人民币利率互换衍生产品定价研究
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摘要
在国际金融市场风云变幻、金融衍生产品层出不穷的今天，利率互换无论在锁定投资收益以规避利率风险方面，还是在利用相对优势套取利差以尽可能降低利息负担方面，都被国外金融界和企业界十分广泛的运用，成为一种管理利率风险的最为基本和有效的金融工具。
目前，随着我国利率互换市场的快速发展，国内利率互换交易日趋活跃，对利率互换定价问题的研究变得更为重要。鉴于利率互换定价对银行间市场乃至整个金融市场发展具有的重要地位，对利率互换定价的研究，无疑具有重要的理论和现实意义，并成为关注的焦点，迫切需要解决。
本文首先对具体有关利率互换产品的定价理论，包括金融衍生产品定价的基本原理、利率互换产品的基本定价模型与方法、利率互换产品定价的实证检验等研究文献进行回顾。然后对利率互换衍生产品的基本特征进行分析，包括结构特征和功能特征等，产品的定价原理即是建立在这些基本的特征之上。文章的核心部分是运用定价模型对利率互换产品的定价进行实证分析和检验。
实证分析以我国利率互换市场上银行机构之间进行的互换交易为例，分四个部分进行：
本文第4章首先对目前银行机构的互换定价方法进行实证分析：基于零息票定价法，在不考虑互换交易双方违约风险的条件下对以一年期定期存款利率与银行间债券7日回购利率为基准利率的互换产品进行定价。然后在无风险定价结果上加上交易对手方的风险溢价，得到互换交易的理论定价。最后将得到的实证结果与互换交易的实际成交利率进行比较，分析研究利率互换产品的定价与浮动端基准利率选择的关系。
从对两笔互换交易的定价实证结果进行比较来看，对于非市场化利率——以一年期定期存款利率为基准利率的互换产品，理论报价利率与实际成交利率差异较大，报价受非市场性因素影响较多。从本章互换交易的定价实证过程也可以看出，目前银行机构采用的互换定价方法存在许多问题：在无风险定价之后对定价结果进行信用溢价调整，有可能会低估交易对手的违约风险；授信制度、保证金制度的落后影响信用溢价的估算等。
第二，本文第5章采用单因素利率均衡模型对目前银行机构采用的人民币利率互换定价方法进行实证检验。首先构建单因素利率均衡模型拟合银行间债券市场的动态利率期限结构，利用利率均值回复的实证结果对以7日回购利率为基准利率的人民币利率互换交易进行无风险定价，并在定价结果上加上交易方的风险溢价，得到互换交易的理论定价，得到的互换理论利率仍略低于实际成交利率。
第三，针对目前银行机构对人民币利率互换交易的定价方法(无风险互换定价+信用溢价)的不足，本文第6章把交易双方的违约风险因素包括在互换的理论定价过程之中，采用双向违约风险模型对银行间的人民币利率互换交易进行定价。首先根据根据交易对手发行债券的收益率以及对手本身情况计算双方在进行互换交易时的违约概率，然后采用双方违约风险估算模型，对违约风险条件下人民币利率互换交易进行定价实证分析。实证结果表明：与第4章和第5章的定价结果相比，双向违约风险模型对互换交易理论价格的拟合结果最好，同时对目前银行机构采用的互换定价方法中的不足之处有了较大改进。因此，本章阐述的定价方法能够提供一种较为有效的对利率互换定价的方法，可以作为实际互换交易过程中的定价参考。
第四，利用前述实证结果，本文第7章首先对互换定价的结果进行全面分析，分析结果显示：利用双向违约风险模型对互换利率期限结构的拟合结果较好，但互换理论报价与金融债收益率之间价格偏离较大。第7章在分析利率互换定价的影响因素之后，结合实证研究结果，提出基于互换定价偏离的套利交易策略。
最后，我们对本研究的结论以及未来进一步促进互换市场发展的政策建议进行了简要的讨论。
As international financial market are changing rapidly and financial derivativesare following each other in rapid succession, interest rate swap are now widelyadopted in business and in the world of finance, not only to lock in investment profitand manage interest-rate risk but also to hedge from price spread and reduce interestobligations. IRS has been a basic and effective financial instrument to manageinterest rate risk.
