3):229-253.
[105] Wu L., Zhang F.X. A no-arbitrage analysis of econom ic determinants of thecredit spread term structure [J], Management Science,2008,54(6):1160-1175.
[106] Chance D.M. Default Risk and the Duration of Zero Coupon Bonds [J], Journalof Finance,1990,45(1):265-274.
[107] Nawalkha S.K. A con tingent claim s analysis of the interest-rate-riskcharacteristics of corporate liabilities [J], Journal of Banking&Finance,1996,20(2):227-245.
[108] Xie Y.A., Liu S., Wu C. Duration, default risk, and the term structure of interestrates [J]. Journal of Financial Research,2005,28(4):539-554.
[109] Kraft K., Munk C. Bond durations: Cor porates vs. T reasuries [J], Journal ofBanking&Finance,2007,31(12):3720-3741.
[110] Duffee G.R. The relation between T reasury yields and corporate bond yieldspreads [J], Journal of Finance,1998,53(6):2225-2241.
[111] Acharya V.V., Carpenter J.N. Cor porate bond valuation and hedging wit hStochastic Interest Rates and Endogenous Bankruptcy [J], Review of FinancialStudies,2002,15(5):1355-1383.
[112] Jacoby G., Roberts G.S. Default and call-adjusted duration for corporate bonds[J], Journal of Banking and Finance,2003,27(12):2297-2321.
[113] Sarkar S., Hong G. Effective duration of callable corporate bonds: Theory andevidence [J]. Journal of Banking and Finance,2004,28(3):499-521.
[114] Xie Y.A., Liu S., W u C., et al. The effects of default and call risk on bondduration [J], Journal of Banking&Finance,2009,33(9):1700-1708.
[115] Ho T.S.Y., Lee S.B. A unified credit and interest rate arbi trage-free contingentclaim model [J], Journal of Fixed Income,2009,18(3):5-17.
[116] Meder A. Managing Pension Liabi lity Credit Risk: Maintaining a T otalPortfolio Perspective [J], Journal of Portfolio Management,2009,36(1):90-99.
[117] Landes L., Stoffels J., Seifert J. An Empirical test of a Duration-Based Hedge:The Case of Corporate Bonds [J], Jour nal of Futures Markets,1985,5(2):173-182.
[118] Cornell B., Green K. The Investm ent Performance of Low-Grade Bond Funds[J], Journal of Finance,1991,46(1):29-48.
[119] Ambastha M., Dor A. B., Dynkin L., et al. Empirical Duration of CorporateBonds and Credit Market Segm entation [J], Journal of Fixed Incom e,2010,20(1):5-27.
[120] Cheyette O., T omaich T. Empirical Credit Risk [R], W orking Paper, BarraFixed Income Research,2003.
[121] Collin-Dufresne P., Goldstein R., Martin J. The determ inants of cred it spreadchanges [J], Journal of Finance,2001,56(6):2177-2207.
[122] Cheyette O., Postler B. Em pirical Credit Risk [J], J ournal of PortfolioManagement,2006,32(4):79-92.
[123] Blanchet-Scalliet C., Jeanblanc M. Hazard rate for credit risk and hedgingdefaultable contingent claims [J], Finance and Stochastics,2004,8(1):145-159.
[124] Campi L., Polbennikov S., Sbuelz A. Systematic equity-based credit risk: ACEV model with jump to default [J], Journal of Economic Dynamics&Control,2009,33(1):93-108.
[125] Ederington L. The hedging performance of the new futures markets [J], Journalof Finance,1979,34(1):157-170.
[126] Figlewski S. Hedging perform ance and basis risk in stock index futures [J],Journal of Finance,1984,39(3):657-669.
[127] Figlewski S. Hedging with stock inde x futures: Theory and application in anew market [J], Journal of Futures Markets,1985,5(2):183-199.
[128] Hill J., Schneeweis T. A note on the hedging effectiveness of foreign currencyfutures [J]. Journal of Futures Markets,1981,1(4):659-664.
[129] Hill J., Schneeweis T. The hedging effectiveness of foreign currency futures [J],Journal of Futures Markets,1981,1(1):77-88.
[130] Witt H.J., Schroeder T.C., Hayenga M.L. Comparison of analytical approachesfor estimating hedge ratios for agricultural commodities [J], Journal of FuturesMarkets,1987,7(2):135-146.
[131] Brown S.L. A reformulation of the por tfolio model of hedging [J], Am ericanJournal ofAgricultural Economics,1985,67(3):508-512.
[132] Myers R. J. Estim ating time-varying optimal hedge ratios on futures m arkets[J], Journal of Futures Markets,1991,11(1):39-53.
[133] Wilkinson K.J., Rose L.C., Y oung M.R. Com paring the Ef fectiveness ofTraditional and Time Varying Hedge Ratios Using New Zealand and AustralianDebt Futures Contracts [J], The Financial Review,1999,34(3):79-94.
[134] Becker C., Guill G.D. Using CLOs to Manage the Credit Risk of CorporateLoan Portfolios [J], Journal ofApplied Finance,2009,1:28-37.
[135] Skinner F.S., Nuri J. Hedging emerging market bonds and the rise of the credi tdefault swap [J], International Revi ew of Financial Analysis,2007,16(5):452-470.
[136] Bielecki T.R., Jeanblanc M., Rutkowski M. Hedging of baske t creditderivatives in the credit default swap m arket [J], Journal of Credit Risk,2007,3(1):92-132.
[137] Korn O. Risk m anagement with default-risky forwards [J], Risk Managem ent,2010,62(2):102-125.
[138] Saunders D., Xiouros C., Zenios S.A. Credit risk optimization using factormodels [J],Annals of Operations Research,2007,152(1):49-77.
[139] Vasicek O. The Loan Loss Distribution[R], T echnical Docum ent, KM VCorporation, San Fransisco,1987.
[140] Vasicek O. Limiting loan loss probability distribution[R], Technical Document,KMV Corporation, San Fransisco,1991.
