臺灣博碩士論文加值系統

本文嘗試建構一個離散的均衡利率期限結構模型，除了探討期限結構的特性，本文主要的特色是假設有兩群持有異質信念的投資人。這個假設是跟CIR模型的同質預期最大的差異。在本文的架構中，每群投資人計劃一個最適的投資策略，然後再利用投資人的最適策略加上市場結清條件，可進一步求解市場結清價格。為了明確的表達異質信念的構想，以及投資人持有異質信念對均衡利率期限結構的影響，第一個基本模型以相對報酬的型式進行分析，其中股票扮演著基準財(numraire)的角色。然而，為了使本文的模型可以探討更具一般化的問題，第二個延伸模型不只將通貨膨脹及時間偏好問題納入考量，還多加考慮投資人的消費問題及風險趨避度。本文中的兩個模型都得到相似的結果，就如同Miller (1977)中提到的關念，證券市場上的投資決策將反應樂觀者的看法。同時，只要潛在投資人可以吸收市場上的發行量，則投資人間的看法越分歧，將會增加市場均衡價格以及價格的波動性。再者，從本文的結果亦可知，只要市場上對未來利率水準的平均預期夠高時，殖利率曲線將會呈現正斜率狀態。最後，從本文的推論中亦可得知一些有關同質預期的特色，在同質預期下，各別投資人的風險態度將會被忽略，且無法探討交易量的問題。由於這些原因，使得本文認為同質預期這個假設，應該被適度的放寬。

This paper attempts to establish a discrete-time model of equilibrium term structure of interest rates. In addition to discussing some properties of term structure of interest rates, the main feature of our model is that it contains two groups of agents who adopt heterogeneous beliefs on future interest rates. This also is the major difference with CIR model. In our framework each group plans an optimal trading strategy. After getting those optimal trading strategy, we can derive equilibrium interest rates from market clearing condition. In order to make the idea of heterogeneous beliefs clear and realize the effect of heterogeneous beliefs on equilibrium term structure, the first model in this paper discusses in form of relative returns, where the stock acts as numeraire. However, to modify our model containing more general properties, the second model takes into account not only inflation and time preference but also investors' attitude toward risk and consumption problem. Both models obtain similar results. As the concept mentioned in Miller (1977), investment decisions made through security markets will reflect the opinions of the optimists. Also, as long as potential investors can absorb the issue, an increase in the divergence of opinion will increase the market clearing price and price volatility. Furthermore, we know that if and only if the average anticipated future interest rate is high enough, yield curve will be positive slope. Finally, we also get something from our corollary in second model. Under assumption of homogeneous beliefs, individual degree of risk aversion is ignored. That is also why we think that the assumption of homogeneous beliefs is a little pity.

Contents
1 Introduction 3
1.1 Motivation..............................................3
1.2 Literature Review.......................................4
1.3 Dissertation Framework..................................9
2 Basic Model 10
2.1 Model Setting..........................................10
2.2 Optimal Trading Strategy...............................13
2.3 Comparative Static Analysis and Trading Volume.........16
2.4 Equilibrium Term Structure with Different Opinions.....19
3 Extended Model with Consumption 23
3.1 Model Setting..........................................23
3.2 Optimal Trading Strategy and Equilibrium Conditions....24
3.3 Trading Volume.........................................30
3.4 Equilibrium Term Structure with Diverse Opinions and
Different Degree of Risk Aversion...................33
4 Concluding Remarks 37
References 39

Blanchard, Olivier J. (1981), “Output, the Stock Market, and Interest Rates,” The American Economic Review, Vol. 71, pp.132-143.

Cox, John C., Jonathan E. Ingersoll and Stephen A. Ross (1985a), “An Intertemporal General Equilibrium Model of Asset Prices,” Econometrica, Vol. 53, pp.363-384.

Cox, John C., Jonathan E. Ingersoll and Stephen A. Ross (1985b), “A Theory of The Term Structure of Interest Rates,” Econometrica, Vol. 53, pp.385-407.

Diebold, Francis X., Monika Piazzesi and Glenn D. Rudebusch (2005), “Modeling Bond Yields in Finance and Macroeconomics,”

Harrison, J. Michael and David M. Kreps (1979), “Martingales and Arbitrage in Multiperiod Securities Markets,” Journal of Economic Theory, Vol. 20, pp.381-408.

Heath, David, Robert Jarrow and Andrew Morton (1990), “Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation,” The Journal of Financial and Quantitative Analysis, Vol. 25, pp.419-440.

Heath, David, Robert Jarrow and Andrew Morton (1992), “Bond Pricing and The Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation,” Econometrica, Vol. 60, pp.77-105.

Ho, Thomas S. Y. and Sang-Bin Lee (1986), “Term Structure Movements and Pricing Interest Rate Contingent Claims,” The Journal of Finance, Vol. 41, pp.1011-1029.

Hull, John and Alan White (1990b), “Pricing Interest-Rate-Derivative Securities,” The Review of Financial Studies, Vol. 3, pp.573-592.

Hull, John and Alan White (1993), “One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities,” Journal of Financial and Quantitative Analysis, Vol. 28, pp.235-254.

Kurz, Mordecai (1994a), “On rational belief equilibria,” Economic Theory, Vol. 4, pp.859-876.

Kurz, Mordecai (1994b), “On the structure and diversity of rational beliefs,” Economic Theory, Vol. 4, pp.877-900.

Miller, Edward M. (1977), “Risk, Uncertainty, and Divergence of Opinion,” The Journal of Finance, Vol. 32, pp.1151-1168.

Modigliani, Franco and Robert J. Shiller (1973), “Inflation, Rational Expectations and the Term Structure of Interest Rates,” Economica, Vol. 40, pp.12-43.

Pliska, S. R., Introduction to Mathematical Finance: Discrete Time Models, Malden, Mass.: Basil Blackwell, 1997

Rudebusch, Glenn D. (2005), “Monetary Policy Inertia: Fact or Fiction?,”

Scheinkman, Jose and Wei Xiong (2003), “Heterogeneous Beliefs, Speculation and Trading in Financial Markets,” Mathematical Finance, pp.218-250.

Turnovsky, Stephen J. (1989), “The Term Structure of Interest Rates and the Effects of Macroeconomic,” Journal of Money, Credit and Banking, Vol. 21, pp.321-347.

Turnovsky, Stephen J. and Marcus H. Miller (1984), “The Effects of Government Expenditure on the Term Structure of Interest Rates,” Journal of Money, Credit and Banking, Vol. 16, pp.16-33.

Vasicek, Oldrich (1977) “An equilibrium characterization of the term structure,” Journal of Financial Economics, Vol. 5, pp.177-188.

Williams, Joseph T. (1977), “Capital Asset Prices with Heterogeneous Beliefs,” Journal of Financial Economics, Vol. 5, pp.219-239.

Wu, Ho-Mou and Wen-Chung Guo (2003), “Asset price volatility and trading volume with rational beliefs,” Economic Theory, pp.1-35.