Nowadays, with the rapid development of national interest rate swap market,transactions in interest rate swap are more and more active and the study on interestrate swap pricing has beome more and more important. Since the interest rate swappricing plays an important role not only in the development of inter-bank market butalso in the development of whole financial market, the study on interest rate swappricing is of profound theoretical and practical significance and has become a focusthese days.
In this paper we review some pricing theory on interest rate swap,including thefundamental pricing theory of derivatives, the model of interest rate swap pricing andsome empirical analysis on interest rate swap pricing. Then we describe the propertiesof interest rate swap including structural properties and funtional properties, on whichthe pricing theory are based. The main part of this paper is to price the RMB interestrate swap with some pricing models.
We take those RMB Interset Rate Swap between national banks as examples tobegin our empirical investigation, which are made up of 4 parts.
First, in this paper we make an empirical investigation on the pricing model ofInterest Rate swap adopted by national banks(pricing under risk-free plus creditpremium): based on Zero Coupon Pricing Methodology, we carry out case simulationand price 2 interest rate swap which are based on the fixed interest rate for 1 yeardeposits and the market interest rate R007 under the circumstance of risk-free. We getan risk-free result and plus the credit premium of transaction parties to it, then we get the formula price of swap transaction. We compare market prices of interest rateswaps with formula prices. From those empirical results of 2 examles, we show thatthere is a great price differential between formular price and market price of RMBinterest rate swao based on 1 year deposits, that is to say, as for interest rate swapbased on non-market interest rate, its pricing is more easily influenced by manynon-market factors. We could also draw the conclusion that there are many problemsin the pricing modle adopted by our commercial banks such as: underestimating theloss of default risk from swap transaction partners. And because the system of creditrating of the opposite party and guaranty money or securities.is backward, the pricingof credit premium of transaction partners is very difficult.
Second, in Chapter 5 we make an empirical investigation on the pricing model ofRMB interest rate swap adopted by banks(pricing under risk-free plus creditpremium): based on single-factor term structure modle. Through the single-factorterm structure modle, we fit the dynamic term structure of interest rate of interbankmarket, we price RMB interest rate swap based on market interest rate R007 underthe circumstance of risk-free, we get an risk-free result and plus the credit premium oftransaction parties to it, then we get the formula price of swap transaction. Theempirical results are still lower than that of market price.
Third, aiming at the problems in those interest rate swap pricing modles adoptedby national banks, in chapter 6 we consider the default risk of transaction partieswhen pricing the RMB interest rate swap and through two-side default risks modlewe price RMB interest rate swap. We calculate the default probablility of transactionparties based on its bond yield and through two-side default risks modle we priceRMB interest rate swap. From the empirical results, we show that compared with theformula price of chapter 4 and chapter 5, the formula price of chapter 6 is strikinglyclose to the market price. It also could prove that the two sides default risk modle ismore effective than that those pricing modles adopted by national banks when pricingRMB interest rate swap. The pricing result suggests that method expatiated in thischapter can offer a quite effective method for interest rate swap pricing, and can bemade a pricing reference in the course of realistic transactions.
Fourth, in chapter 7 we make a comprehensive analysis of the pricing results ofRMB interest rate swap. We show that the fitting to swap term structure through thetwo sides risks motile is the best, but there is still a price differential between swapquotation price and yield of financial bonds. Then we examine all relevant factorsaffecting the swap pricing and combined with the empirical results we claim some setof arbitraging strategy based on the price differential.
In the finality, we make a brief discussion on the conclusion in this paper and thesuggestion to promote developments of RMB interest rate swap.