[141] W ilde T. Probing Granularity [J], Risk,2001,14(8):103-106.
[142] Frey R., McNeil A. Dependent Defaults in Models of Portfolio Credit Risk [J],Journal of Risk,2003,6(1):59-92.
[143] Gordy M. A risk-factor m odel foundation for ratings-based bank capital rules[J], Journal of Financial Intermediation,2003,12(3):199-232.
[144] Vasicek O. Loan portfolio value [J], Risk,2002,160-162.
[145] Bonti G., Kalkbrener M., Lotz C., et al. Credit risk concentrations under stress[J], Journal of Credit Risk,2006,2(3):115-136.
[146] Rosen D., Saunders D. Analytical m ethods for hedging system atic credit riskwith linear factor portfolios [J], Jo urnal of Econom ic Dynamics&Control,2009,33(1):37-52.
[147] Ioannides M., Skinner F.S. Hedging Corporate Bonds [J], Journal of BusinessFinance&Accounting,1999,26(7):919-944.
[148] Schaefer S.M., S trebulaev I.A. S tructural m odels of credit risk are useful:Evidence from hedge ratios on corporat e bonds [J], Journal of FinancialEconomics,2008,90(1):1-19.
[149] Elouerkhaoui Y. Pricing and he dging in a dynam ic credit m odel [J],International Journal of Theoretical andApplied Finance,2007,10(4):703-731.
[150] Becherer D., Ward I. Optimal Weak Static Hedging of Equity and Credit RiskUsing Derivatives [J],Applied Mathematical Finance,2010,17(1):2-28.
[151] Frey R., Backhaus J. Pricing and hedging of portfo lio credit Derivatives withinteracting def ault in tensities [J], In ternational Journal of Theoretical andApplied Finance,2008,11(6):611-634.
[152] Frey R., Backhaus J. Dynamic hedging of synthetic CDO tranches with spreadrisk and default contagion [J], Journal of Economic Dynamics&Control,2010,34(4):710-724.
[153] Cousin A., Laurent J.P. Hedging issues for CDOs, Risk Books [M], G. Meissner,2008.
[154] Laurent J.P., Cousin A., Ferm anian J.D. Hedging default risks of CDOs i nMarkovian contagion m odels [J], Qu antitative Finance,2011,11(12):1773-1791.
[155]魏明，王琼.信用衍生品对我国信用风险管理的作用及其实施策略[J]，管理世界，2003，10：142-142.
[156]潘杰义，王琼，陈金贤.信用风险管理创新工具——信用衍生品的发展与评述[J]，西北师大学报，2003，40(3)：122-124.
[157]任宏之.辩证分析信用衍生品功能的利与弊——以07金融危机为例[J]，金融经济,2011，2：37-38.
[158]刘新，祁源，喻靖.关于我国银行业应用信用衍生品防范信用风险问题的研究[J]，经济师，2010，1：9-11.
[159]陈正声，秦学志，王玥.扭曲Copula函数在BDS定价及其敏感度分析中的应用[J]，系统管理学报，2010，19(3)：345-350.
[160] Chambers D.R. The Managem ent of Default-Free Bond P ortfolios [D], Ph.D.dissertation, University of North Carolina, Chapel Hill,1981.
[161]范龙振.上交所利率期限结构的三因子广义高斯仿射模型[J]，管理工程学报，2005,19(1)：82-86.
[162]任姝仪，杨丰梅，周荣喜.中国国债利率期限结构Nelson-Siegel族模型实证比较[J]，系统工程，2011，29(10)：30-34.
[163]周子康，王宁，杨衡.中国国债利率期限结构模型研究与实证分析[J]，金融研究，2008，3：132-150.
[164] Galluccio S., Roncoroni A. A new m easure of cross-sec tional risk and itsempirical implications for portfolio risk management [J], Journal of Banking&Finance,2006,30(8):2387-2408.
[165] Roncoroni A., Galluccio S., Guiotto P. Shape Factors and Cross-sectional Risk[J], Journal of Economic Dynamics&Control,2010,34(11):2320-2340.
[166] Fama E., Bliss R. The Inform ation in Long-m aturity Forward Rates [J],American Economic Review,1987,77(4):680-692.
[167]黄云清，舒适，陈艳萍等.数值计算方法[M]，北京：科学出版社，2009.
[168]苏云鹏，杨宝臣，李冬连.基于遗传算法的扩展Nelson-Siegel模型及实证研究[J]，统计与信息论坛，2011，1：15-19.
[169] Nawalkha S.K., Soto G.M. Managing in terest risk: The next challenge?[J],Journal of Investment Management,2009,7(3):2-19.
[170]沈其君. SAS统计分析[M]，南京：东南大学出版社，2002.
[171] Matsumura S., Moreira B. Assessing macro influence on Brazilian yield curvewith affine models [J],Applied Economics,2011,43(15):1847-1863.
[172]康书隆，王志强.中国国债利率期限结构的风险特征及其内含信息研究[J]，世界经济，2010，7：122-143.
[173] Dai Q., Singleton K. E xpectation puzzles, time varying risk premia, and affinemodels of the term structure [R], Working Paper, Stanford University,2002.
[174]林元烈.应用随机过程[M]，北京：清华大学出版社，2002.
[175] Grasselli M., T ebaldi C. S tochastic Jacobian and Riccati ODE in af fine termstructure models [J], Decisions in Economics&Finance,2007,30(2):95-108.
[176] Gibbons M.R., Ramaswamy K. A test of the Cox, Ingersoll, and Ross model ofthe term structure [J]. Review of Financial Studies,1993,6:619-658.
[177] Dai Q., Singleton K.J. Specification analysis of affine term structure models [J].Journal of Finance,2000,55:1943-1978.
[178] Fisher M., Gilles C. Estimating exponential-affine models of the term structure
[R]. Technical Report, Federal Reserve Bank ofAtlanta,2000.
