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研究生:黃子宜
研究生(外文):TZU-YI HUANG
論文名稱:利率模型研究:無套利理論與一般均衡理論之連結
論文名稱(外文):A Connection of the Arbitrage-Free Approach and the General Equilibrium Approach to Interest Rate Modeling
指導教授:巫和懋巫和懋引用關係
指導教授(外文):HO-MOU HU
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:國際企業學研究所
學門:商業及管理學門
學類:企業管理學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
中文關鍵詞:利率利率模型無套利一般均衡
外文關鍵詞:interest rateinterest rate modelingarbitragegeneral equilibriumpricing kernel
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對於利率模型的建構,主要有兩個理論方法。一個是一般均衡理論,另一個則是無套利理論。2001年Jin及Glasserman發表的論文中對於這兩種不同的模型提供了一完整的連結。藉著在連續時間中建構了一個pricing kernel model以作為這兩個理論之間的橋樑。透過這樣的連結,給定兩者中某一個的模型參數,即可以轉換至另一個模型上。除此之外,也經由這個連結,能夠對無套利模型提供一個支持它的生產經濟的均衡模型。
本論文試圖在離散時間的架構下追求一個相似的目標,也就是建立離散時間下兩種理論的連結。並得到以下四個主要貢獻:一、建構一個離散時間的pricing kernel model 以作為利率期間結構模型。二、建立pricing kernel model 與Heath, Jarrow, and Morton’s model離散時間下的連結,並提供兩者之間轉換的方式。三、建立一個生產經濟的均衡模型來支持所建立之pricing kernel model。四、在此模型下探討利率之特性,諸如:利率為正值、債券價格隨到期時間遞減的性質。
There are two main approaches in constructing models of interest rates. One is the general equilibrium approach. The other is the arbitrage-free approach. Jin and Glasserman (2001) developed a precise connection among the two approaches by using a pricing kernel model as the “bridge” in a continuous time economy. Given the primitive data of either perspective, they can obtain primitive data of the other, i.e. each of the two models can be transformed into the other. Through these connections they also find a production economy with a representative-consumer to support arbitrage-free models.
This thesis attempts to accomplish a similar goal in a discrete time economy. There are four main contributions in this thesis. First, to construct a discrete time pricing kernel model, we incorporate the discounted marginal utility of optimal consumption and fit the model to the term structure of interest rate. Second, we build a connection between the pricing kernel model and Heath, Jarrow, and Morton’s discrete time framework, and gives transformation formulas between the primitive parameters of these two models. Third, a production economy is offered to support the pricing kernel model. Fourth, we attempt to provide foundations for the properties of the interest rates including that the interest rates are positive and that the bond price vanishes to zero as its expiration time approaches infinity, which require adding more assumptions in the pricing kernel model.
1 Introduction 1
1.1 Motivation 1
1.2 Objectives 3
1.3 Framework 4
2 Review of the Literature 5
2.1 An Overview of Interest Rate Models 5
2.2 Heath, Jarrow, and Morton’s Continuous Time Model 7
2.3 Heath, Jarrow, and Morton’s Discrete Time Model 9
2.4 Cox, Ingersoll, and Ross’s Continuous Time General
librium Model 11
2.5 Sun (1992): Discrete Time Approximation of CIR 13
2.6 Jin and Glasserman (2001): The Pricing Kernel Approach 15
3 A Pricing Kernel Model 17
3.1 Terminology 17
3.2 Pricing Kernel 19
3.3 Interest Rates and Bank Account’s Derivation 21
4 The Connection with HJM’s Model (Arbitrage-Free
Approach) 24
4.1 Assumptions 24
4.2 Connection to HJM''s Model 29
5 The Connection with CIR’s Model (Equilibrium Approach)32
5.1 Supporting Equilibrium 32
5.2 Properties 34
6 Conclusion and Thoughts for Further Study 37
6.1 Conclusion 37
6.2 Thoughts for Further Study 38
Reference 40
Brock, W., 1982, “Asset Prices in a Production Economy,” in J. McCall (ed.), The Economics of Information and Uncertainty, University of Chicago Press, Chicago.
Cox, J. C., J. E. Ingersoll, and S. A. Ross, 1985a, “An Intertemporal General Equilibrium Model of Asset Prices,” Econometrica, 53, 363-384.
Cox, J. C., J. E. Ingersoll, and S. A. Ross, 1985b, “A Theory of Term Structure of Interest Rates,” Econometrica, 53, 385-408.
Cox, J. C., S. A. Ross, and M. Rubinstein, 1979, “Option Pricing: A Simplified Approach,” Journal of Financial Economics, 7, 229-64.
Duffie, D., 1996, Dynamic Asset Pricing Theory, 2nd ed., Princeton University Press, Princeton, N.J.
Flesaker, B., and L. Hughston, 1996a, “Positive Interest,” Risk Magazine, January.
Flesaker, B., and L. Hughston, 1996b, “Positive Interest: Foreign Exchange,” in L. Hughston (ed.), Vasicek and Beyond, Risk Publications, London.
Harrison, J., and S. Pliska, 1981, “Martingales and Stochastic Integrals in the Theory of Continuous Trading,” Stochastic Processes and their Application, 11, 215-260.
Heath, D., R. Jarrow, and A. Morton, 1992, “Bond Pricing and Term Structure of Interest Rate: Anew Methodology for Contingent Claims Valuation,” Econometrica, 60, 77-105.
Heath, D., R. Jarrow, and A. Morton, 1990, “Bond Pricing and Term Structure of Interest Rate: A Discrete Time Approximation,” Journal of Financial and Quantitative Analysis, 25, 419-440.
Hull, J and A. White, 1993, “Bond Option Pricing on a Model for the Evolution of Bond Prices,” Advances in Futures and Options Research, 6, 1-13.
Hull, J and A. White, 1994, “Numerical Procedures for Implementing Term Structure Models Ⅱ: Two Factor models,” Journal of Derivatives, 2, 2, 37-48.
Ho, T. and S. Lee, 1986, “Term Structure Movements and Pricing Interest Rate Contingent Claim,” The Journal of Finance, 5, 1011-1029.
James, J. and N. Webber, 2000, Interest Rate Modelling, John Wiley & Sons.
Jin, Y. and P. Glasserman, 2001, “Equilibrium Positive Interest Rates: A Unified View,” The Review of Financial Studies, 14, 187-214.
Rogers, L. C. G., 1997, “The Potential Approach to the Term Structure of Interest Rates and Foreign Exchange Rates,” Mathematical Finance, 7, 157-176.
Sun T. S., 1992, “Real and Nominal Interest Rates: A Discrete-Time Model and Its continuous-Time Limit,” The Review of Financial Studies, 5, 581-611.
Vasicek, O., 1977, “An Equilibrium Characterization of the Term Structure,” Journal of Financial Economics, 5, 177-188.
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