目前，随着我国利率互换市场的快速发展，国内利率互换交易日趋活跃，对利率互换定价问题的研究变得更为重要。鉴于利率互换定价对银行间市场乃至整个金融市场发展具有的重要地位，对利率互换定价的研究，无疑具有重要的理论和现实意义，并成为关注的焦点，迫切需要解决。
本文首先对具体有关利率互换产品的定价理论，包括金融衍生产品定价的基本原理、利率互换产品的基本定价模型与方法、利率互换产品定价的实证检验等研究文献进行回顾。然后对利率互换衍生产品的基本特征进行分析，包括结构特征和功能特征等，产品的定价原理即是建立在这些基本的特征之上。文章的核心部分是运用定价模型对利率互换产品的定价进行实证分析和检验。
实证分析以我国利率互换市场上银行机构之间进行的互换交易为例，分四个部分进行：
本文第4章首先对目前银行机构的互换定价方法进行实证分析：基于零息票定价法，在不考虑互换交易双方违约风险的条件下对以一年期定期存款利率与银行间债券7日回购利率为基准利率的互换产品进行定价。然后在无风险定价结果上加上交易对手方的风险溢价，得到互换交易的理论定价。最后将得到的实证结果与互换交易的实际成交利率进行比较，分析研究利率互换产品的定价与浮动端基准利率选择的关系。
从对两笔互换交易的定价实证结果进行比较来看，对于非市场化利率——以一年期定期存款利率为基准利率的互换产品，理论报价利率与实际成交利率差异较大，报价受非市场性因素影响较多。从本章互换交易的定价实证过程也可以看出，目前银行机构采用的互换定价方法存在许多问题：在无风险定价之后对定价结果进行信用溢价调整，有可能会低估交易对手的违约风险；授信制度、保证金制度的落后影响信用溢价的估算等。
第二，本文第5章采用单因素利率均衡模型对目前银行机构采用的人民币利率互换定价方法进行实证检验。首先构建单因素利率均衡模型拟合银行间债券市场的动态利率期限结构，利用利率均值回复的实证结果对以7日回购利率为基准利率的人民币利率互换交易进行无风险定价，并在定价结果上加上交易方的风险溢价，得到互换交易的理论定价，得到的互换理论利率仍略低于实际成交利率。
第三，针对目前银行机构对人民币利率互换交易的定价方法(无风险互换定价+信用溢价)的不足，本文第6章把交易双方的违约风险因素包括在互换的理论定价过程之中，采用双向违约风险模型对银行间的人民币利率互换交易进行定价。首先根据根据交易对手发行债券的收益率以及对手本身情况计算双方在进行互换交易时的违约概率，然后采用双方违约风险估算模型，对违约风险条件下人民币利率互换交易进行定价实证分析。实证结果表明：与第4章和第5章的定价结果相比，双向违约风险模型对互换交易理论价格的拟合结果最好，同时对目前银行机构采用的互换定价方法中的不足之处有了较大改进。因此，本章阐述的定价方法能够提供一种较为有效的对利率互换定价的方法，可以作为实际互换交易过程中的定价参考。
第四，利用前述实证结果，本文第7章首先对互换定价的结果进行全面分析，分析结果显示：利用双向违约风险模型对互换利率期限结构的拟合结果较好，但互换理论报价与金融债收益率之间价格偏离较大。第7章在分析利率互换定价的影响因素之后，结合实证研究结果，提出基于互换定价偏离的套利交易策略。
最后，我们对本研究的结论以及未来进一步促进互换市场发展的政策建议进行了简要的讨论。
As international financial market are changing rapidly and financial derivativesare following each other in rapid succession, interest rate swap are now widelyadopted in business and in the world of finance, not only to lock in investment profitand manage interest-rate risk but also to hedge from price spread and reduce interestobligations. IRS has been a basic and effective financial instrument to manageinterest rate risk.