[179] Pedersen, A.R. A new approach to m aximum-likelihood estim ation forstochastic dif ferential equations ba sed on discrete observations [J].Scandinavian Journal of Statistics,1995,22:55-71.
[180] Brandt M., He P. Simulated likeli hood estim ation of af fine term structuremodels from panel data [R]. Working Paper, University of Pennsylvania,2002.
[181] Duffee G.R., Stanton R.H. Estim ation of dynam ic term structure m odels [R],Working Paper, Haas School of Business, U.C. Berkeley,2004.
[182] Rosen D., Saunders D. Risk factor contributions in portfolio credit risk models[J], Journal of Banking&Finance,2010,34(2):336-349.
[183] van der Vaart A. AsymptoticStatistics [M], Cambridge University Press,1998.
[184] McNeil A., Frey R., Em brechts P. Quantitative Risk Managem ent [M].Princeton University Press,2005.
[185] Neu P., Kuhn R. Credit risk enhancem ent in a network of interdependent firm s[J], PhysicaA,2004,342(3):639-655.
[186] Hatchett J.P.L., Kuhn R. Ef fects of economic interactions on credit risk [J],Journal of PhysicsA: Mathematical and General,39(10):2231-2251.
[187] Hatchett J.P.L., Kuhn R. Credit cont agion and credit risk [J], QuantitativeFinance,2009,9(4):373-382.
[188] Davis M., Lo V. Infectious defaults [J], Quantitative Finance,2001,1(4):382-387.
[189] Jarrow R., Yu F. Counterparty risk and the pricing of derivative securities [J],Journal of Finance,2001,56(5):1765-1799.
[190] Artzner P., Delbaen F., Eber J., et al. Coherent Measures of R isk [J].Mathematical Finance,1999,9(3):203-228.
[191] Rockafeller R., Uryasev S. Optim ization of Conditional V alue-at-Risk [J],Journal of Risk,2000,2(3):21-41.
[192] Aytac I., Ronnie S. Optim al static–dynamic hedges for barrier options [J],Mathematical Finance,2006,16(2):359-385.
[193] Jonathan D. Basis Convergence and Long Memory in Volatility When DynamicHedging with Futures [J], Journal of Financial&Quantitative Analysis,2007,42(4):1021-1040.
[194] Li M.Y.L. Dynamic hedge ratio for stock index futures: application of thresholdVECM [J],Applied Economics,2010,42(11):1403-1417.
[195] Li D.X. On default correlation: a copula function approach [J], Journal of FixedIncome,2000,9(4):43–54.
[196] Laurent J.P., Gregory J. Basket defa ult Swaps, CDOs and factor copulas [J],Journal of Risk,2005,7(4):103–122.
[197] Wu P.C. Applying a factor copula to value basket credit linked notes with issuerdefault risk [J], Finance Research Letters,2010,7(3):178-183.
[198] Moreira F.F. Copula-Based Form ulas to Estimate Unexpected Credit Losses(The Future of Basel Accords?) Fern ando F. Moreira Copula-Based Form ulasto Estimate Unexpected Credit Lo sses [J], Financial Markets, Institutions&Instruments,2010,19(5):381-404.
[199] Bertocchi M., Giacometti R., Zenios S. A. Risk factor analysis and portfolioimmunization [J], European Journal of Operational Research,2005,161(2):348-363.
[200] Meligkotsidou L., Vrontos I.D. Detecting structural breaks and identifying riskfactors in hedge fund returns: A Bayesian approach [J], Journal of Banking&Finance,2008,32(11):2471-2481.
[201] Bali T.G., Brown S.J., Caglayan M.O. Do hedge funds’exposures to risk factorspredict their future returns?[J], Journal of Financial Economics,2011,101(1):36-68.
[2] Crosbie P. Modeling default risk [R]. Technical Report, KMV Corporation,1999.
[3] Credite S uisse Finan cial Produ cts, Cr editRisk+: a credit risk managem entframework [R],1997.
[4] Macaulay F. Some theoretical problems suggested by the move ment of interestrates, bond yields and stock prices in the United States Since1856[M], New York:Columbia University Press,1938.
[5] Fisher L., Weil R. Coping with th e risk of interest-rate fluc tuations: Returns tobondholders from naive and optim al strategies [J], Journal of Business,1971,44(4):408-431.
[6] Cooper I.A. Asset value, interest-rate ch ange, and duration [J], Journal ofFinancial and QuantitativeAnalysis,1977,12(5):701-723.
[7] Kaffky T.E., Ma Y.Y., Nozari A. Ma naging yield curve exposure: introducingreshaping durations [J], Journal of Fixed Income,1992,2(3):39-45.
[8] Rogers L., Tehranchi M. Can the implied volatility surface move by parallel shifts[J], Finance&Stochastics,2010,14(2):235-248.
[9] Fong G. and O. Vasicek, A risk minimization strategy for portfolio immunization[J], Journal of Finance,1984,39(5):1541-1546.
[10] Nawalkha S.K., Cham bers D. R. An i mproved immunization strategy:M-Absolute [J], FinancialAnalysts Journal,1996,52(5):69-76.
[11] Balbas A., Ibanez A. When can you immunize a bond portfolio?[J], Journal ofBanking&Finance,1998,22(12):1571-1595.
[12] Nawalkha S.K., Chambers D.R. The M-Vector Model: Derivation and Testing ofExtensions to the M-Square Model [J], Journal of Portfolio Managem ent,1997,23(2):92-98.
[13] Nawalkha S.K., Soto G.M., Zhang J. Generalized M-vector m odels for hedginginterest rate risk [J], Journal of Banking&Finance,2003,27(8):1582-1604.
[14] Navarro E., Nave G. M. The structur e of spot rates and immunization: Somefurther results [J]. Spanish Economic Review,2001,3(4):273-294.
[15] Ho T.S.Y. Key rate durations: Measures of interest rate risk [J], Journal of FixedIncome,1992,2(2):29-44.