Nowadays, with the rapid development of national interest rate swap market,transactions in interest rate swap are more and more active and the study on interestrate swap pricing has beome more and more important. Since the interest rate swappricing plays an important role not only in the development of inter-bank market butalso in the development of whole financial market, the study on interest rate swappricing is of profound theoretical and practical significance and has become a focusthese days.
In this paper we review some pricing theory on interest rate swap,including thefundamental pricing theory of derivatives, the model of interest rate swap pricing andsome empirical analysis on interest rate swap pricing. Then we describe the propertiesof interest rate swap including structural properties and funtional properties, on whichthe pricing theory are based. The main part of this paper is to price the RMB interestrate swap with some pricing models.
We take those RMB Interset Rate Swap between national banks as examples tobegin our empirical investigation, which are made up of 4 parts.
First, in this paper we make an empirical investigation on the pricing model ofInterest Rate swap adopted by national banks(pricing under risk-free plus creditpremium): based on Zero Coupon Pricing Methodology, we carry out case simulationand price 2 interest rate swap which are based on the fixed interest rate for 1 yeardeposits and the market interest rate R007 under the circumstance of risk-free. We getan risk-free result and plus the credit premium of transaction parties to it, then we get the formula price of swap transaction. We compare market prices of interest rateswaps with formula prices. From those empirical results of 2 examles, we show thatthere is a great price differential between formular price and market price of RMBinterest rate swao based on 1 year deposits, that is to say, as for interest rate swapbased on non-market interest rate, its pricing is more easily influenced by manynon-market factors. We could also draw the conclusion that there are many problemsin the pricing modle adopted by our commercial banks such as: underestimating theloss of default risk from swap transaction partners. And because the system of creditrating of the opposite party and guaranty money or securities.is backward, the pricingof credit premium of transaction partners is very difficult.
Second, in Chapter 5 we make an empirical investigation on the pricing model ofRMB interest rate swap adopted by banks(pricing under risk-free plus creditpremium): based on single-factor term structure modle. Through the single-factorterm structure modle, we fit the dynamic term structure of interest rate of interbankmarket, we price RMB interest rate swap based on market interest rate R007 underthe circumstance of risk-free, we get an risk-free result and plus the credit premium oftransaction parties to it, then we get the formula price of swap transaction. Theempirical results are still lower than that of market price.
Third, aiming at the problems in those interest rate swap pricing modles adoptedby national banks, in chapter 6 we consider the default risk of transaction partieswhen pricing the RMB interest rate swap and through two-side default risks modlewe price RMB interest rate swap. We calculate the default probablility of transactionparties based on its bond yield and through two-side default risks modle we priceRMB interest rate swap. From the empirical results, we show that compared with theformula price of chapter 4 and chapter 5, the formula price of chapter 6 is strikinglyclose to the market price. It also could prove that the two sides default risk modle ismore effective than that those pricing modles adopted by national banks when pricingRMB interest rate swap. The pricing result suggests that method expatiated in thischapter can offer a quite effective method for interest rate swap pricing, and can bemade a pricing reference in the course of realistic transactions.
Fourth, in chapter 7 we make a comprehensive analysis of the pricing results ofRMB interest rate swap. We show that the fitting to swap term structure through thetwo sides risks motile is the best, but there is still a price differential between swapquotation price and yield of financial bonds. Then we examine all relevant factorsaffecting the swap pricing and combined with the empirical results we claim some setof arbitraging strategy based on the price differential.
In the finality, we make a brief discussion on the conclusion in this paper and thesuggestion to promote developments of RMB interest rate swap.
引文
① 数据来源：国际清算组织衍生品交易统计，www.bis.org
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③ 万正晓．关于利率互换定价模型的设计与软件开发．河南师范大学学报，2002，8：96～99
④ 张玲，谢志平．违约风险条件下利率互换合约的定价．系统工程，2002，2：26～29
⑤ 李朝民．利率互换案例分析．经济经纬，2003．6：132～134．
⑥ 谢为安，谢一清．金融互换的价值．上海综合经济2003，11：15～18
① 谢赤．期限结构估测法及其在利率互换定价中的应用．中国软科学，2003，9：133～135
② 谢赤．利率互换与经济暴露及债券误定价问题研究．管理工程学报，2003，1：91～93
③ 朱世武，邢艳丹．利率互换定价存在的障碍及解决办法．金融理论与实践，2006，6：9～11
④ 瞿炯．利率互换在银行间市场的应用．中国城乡金融报，2006年2月14日
⑤ 徐莉莉．利率互换一新业务，新影响．渤海证券研究报告，2006．7
⑥ 闵晓平，田澎．利率产品定价与利率期限结构关系分析．数量经济技术经济研究．2005，2：157～161
⑦ 严高剑，李志强，人民币利率互换报价分析．中信证券研究报告，2006，7
① 巫燕玲．人民币利率互换试点试行在即，双轮驱动企业避险．中国经营报，2006年2月19日
② 王栋琳．利率互换为银行打开想象空间．中国证券报，2006年2月21日
① 万正晓．关于利率互换定价模型的设计与软件开发．河南师范大学学报(自然科学版)，2002，8：96～99
① McCulloch J H. Measuring the Term Structure of Interest Rates. Journal of Business, 1971,11 : 19～31
① Vasicek O A, Fong H G Term Structure Modeling Using Exponential Splines..Journal of Finance, 1982: 339～348
① Nelson, Siegel. Parsimonious modeling of yield curves. Journal of Bussiness, 1987, 6:361～372
② Nelson C R, Siegel AF. Parsimonious Modeling of Yield Curves. Journal of Business, 1987,(60):473～486
③ Svensson L. Estimating and Interpreting Forward Interest Rates: Sweden: [IMF Working Paper], 1992, 94, No
① Bolder D. Streliski D. Yield Curve Modeling at the Bank of Canada. Technical Report No.84, 1999
① 大公国际资信评估有限公司．中国银行业信用风险分析——2006-2007回顾与展望，2007
① Vasicek O A, Fong H G. Term Structure Modeling Using Exponential Splines.Jounnal of Finance, 1982: 339～348
① Vasicek, O. An Equilibrium Characterization of The Term Structure [J]. Journa lof Financial Economics, 1977, 5:177～188
② Cox. J .C. ,J. E. In gersollJr., and S.A. Ross. A Theory of the Term Structure of Interest Rates. Econometrica, 1985, 53:384～407
① Chan, K.C.,G.A.Karoyli, F.A.Longstaff and A.B.Sanders .An Empirical Comparison of Alternative Models of the Short-term Interest Rate. Journal of Finance, 1992,47:1209～1227
② Hansen. Large Sample Properties of Generalized Method of Moments Estimation. Econometrica, 1982, 50: 1029～1054
① Chart, K. C., G. A. Karoyli, F. A. Longstaffand A. B. Sanders.An Empirical Comparison of Alternative Models of the Short-tern Interest Rate. Journal of Finance, 1982, 47:1209～1227
① Michael T. Cliff. GMM and MINZ Program Libraries for MATLAB: [Working Paper], 2003
① 吴冲锋，王海成，吴文峰．金融工程研究．上海：上海交通大学出版社，2000
① 大公国际资信评估有限公司．中国银行业信用风险分析—2006．2007回顾与展望，2007
② Bicksler J. and Chen A., , An Economic Analysis of Interest Rate Swaps, The Journal of Finance, 1986, 3: 645-655.