[16] Ho T.S.Y., Chen M.Z. H., Eng F.H.T. VAR Analytics: Portfolio S tructure, KeyRate Convexities, and VAR Betas [J], Journal of Portfolio Managem ent,1996,23(1):89-98.
[17] Litterman R., Scheinkman J. Common factors affecting bond returns [J], Journalof Fixed Income,1991,1(1):54-61.
[18] Barber J.R., Cooper M.L. I mmunization Using Principal Com ponent Analysis[J], Journal of Portfolio Management,1996,23(1):99-105.
[19] Bliss R.R. Movem ents in the term st ructure of interest rates [J], Econom icReview,1997,82(4):16-33.
[20] Nawalkha S.K., Soto G.M., Beliaeva N.A. Interest Rate Risk Modeling: TheFixed Income Valuation Course [M], Hoboken: John Wiley&Sons,2005.
[21] Granito M. Bond Portfolio Immunization [M], Green-wich: JAI Press,1984.
[22] Chambers D.R., Carleton W.T., McEnally R.W. Immunizing Default-Free BondPortfolios with a Duration V ector [J], Journal of Financial and QuantitativeAnalysis,1988,23(1):89-104.
[23] Nawalkha S.K. The Duration Vector: Acontinuous-time extension to default-freeinterest rate contingent claims [J], J ournal of Banking&Finance,1995,19(8):1359-1378.
[24] Merton R.C. The theory of rational option pricing [J], Bell Journal of Economics,1973,4(1):142-183.
[25] Willner R. A New T ool for Portfolio Managers: Level, Slope, and CurvatureDurations [J], Journal of Fixed Income,1996,6(1):48-59.
[26] Diebold F.X., Ji L., Li C. A Thre e-Factor Y ield Curve Model: Non-Af fineStructure, System atic Risk Sources, and Generalized Duration [R], WorkingPaper, PIER,2006.
[27] Kondratiuk-Janyska A., Kaluszka M. On new imm unization strategies underrandom shocks on the term structure of in terest rates [J], Operations Researchand Decisions,2009,1:91-101.
[28] Llano-Ferro F. Modelling bond duration and convexity under interest rate andtime to m aturity variations [J], International Research Journal of Finance andEconomics,2009,26:144-147.
[29] Ki m S.H. Interest rate risk of bond investm ent [J], Journal of internationalbusiness and economics,2011,11(3):123-127.
[30]薛一飞，张维，刘豹.我国债券投资中一种利率风险最小化模型的分析[J]，系统工程理论方法与应用，1999,8(1)：2-10.
[31]张继强.债券利率风险管理的三因子模型[J]，数量经济技术经济研究，2004,1:62-67.
[32]文忠桥.国债投资的利率风险免疫研究[J]，数量经济技术经济研究，2005，8：93-101.
[33]龚朴，何旭彪.非平移收益曲线的风险免疫策略[J]，管理科学学报,2005，8(4)：60-67.
[34]王宗军，冯娟.利率风险管理的三因子久期模型[J]，系统管理学报，2007，16(6)：698-700.
[35]刘艳萍，巩玉芳，迟国泰.基于利率非平行移动风险控制的资产负债组合优化模型[J]，管理学报，2009，6(9)：1215-1225.
[36]刘艳萍，王婷婷，迟国泰.基于方向久期利率风险免疫的资产负债组合优化模型[J]，管理评论，2009，21(4)：12-33.
[37]李正红.中国债券投资的利率风险研究[D]，西北工业大学博士学位论文，2006.
[38]焦志常.固定收益证券组合投资于风险管理研究[D]，吉林大学博士学位论文，2006.
[39]朱峰.国债利率风险免疫策略研究[D]，厦门大学博士学位论文，2004.
[40] Vasicek O.A. An equilibrium characterization of the term structure [J], Journalof Financial Economics,1977,5(2):177-188.
[41] Cox J.C., Ingersoll J.E., Ross S.A. An intertemporal general equilibrium modelof asset prices [J], Econometrica,1985,53(2):363-384.
[42] Cox J.C., Ingersoll J.E., Ross S.A. A theory of the term structure of interest rates[J], Econometrica,1985,53(2):385-407.
[43] Brennan M.J., Schwartz E.S. An equilibrium model of bond pricing and a test ofmarket efficiency [J], Jo urnal of Fin ancial and Quantitative Analysis,1982,17(3):307-329.
[44] Fong H.G., Vasicek O.A. Interest rate volatility as a stoc hastic factor [R],Working Paper, GiffordAssociates,1992.
[45] Longstaff F.A., Schwartz E.S. Interest-rate volatility and the term structure: Atwo-factor general equilib rium model [J], Journal of Finance,1992,47(4):1259-1282.
[46] Duffie D., Kan R. A yield-factor m odel of inte rest ra tes [J], Mathem aticalFinance,1996,6(4):379-406.
[47] Ho T.S.Y., Lee S.B. T erm structur e m ovement and pricing interest ratecontingent claims [J], Journal of Finance,1986,41(5):1012-1029.
[48] Hull J., W hite A. Pricing inte rest-rate derivative securities [J], Review ofFinancial Studies,1990,3(4):573-592.
[49] Heath D., Jarrow R., Mort on A. Bond pricing and the te rm structure of interestrates: a dis crete time approximation [J], Journal of Financial and Quantita tiveAnalysis,1990,25(4):419-440.
[50] Heath D., Jarrow R., Morton A. Con tingent claim valuat ion with a randomevolution of interest rates [J], Review of Futures Markets,1990,9:54-82.
[51] Heath D., Jarrow R., Mort on A. Bond pricing and the te rm structure of interestrates: A new m ethodology for contingent claims valuation [J], Econom etrica,1992,60(1):77-105.
[52] Heath D., Jarrow R., Morton A. Easier done than said [J], risk,1992,5(9):77-80.
[53] Diebold F., Li C. For ecasting the term structure of government bond yields [J],Journal of Econometrics,2006,130(2):337-364.