① Darrel Duffle and Ming Huang. Swap Rates and Credit Quality: [dissertation]. Graduate School of Business, Stanford University, 1995
① 约翰．C．赫尔著．期货与期权市场导论．周春生，付佳译．北京：北京大学出版社，2006
① 大公国际资信评估有限公司．中国银行业信用风险分析—2006．2007回顾与展望，2007
① 迈哈伊．马图著．结构化衍生工具．林涛，杜育欣译．北京：经济科学出版社．2000
① Darrel Duffie and Ming Huang. Swap Rates and Credit Quality: [dissertation] Graduate School of Business, Stanford University, 1995
① 朱国华，毛小云．金融互换交易．上海：上海财经大学出版社．2006
① 朱国华．毛小云．金融互换交易．上海：上海财经大学出版社．2006
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[4] Bruno Solnik. Swap pricing and default risk: A Note. Journal of International Financial Management and Accounting, 1990,Vo 1.2, No.1 :79～91
[5] Bolder D, Streliski D. Yield Curve Modeling at the Bank of Canada. [Technical Report] No.84, 1999
[6] Cooper,I.and A.Mello. The Default Risk on Swaps. The Journal of Finance, 1991, 46: 597-620
[7] Chan, Karoyli, Longstaff and Sanders. An Empirical Comparison of Alternative Models of the Short Term Interest Rate. Journal of Finance, 1992, 47:1209-1227
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[13] F.A.Longstaff and E.S.Schwartz. Valuing Risky Debt: A New Approach: [ Working Paper].The Anderson Graduate School of Management,UCLA, 1993
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[16] Huge B and Lando D. Swap Pricing with Two-Sided Default Risk in a Rating-Based Model: [Working paper], Centre for analytical, 1999
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[38] Vasicek, O. An Equilibrium Characterization of The Term Structure [J]. Journa lof Financial Economics, 1977, 5:177-188
[39] Wall,L.D. Interest rate swaps in an agency theoretic model with uncertain interest rates. Journal of Banking and Finance, 1989, 13:261-270
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[44] 姚长辉，梁跃军．我国国债收益率曲线的实证研究．金融研究，1998，8：12～18
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[48] 谢赤，吴雄伟．扩散过程下单因素利率模型的统一框架．系统工程学报，2002，12：562～565
[49] 范龙振．上交所债券利率期限结构与两因子Vasicek模型．复旦学报(自然科学版)，2003，5：773～778
[50] 陈典发．利率期限结构的一致性．系统工程，2002，1：17～19
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[52] 傅曼丽，董荣杰，屠梅曾．动态利率模型估计方法的一个实证检验．华中科技大学学报(自然科学版)，2005，4：367～372
[52] 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．财经研究，2004，10：62～69
[54] 李和金，郑兴山，李湛．非参数利率期限结构模型的实证检验．上海交通大学学报，2003，4：607～609
[55] 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．管理工程学报，2004，1：72～75
[56] 赵宇龄．中国国债收益率曲线构造的比较分析．上海金融，2003，9：29～31
[57] 朱世武，陈健恒．利用均衡利率模型对浮动利率债券定价．世界经济，2003，10：48～60
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[63] 谢赤．利率互换与经济暴露及债券误定价问题研究．管理工程学报，2003，1：91～93
[64] 朱世武，邢艳丹．利率互换定价存在的障碍及解决办法．金融理论与实践，2006，6：9～11
[65] 梁国巍．利率互换风险定价研究：[硕士学位论文]．武汉：武汉理工大学，2005
[66] 徐莉莉．利率互换一新业务，新影响．渤海证券研究报告，2006，7
[67] 闵晓平，田澎．利率产品定价与利率期限结构关系分析．数量经济技术经济研究， 2005，2：157～161
[68] 严高剑，李志强，人民币利率互换报价分析，中信证券研究报告，2006，7
[69] 巫燕玲，人民币利率互换试点试行在即，双轮驱动企业避险，中国经营报，2006年2月19日
[70] 朱国华，毛小云．金融互换交易．上海：上海财经大学出版社．2006：139～141
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[74] 黄河．互换交易．武汉：武汉大学出版社，2005
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① 中国货币网，www.chinamoney.com.cn(中国外汇交易中心暨全国银行间同业拆借中心主办)．衍生品交易统计，2007年6月
① Bicksler J, A Chen. An Economic Analysis of Interest Rate Swap. The Journal of Finance, 1986, July: 645～655
② Smith, C.W.,Smithson,C., Wakeman,L.W. The market for interest rate swaps. Financial Management, 1988, 11:34～44
③ Wall,L.D. Interest rate swaps in an agency theoretic model with uncertain interest rates. Journal of Banking and Finance, 1989, 13:261～270
① John F. Marshall, Vipul K. Bansal. Allyn & Bacon. Financial Engineering: A Complete Guide to Financial Innovation. New York:New York Institute of Finance, 1992:57～64
② Turnbull S. Swaps: A Zero Sum Game? Financial Management, 1987, 16:15～21
① Bicksler,J. and A Chert. An Economic Analysis of Interest Rate Swap. The Journal of Finance, 1986, July: 645～655
② Bruno Solnik. Swap pricing and default risk: A Note. Journal of International Financial Management and Accounting, 1990,Vo 1.2, No. 1:79～91
③ Sun T Sundaresan S and Wang C. Interest rate swaps: An empirical investigation. Journal of Financial Economics, 1993,Vo 1.3,No.4:77～99
① F.A.Longstaff and E.S.Schwartz. Valuing Risky Debt: A New Approach: [Working Paper].The Anderson Graduate School of Management, UCLA, 1993
② Minton B. An empirical examination of basic valuation models for plainvanilla U.S. interest swaps. Journal of Financial Economics,1997, Vol.4, No.4:251～277
③ Li Haitao. Essays on swap markets: [dissertation].Connecticut: Yale University, 1998
④ Cooper, Ⅰ.and A.Mello. The Default Risk on Swaps. The Journal of Finance, 1991, 46:597～620
⑤ R. H. Litzenberger. Swaps: Plain and Fanciful. Journal of Finance, 1992, 47:831～850
⑥ Sorensen,E.and T.Bollier. Pricing Swap Default Risk. Financial Analysts Journal, 1994, May-June: 23～31
① D .Madan and H.Unal. Pricing the Risks of Default: [Working Paper], College of Business, University of Maryland, 1994
② Darrel Duffle and Ming Huang. Swap Rates and Credit Quality: [dissertation] Graduate School of Business, Stanford University, 1995
③ Huge B and Lando D. Swap Pricing with Two-Sided Default Risk in a Rating-Based Model: [Working paper], Centre for analytical, 1999
④ Jarrow R, Turnbull S. The impact of defaul risk on swap prices and swap values. Risk, 1997, 10:70～75
⑤ Gupta, A. and M. Subrahmanyam. An Empirical Examination of the Convexity Bias in the Pricing of Interest Rate Swaps. Journal of Financial Economics, 2000, 55:239～252