[54] Duffee G. R. Term premia and interest rate forecasts in affine models [J], Journalof Finance,2002,57(1):405-443.
[55]郑振龙，柯鸿，莫天瑜.利率仿射模型下的利率风险价格形式实证研究[J]，管理科学学报，2010，13(9):4-15.
[56] Ang A., Piazzesi M. A no-arbitrage vector autoregr ession of term struc turedynamics with m acroeconomic and latent variables [J], Journal of MonetaryEconomics,2003,50(4):745-787.
[57] Hordahl P., Tristani O., Vestin D. A joint econometric model of macroeconomicand term-structure dynam ics [J], Journal of Econom etrics,2006,131(1):405-444.
[58] Moench E. Forecasting the y ield curve in a data-rich environ ment: Ano-arbitrage factor-augmented VAR approach [J]. Journal of Econometrics,2008,146(1):26-43.
[59] Carriero A. Forecasting the Yield Curve Using Priors from No Arbitrage AffineTerm S tructure Mode ls [J], Intern ational Econom ic Review,2011,52(2):425-459.
[60] Pooter M., Ravazzolo F., Dijk D. T erm S tructure Forecasting Usin g MacroFactors and forecast combination [R], Working Paper, Norges Bank,2010.
[61] Nelson R., Siegel F. Parsim onious m odeling of yield curves [J], Journal ofBusiness,1987,60(4):473-489.
[62] Christensen J., Diebold F.X., Rudebusch G.D. The Affine Arbitrage-Free Classof Nelson-Siegel Term Structure Models [R], Working Paper, National Bureau ofEconomic Research,2007.
[63] Diebold F.X., Rudebusch G.D., Aruoba S.B. The Macroeconom y and the Y ieldCurve: A Dynamic Latent Factor Appro ach [J], Journal of Econom etrics,2006,131(1):309-338.
[64] Yu W.C., Zivot E. Fo recasting the term structures of T reasury and corporateyields using dyna mic Nelson-Siegel m odels [J], International Journal ofForecasting,2011,27(2):579-591.
[65] Cochrane J., Piazzesi M. Bond risk premia [J], Am erican Economic Review,2005,95(1):138-160.
[66] Almeida C., Gomes R., Leite A., et al. Does Curvature Enhance Forecasting [J],International Journal of Theoretical&Applied Finance,2009,12(8):1172-1196.
[67] Svensson L. Estim ating and Interpre ting F orward In terest Ra tes: Sweden1992-1994[R], Working Paper, National Bureau of Economic Research,1994.
[68] Ludvigson S.C., Ng S. Macro Factors in Bond Risk Prem ia [J], Review ofFinancial Studies,2009,22(12):5027-5067.
[69] Laurini M., Hotta L., Bayesian extensions to Diebold-Li term structure model [J],International Review of FinancialAnalysis,2010,19(5):342-350.
[70]叶振军，张庆翠，王春峰.时变参数N-S利率期限结构模型的主微分分析及其实证研究[J].预测,2009，28(4)：62-65.
[71]胡志强，王婷.基于Nelson-Siegel模型的国债利率期限结构预测[J]，经济评论，2009，6:57-66.
[72]王志强，康书隆. Nelson-Siegel久期配比免疫模型的改进与完善[J]，数量经济技术经济研究，2010，12:133-147.
[73] Cox J.C., Ingersoll J.E., Ross S.A. Du ration and the Measurement of Basis Risk[J], Journal of Business,1979,52(1):51-61.
[74] Boyle P.P. I mmunization under stochastic models of the term structure [J],Journal of the Institute ofActuaries,1978,105:177-187.
[75] Wu X.P. A New S tochastic Dura tion Based on the V asicek and CIR T ermStructure Theories [J], Journal of Bu siness Finance&Accounting,2000,27(7):912-932.
[76] Kwon O. On the equivalence of a cla ss of af fine term s tructure models [J],Annals of Finance,2009,5(2):263-279.
[77] Munk C. Stochastic duration and fast coupon bond option pricing in multi-factor[J]. Review of Derivatives Research,1999,3(2):157-181.
[78] Bjork T., Svensson L. On the existen ce of finite dim ensional realizations fornonlinear forward rate models [J], Mathematical Finance,2001,11(2):205-243.
[79] Kwon O.K. Duration, factor sensitivities, and interest rate Greeks [J], Annals ofFinance,2007,3(4):472-486.
[80] Au K.T., Thurston D.C. A New Cla ss of Duration Measures [J], Econom icsLetters,1995,47(3):372-375.
[81] Fruhwirth M. The Heath-Jarrow-Morton Duration and Convexity: A GeneralizedApproach [J], International Journal of Theoretical and Applied Finance,2002,5(7):695-700.
[82] Kraft H. Elasticity approach to portfolio optimization [J], Mathematical Methodsof Operations Research,2003,58(1):159-182.
[83] Wei J.Z. A si mple approach to bond option pricing [J], Journal of FuturesMarkets,1997,17(2):132-160.
[84] Chu C.C., Kwok Y.K. Valuation of gua ranteed annuity options in af fine termstructure models [J], International Jour nal of Theoretical a nd Applied Finance,2007,10(2):363-387.
[85] Ahlgrim K.C., D’arcy S.P., Gorvett R.W. The effective duration and convexity ofliabilities for property-liabil ity insurers under stochastic interest rates [C], Thegeneva papers on risk and insurance theory,2004,29(1):75-108.
[86]刘湘云.基于动态随机优化方法的商业银行利率风险最优控制[J]，系统管理学报，2008，17(5)：509-591.
[87]曾黎.基于违约风险的Vasicek利率风险研究[J]，数学理论与应用,2010，30(1)：67-70.
[88]王克明，梁戍.基于利率期限结构的随机久期与凸度模型构建及应用[J]，统计与决策，2010,24:158-160.
[89] Black F., Scholes M. The pricing of options and corporate liabilities [J], Journalof Political Economy,1973,81(3):637-654.