⑥ Antulio N. Bomfim. Counterparty Credit Risk in Tnterest Rate Swaps during Times of Market Stress. Federal Reserve Board, 2002
① 庄东辰．利率期限结构的实证研究．中国证券报，1996年6月19日
② 宋淮松．我国零息国债收益率曲线初探．中国证券报，1997年2月18日
③ 杨大楷，杨勇．关于我国国债收益率曲线的研究．财经研究，1997，7：14～20
④ 姚长辉，粱跃军．我国国债收益率曲线的实证研究．金融研究，1998，8：12～18
⑤ 陈雯，陈浪南．国债利率期限结构：建模与实证．世界经济，2000，8：24～28
⑥ 杨春鹏，曹兴华．我国国债收益率曲线的构造与实证研究．投资与证券，2002，10：80～82
⑦ 郑振龙，林海．中国市场利率期限结构的静态估计．武汉金融，2003，7：33～36
⑧ 谢赤．吴雄伟．扩散过程下单因素利率模型的统一框架．系统工程学报，2002，12：562～565
⑨ 范龙振．上交所债券利率期限结构与两因子Vasicek模型．复旦学报(自然科学版)．2003，5：773～778
⑩ 陈典发．利率期限结构的一致性．系统工程，2002，1：17～19
① 唐齐鸣，高翔．我国同业拆借市场利率期限结构的实证研究．统计研究，2005，5：33～36
② 傅曼丽，董荣杰，屠梅曾．动态利率模型估计方法的一个实证检验．华中科技大学学报(自然科学版)，2005．4：367～372
③ 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．财经研究，2004，10：62～69
④ Nowman B．Gaussian Estimation of Single-factor Continuous Time Models of The Term Structure of Interest Rates．Journal ofFinance，1997，52：1695～1706
⑤ Chan，Karoyli，Longstaff and Sanders．An Empirical Comparison of Alternative Models 0f the Short—Tem Interest Rate．Journal ofFinance,1992．47：1209～1227
⑥ 李和金，郑兴山，李湛．非参数利率期限结构模型的实证检验．上海交通大学学报，2003．4：607～609
⑦ 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．管理工程学报，2004，1：72～75
① 赵字龄．中国国债收益率曲线构造的比较分析．上海金融，2003，(9)：29-31
② 朱世武，陈健恒．利用均衡利率模型对浮动利率债券定价．世界经济，2003，10：48-60
③ 万正晓．关于利率互换定价模型的设计与软件开发．河南师范大学学报，2002，8：96～99
④ 张玲，谢志平．违约风险条件下利率互换合约的定价．系统工程，2002，2：26～29
⑤ 李朝民．利率互换案例分析．经济经纬，2003．6：132～134．
⑥ 谢为安，谢一清．金融互换的价值．上海综合经济2003，11：15～18
① 谢赤．期限结构估测法及其在利率互换定价中的应用．中国软科学，2003，9：133～135
② 谢赤．利率互换与经济暴露及债券误定价问题研究．管理工程学报，2003，1：91～93
③ 朱世武，邢艳丹．利率互换定价存在的障碍及解决办法．金融理论与实践，2006，6：9～11
④ 瞿炯．利率互换在银行间市场的应用．中国城乡金融报，2006年2月14日
⑤ 徐莉莉．利率互换一新业务，新影响．渤海证券研究报告，2006．7
⑥ 闵晓平，田澎．利率产品定价与利率期限结构关系分析．数量经济技术经济研究．2005，2：157～161
⑦ 严高剑，李志强，人民币利率互换报价分析．中信证券研究报告，2006，7
① 巫燕玲．人民币利率互换试点试行在即，双轮驱动企业避险．中国经营报，2006年2月19日
② 王栋琳．利率互换为银行打开想象空间．中国证券报，2006年2月21日
① 万正晓．关于利率互换定价模型的设计与软件开发．河南师范大学学报(自然科学版)，2002，8：96～99
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① 大公国际资信评估有限公司．中国银行业信用风险分析——2006-2007回顾与展望，2007
① Vasicek O A, Fong H G. Term Structure Modeling Using Exponential Splines.Jounnal of Finance, 1982: 339～348
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① Michael T. Cliff. GMM and MINZ Program Libraries for MATLAB: [Working Paper], 2003
① 吴冲锋，王海成，吴文峰．金融工程研究．上海：上海交通大学出版社，2000
① 大公国际资信评估有限公司．中国银行业信用风险分析—2006．2007回顾与展望，2007
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① 约翰．C．赫尔著．期货与期权市场导论．周春生，付佳译．北京：北京大学出版社，2006
① 大公国际资信评估有限公司．中国银行业信用风险分析—2006．2007回顾与展望，2007
① 迈哈伊．马图著．结构化衍生工具．林涛，杜育欣译．北京：经济科学出版社．2000
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① 朱国华，毛小云．金融互换交易．上海：上海财经大学出版社．2006
① 朱国华．毛小云．金融互换交易．上海：上海财经大学出版社．2006
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