[90] Merton R.C. On the pricing of corporate debt: The risk structure of interest rates[J], Journal of Finance,1974,29(2):449-470.
[91] Black F., Cox J.C. Valuing corporate securities: Some effects of bond indentureprovisions [J], Journal of Finance,1976,31(2):351-367.
[92] Geske R. The valuation of corporate li abilities as compound options [J], Journalof Financial and QuantitativeAnalysis,1977,12(4):542-552.
[93] Longstaff F.A., Schwartz E.S. A simple approach to valuing risky f ixed andfloating rate debt [J], Journal of Finance,1995,50(3):789-819.
[94] Anderson R. W., Sundaresan S. Design and valuation of debt contracts [J],Review of Financial Studies,1996,9(1):37-68.
[95] Mella-Barral P., Perraudin W. Strategic debt service [J], Journal of Finance,1997,52(2):532-556.
[96] Ericsson J., Reneby J. The valuation of corporate liabilities: Theory and tests [R],Working Paper, McGill University,2001.
[97] Lando D. Credit Risk Modeling: Theo ry and Applications [M], Princeton:Princeton University Press,2004.
[98] Chan-Lau J.A., Sy A.N.R. Distance-to-default in banking: A bridge too far?[R],Working Paper, IMF,2006.
[99] Capuano C. The option-iPoD: The pr obability of default im plied by optionprices based on entropy [R], Working Paper, IMF,2008.
[100] Jarrow R.A., Tumbull S.M. Pricing derivatives on financial securities subject tocredit risk [J], Journal of Finance,1995,50(1):53-85.
[101] Jarrow R.A., Lando D., T umbull S.M. AMarkov model for the term structureof credit risk spreads [J], The Revi ew of Financial S tudies,1997,10(2):481-523.
[102] Hurd T.R., Kuznetsov A. Af fine Ma rkov chain m odels of m ultifirm creditmigration [J], Journal of Credit Risk,2007,3(1):3-29.
[103] Duffie D., Singleton K.J. Modeling term structures of defaultable bonds [J],Review of Financial Studies,1999,12(4):687-720.
[104] Wong H. Y., W ong T.L. Reduced-form models with regim e switching: Anempirical analysis for corporate bonds [J], Asia-Pacific Financial Markets,2007,14(3):229-253.
[105] Wu L., Zhang F.X. A no-arbitrage analysis of econom ic determinants of thecredit spread term structure [J], Management Science,2008,54(6):1160-1175.
[106] Chance D.M. Default Risk and the Duration of Zero Coupon Bonds [J], Journalof Finance,1990,45(1):265-274.
[107] Nawalkha S.K. A con tingent claim s analysis of the interest-rate-riskcharacteristics of corporate liabilities [J], Journal of Banking&Finance,1996,20(2):227-245.
[108] Xie Y.A., Liu S., Wu C. Duration, default risk, and the term structure of interestrates [J]. Journal of Financial Research,2005,28(4):539-554.
[109] Kraft K., Munk C. Bond durations: Cor porates vs. T reasuries [J], Journal ofBanking&Finance,2007,31(12):3720-3741.
[110] Duffee G.R. The relation between T reasury yields and corporate bond yieldspreads [J], Journal of Finance,1998,53(6):2225-2241.
[111] Acharya V.V., Carpenter J.N. Cor porate bond valuation and hedging wit hStochastic Interest Rates and Endogenous Bankruptcy [J], Review of FinancialStudies,2002,15(5):1355-1383.
[112] Jacoby G., Roberts G.S. Default and call-adjusted duration for corporate bonds[J], Journal of Banking and Finance,2003,27(12):2297-2321.
[113] Sarkar S., Hong G. Effective duration of callable corporate bonds: Theory andevidence [J]. Journal of Banking and Finance,2004,28(3):499-521.
[114] Xie Y.A., Liu S., W u C., et al. The effects of default and call risk on bondduration [J], Journal of Banking&Finance,2009,33(9):1700-1708.
[115] Ho T.S.Y., Lee S.B. A unified credit and interest rate arbi trage-free contingentclaim model [J], Journal of Fixed Income,2009,18(3):5-17.
[116] Meder A. Managing Pension Liabi lity Credit Risk: Maintaining a T otalPortfolio Perspective [J], Journal of Portfolio Management,2009,36(1):90-99.
[117] Landes L., Stoffels J., Seifert J. An Empirical test of a Duration-Based Hedge:The Case of Corporate Bonds [J], Jour nal of Futures Markets,1985,5(2):173-182.
[118] Cornell B., Green K. The Investm ent Performance of Low-Grade Bond Funds[J], Journal of Finance,1991,46(1):29-48.
[119] Ambastha M., Dor A. B., Dynkin L., et al. Empirical Duration of CorporateBonds and Credit Market Segm entation [J], Journal of Fixed Incom e,2010,20(1):5-27.
[120] Cheyette O., T omaich T. Empirical Credit Risk [R], W orking Paper, BarraFixed Income Research,2003.
[121] Collin-Dufresne P., Goldstein R., Martin J. The determ inants of cred it spreadchanges [J], Journal of Finance,2001,56(6):2177-2207.
[122] Cheyette O., Postler B. Em pirical Credit Risk [J], J ournal of PortfolioManagement,2006,32(4):79-92.
[123] Blanchet-Scalliet C., Jeanblanc M. Hazard rate for credit risk and hedgingdefaultable contingent claims [J], Finance and Stochastics,2004,8(1):145-159.
[124] Campi L., Polbennikov S., Sbuelz A. Systematic equity-based credit risk: ACEV model with jump to default [J], Journal of Economic Dynamics&Control,2009,33(1):93-108.
[125] Ederington L. The hedging performance of the new futures markets [J], Journalof Finance,1979,34(1):157-170.
[126] Figlewski S. Hedging perform ance and basis risk in stock index futures [J],Journal of Finance,1984,39(3):657-669.
[127] Figlewski S. Hedging with stock inde x futures: Theory and application in anew market [J], Journal of Futures Markets,1985,5(2):183-199.
[128] Hill J., Schneeweis T. A note on the hedging effectiveness of foreign currencyfutures [J]. Journal of Futures Markets,1981,1(4):659-664.
[129] Hill J., Schneeweis T. The hedging effectiveness of foreign currency futures [J],Journal of Futures Markets,1981,1(1):77-88.
[130] Witt H.J., Schroeder T.C., Hayenga M.L. Comparison of analytical approachesfor estimating hedge ratios for agricultural commodities [J], Journal of FuturesMarkets,1987,7(2):135-146.
[131] Brown S.L. A reformulation of the por tfolio model of hedging [J], Am ericanJournal ofAgricultural Economics,1985,67(3):508-512.
[132] Myers R. J. Estim ating time-varying optimal hedge ratios on futures m arkets[J], Journal of Futures Markets,1991,11(1):39-53.
[133] Wilkinson K.J., Rose L.C., Y oung M.R. Com paring the Ef fectiveness ofTraditional and Time Varying Hedge Ratios Using New Zealand and AustralianDebt Futures Contracts [J], The Financial Review,1999,34(3):79-94.
[134] Becker C., Guill G.D. Using CLOs to Manage the Credit Risk of CorporateLoan Portfolios [J], Journal ofApplied Finance,2009,1:28-37.
[135] Skinner F.S., Nuri J. Hedging emerging market bonds and the rise of the credi tdefault swap [J], International Revi ew of Financial Analysis,2007,16(5):452-470.
[136] Bielecki T.R., Jeanblanc M., Rutkowski M. Hedging of baske t creditderivatives in the credit default swap m arket [J], Journal of Credit Risk,2007,3(1):92-132.
[137] Korn O. Risk m anagement with default-risky forwards [J], Risk Managem ent,2010,62(2):102-125.
[138] Saunders D., Xiouros C., Zenios S.A. Credit risk optimization using factormodels [J],Annals of Operations Research,2007,152(1):49-77.
[139] Vasicek O. The Loan Loss Distribution[R], T echnical Docum ent, KM VCorporation, San Fransisco,1987.
[140] Vasicek O. Limiting loan loss probability distribution[R], Technical Document,KMV Corporation, San Fransisco,1991.
[141] W ilde T. Probing Granularity [J], Risk,2001,14(8):103-106.
[142] Frey R., McNeil A. Dependent Defaults in Models of Portfolio Credit Risk [J],Journal of Risk,2003,6(1):59-92.
[143] Gordy M. A risk-factor m odel foundation for ratings-based bank capital rules[J], Journal of Financial Intermediation,2003,12(3):199-232.
[144] Vasicek O. Loan portfolio value [J], Risk,2002,160-162.
[145] Bonti G., Kalkbrener M., Lotz C., et al. Credit risk concentrations under stress[J], Journal of Credit Risk,2006,2(3):115-136.
[146] Rosen D., Saunders D. Analytical m ethods for hedging system atic credit riskwith linear factor portfolios [J], Jo urnal of Econom ic Dynamics&Control,2009,33(1):37-52.
[147] Ioannides M., Skinner F.S. Hedging Corporate Bonds [J], Journal of BusinessFinance&Accounting,1999,26(7):919-944.
[148] Schaefer S.M., S trebulaev I.A. S tructural m odels of credit risk are useful:Evidence from hedge ratios on corporat e bonds [J], Journal of FinancialEconomics,2008,90(1):1-19.
[149] Elouerkhaoui Y. Pricing and he dging in a dynam ic credit m odel [J],International Journal of Theoretical andApplied Finance,2007,10(4):703-731.
[150] Becherer D., Ward I. Optimal Weak Static Hedging of Equity and Credit RiskUsing Derivatives [J],Applied Mathematical Finance,2010,17(1):2-28.
[151] Frey R., Backhaus J. Pricing and hedging of portfo lio credit Derivatives withinteracting def ault in tensities [J], In ternational Journal of Theoretical andApplied Finance,2008,11(6):611-634.
[152] Frey R., Backhaus J. Dynamic hedging of synthetic CDO tranches with spreadrisk and default contagion [J], Journal of Economic Dynamics&Control,2010,34(4):710-724.
[153] Cousin A., Laurent J.P. Hedging issues for CDOs, Risk Books [M], G. Meissner,2008.
[154] Laurent J.P., Cousin A., Ferm anian J.D. Hedging default risks of CDOs i nMarkovian contagion m odels [J], Qu antitative Finance,2011,11(12):1773-1791.
[155]魏明，王琼.信用衍生品对我国信用风险管理的作用及其实施策略[J]，管理世界，2003，10：142-142.
[156]潘杰义，王琼，陈金贤.信用风险管理创新工具——信用衍生品的发展与评述[J]，西北师大学报，2003，40(3)：122-124.
[157]任宏之.辩证分析信用衍生品功能的利与弊——以07金融危机为例[J]，金融经济,2011，2：37-38.
[158]刘新，祁源，喻靖.关于我国银行业应用信用衍生品防范信用风险问题的研究[J]，经济师，2010，1：9-11.
[159]陈正声，秦学志，王玥.扭曲Copula函数在BDS定价及其敏感度分析中的应用[J]，系统管理学报，2010，19(3)：345-350.
[160] Chambers D.R. The Managem ent of Default-Free Bond P ortfolios [D], Ph.D.dissertation, University of North Carolina, Chapel Hill,1981.
[161]范龙振.上交所利率期限结构的三因子广义高斯仿射模型[J]，管理工程学报，2005,19(1)：82-86.
[162]任姝仪，杨丰梅，周荣喜.中国国债利率期限结构Nelson-Siegel族模型实证比较[J]，系统工程，2011，29(10)：30-34.
[163]周子康，王宁，杨衡.中国国债利率期限结构模型研究与实证分析[J]，金融研究，2008，3：132-150.
[164] Galluccio S., Roncoroni A. A new m easure of cross-sec tional risk and itsempirical implications for portfolio risk management [J], Journal of Banking&Finance,2006,30(8):2387-2408.
[165] Roncoroni A., Galluccio S., Guiotto P. Shape Factors and Cross-sectional Risk[J], Journal of Economic Dynamics&Control,2010,34(11):2320-2340.
[166] Fama E., Bliss R. The Inform ation in Long-m aturity Forward Rates [J],American Economic Review,1987,77(4):680-692.
[167]黄云清，舒适，陈艳萍等.数值计算方法[M]，北京：科学出版社，2009.
[168]苏云鹏，杨宝臣，李冬连.基于遗传算法的扩展Nelson-Siegel模型及实证研究[J]，统计与信息论坛，2011，1：15-19.
[169] Nawalkha S.K., Soto G.M. Managing in terest risk: The next challenge?[J],Journal of Investment Management,2009,7(3):2-19.
[170]沈其君. SAS统计分析[M]，南京：东南大学出版社，2002.
[171] Matsumura S., Moreira B. Assessing macro influence on Brazilian yield curvewith affine models [J],Applied Economics,2011,43(15):1847-1863.
[172]康书隆，王志强.中国国债利率期限结构的风险特征及其内含信息研究[J]，世界经济，2010，7：122-143.
[173] Dai Q., Singleton K. E xpectation puzzles, time varying risk premia, and affinemodels of the term structure [R], Working Paper, Stanford University,2002.
[174]林元烈.应用随机过程[M]，北京：清华大学出版社，2002.
[175] Grasselli M., T ebaldi C. S tochastic Jacobian and Riccati ODE in af fine termstructure models [J], Decisions in Economics&Finance,2007,30(2):95-108.
[176] Gibbons M.R., Ramaswamy K. A test of the Cox, Ingersoll, and Ross model ofthe term structure [J]. Review of Financial Studies,1993,6:619-658.
[177] Dai Q., Singleton K.J. Specification analysis of affine term structure models [J].Journal of Finance,2000,55:1943-1978.
[178] Fisher M., Gilles C. Estimating exponential-affine models of the term structure
[R]. Technical Report, Federal Reserve Bank ofAtlanta,2000.
[179] Pedersen, A.R. A new approach to m aximum-likelihood estim ation forstochastic dif ferential equations ba sed on discrete observations [J].Scandinavian Journal of Statistics,1995,22:55-71.
[180] Brandt M., He P. Simulated likeli hood estim ation of af fine term structuremodels from panel data [R]. Working Paper, University of Pennsylvania,2002.
[181] Duffee G.R., Stanton R.H. Estim ation of dynam ic term structure m odels [R],Working Paper, Haas School of Business, U.C. Berkeley,2004.
[182] Rosen D., Saunders D. Risk factor contributions in portfolio credit risk models[J], Journal of Banking&Finance,2010,34(2):336-349.
[183] van der Vaart A. AsymptoticStatistics [M], Cambridge University Press,1998.
[184] McNeil A., Frey R., Em brechts P. Quantitative Risk Managem ent [M].Princeton University Press,2005.
[185] Neu P., Kuhn R. Credit risk enhancem ent in a network of interdependent firm s[J], PhysicaA,2004,342(3):639-655.
[186] Hatchett J.P.L., Kuhn R. Ef fects of economic interactions on credit risk [J],Journal of PhysicsA: Mathematical and General,39(10):2231-2251.
[187] Hatchett J.P.L., Kuhn R. Credit cont agion and credit risk [J], QuantitativeFinance,2009,9(4):373-382.
[188] Davis M., Lo V. Infectious defaults [J], Quantitative Finance,2001,1(4):382-387.
[189] Jarrow R., Yu F. Counterparty risk and the pricing of derivative securities [J],Journal of Finance,2001,56(5):1765-1799.
[190] Artzner P., Delbaen F., Eber J., et al. Coherent Measures of R isk [J].Mathematical Finance,1999,9(3):203-228.
[191] Rockafeller R., Uryasev S. Optim ization of Conditional V alue-at-Risk [J],Journal of Risk,2000,2(3):21-41.
[192] Aytac I., Ronnie S. Optim al static–dynamic hedges for barrier options [J],Mathematical Finance,2006,16(2):359-385.
[193] Jonathan D. Basis Convergence and Long Memory in Volatility When DynamicHedging with Futures [J], Journal of Financial&Quantitative Analysis,2007,42(4):1021-1040.
[194] Li M.Y.L. Dynamic hedge ratio for stock index futures: application of thresholdVECM [J],Applied Economics,2010,42(11):1403-1417.
[195] Li D.X. On default correlation: a copula function approach [J], Journal of FixedIncome,2000,9(4):43–54.
[196] Laurent J.P., Gregory J. Basket defa ult Swaps, CDOs and factor copulas [J],Journal of Risk,2005,7(4):103–122.
[197] Wu P.C. Applying a factor copula to value basket credit linked notes with issuerdefault risk [J], Finance Research Letters,2010,7(3):178-183.
[198] Moreira F.F. Copula-Based Form ulas to Estimate Unexpected Credit Losses(The Future of Basel Accords?) Fern ando F. Moreira Copula-Based Form ulasto Estimate Unexpected Credit Lo sses [J], Financial Markets, Institutions&Instruments,2010,19(5):381-404.
[199] Bertocchi M., Giacometti R., Zenios S. A. Risk factor analysis and portfolioimmunization [J], European Journal of Operational Research,2005,161(2):348-363.
[200] Meligkotsidou L., Vrontos I.D. Detecting structural breaks and identifying riskfactors in hedge fund returns: A Bayesian approach [J], Journal of Banking&Finance,2008,32(11):2471-2481.
[201] Bali T.G., Brown S.J., Caglayan M.O. Do hedge funds’exposures to risk factorspredict their future returns?[J], Journal of Financial Economics,2011,101(1):36-68.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |