This paper uses an intertemporal general equilibrium asset pricing model to study the term structure of interest rates. In this model, anticipations, risk aversion, investment alternatives, and preferences about the timing of consumption all play a role in determining bond prices. Many of the factors traditionally mentioned as influencing the term structure are thus included in a way which is fully consistent with maximizing behavior and rational expectations. The model leads to specific formulas for bond prices which are well suited for empirical testing. 1. INTRODUCTION THE TERM STRUCTURE of interest rates measures the relationship among the yields on default-free securities that differ only in their term to maturity. The determinants of this relationship have long been a topic of concern for economists. By offering a complete schedule of interest rates across time, the term structure embodies the market's anticipations of future events. An explanation of the term structure gives us a way to extract this information and to predict how changes in the underlying variables will affect the yield curve. In a world of certainty, equilibrium forward rates must coincide with future spot rates, but when uncertainty about future rates is introduced the analysis becomes much more complex. By and large, previous theories of the term structure have taken the certainty model as their starting point and have proceeded by examining stochastic generalizations of the certainty equilibrium relationships. The literature in the area is voluminous, and a comprehensive survey would warrant a paper in itself. It is common, however, to identify much of the previous work in the area as belonging to one of four strands of thought. First, there are various versions of the expectations hypothesis. These place predominant emphasis on the expected values of future spot rates or holdingperiod returns. In its simplest form, the expectations hypothesis postulates that bonds are priced so that the implied forward rates are equal to the expected spot rates. Generally, this approach is characterized by the following propositions: (a) the return on holding a long-term bond to maturity is equal to the expected return on repeated investment in a series of the short-term bonds, or (b) the expected rate of return over the next holding period is the same for bonds of all maturities. The liquidity preference hypothesis, advanced by Hicks [16], concurs with the importance of expected future spot rates, but places more weight on the effects of the risk preferences of market participants. It asserts that risk aversion will cause forward rates to be systematically greater than expected spot rates, usually

https://pages.stern.nyu.edu/~dbackus/BCZ/discrete_time/CIR_Econometrica_85.pdf

A Theory of the Term Structure of Interest Rates.

We present two classes of improved estimators for mutual information M(X,Y), from samples of random points distributed according to some joint probability density mu(x,y). In contrast to conventional estimators based on binnings, they are based on entropy estimates from k -nearest neighbor distances. This means that they are data efficient (with k=1 we resolve structures down to the smallest possible scales), adaptive (the resolution is higher where data are more numerous), and have minimal bias. Indeed, the bias of the underlying entropy estimates is mainly due to nonuniformity of the density at the smallest resolved scale, giving typically systematic errors which scale as functions of k/N for N points. Numerically, we find that both families become exact for independent distributions, i.e. the estimator M(X,Y) vanishes (up to statistical fluctuations) if mu(x,y)=mu(x)mu(y). This holds for all tested marginal distributions and for all dimensions of x and y. In addition, we give estimators for redundancies between more than two random variables. We compare our algorithms in detail with existing algorithms. Finally, we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from independent component analysis (ICA), for improving ICA, and for estimating the reliability of blind source separation.

Estimating mutual information.

Stable URL:http://links.jstor.org/sici?sici=0021-9398%28198710%2960%3A4%3C473%3APMOYC%3E2.0.CO%3B2-6The Journal of Business is currently published by The University of Chicago Press.Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtainedprior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content inthe JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/journals/ucpress.html.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.JSTOR is an independent not-for-profit organization dedicated to and preserving a digital archive of scholarly journals. Formore information regarding JSTOR, please contact support@jstor.org.http://www.jstor.orgMon Apr 2 07:44:52 2007

Parsimonious modeling of yield curves

This paper presents a unifying theory for valuing contingent claims under a stochastic term structure of interest rates. The methodology, based on the equivalent martingale measure technique, takes as given an initial forward rate curve and a family of potential stochastic processes for its subsequent movements. A no arbitrage condition restricts this family of processes yielding valuation formulae for interest rate sensitive contingent claims which do not explicitly depend on the market prices of risk. Examples are provided to illustrate the key results.

Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation

Risk measurement when shares are subject to infrequent trading

http://www.ressources-actuarielles.net/ext/isfa/1226.nsf/9c8e3fd4d8874d60c1257052003eced6/e11e4bc52747d1ddc125772400459afe/$FILE/Vasicek77.pdf

An equilibrium characterization of the term structure

SUMMARY A test of the composite hypothesis of normality is introduced. The test is based on the property of the normal distribution that its entropy exceeds that of any other distribution with a density that has the same variance. The test statistic is based on a class of estimators of entropy constructed here. The test is shown to be a consistent test of the null hypothesis for all alternatives without a singular continuous part. The power of the test is estimated against several alternatives. It is observed that the test compares favourably with other tests for normality.

A Test for Normality Based on Sample Entropy

BAYESIAN DECISION THEORY provides formal procedures which utilize information available prior to sampling, together with the sample information, to construct estimates which are optimal with respect to the minimization of the expected loss. This paper presents a method for generating Bayesian estimates of the regression coefficient of rates of return of a security against those of a market index. The distribution of the regression coefficients across securities is used as the prior distribution in the analysis. Explicit formulas are given for the estimates. The Bayesian approach is discussed in comparison with the current practice of sampling-theory procedures.

A note on using cross-sectional information in bayesian estimation of security betas

TERM STRUCTURE OF interest rates provides a characterization of interest rates as a function of maturity. It facilitates the analysis of rates and yields such as discussed in Dobson, Sutch, and Vanderford [1976], and provides the basis for investigation of portfolio returns as for example in Fisher and Weil [1971]. Term structure can be used in pricing of fixed-income securities (cf., for instance, Houglet [1980]), and for valuation of futures contracts and contigent claims, as in Brennan and Schwartz [1977]. It finds applications in analysis of the effect of taxation on bond yields (cf. McCulloch [1975a] and Schaefer [1981]), estimation of liquidity premia (cf. McCulloch [1975b]), and assessment of the accuracy of market-implicit forecasts (Fama [1976]). Because of its numerous uses, estimation of the term structure has received considerable attention from researchers and practitioners alike. A number of theoretical equilibrium models has been proposed in the recent past to describe the term structure of interest rates, such as Brennan and Schwartz [1979], Cox, Ingersoll, and Ross [1981], Langetieg [1980], and Vasicek [1977]. These models postulate alternative assumptions about the nature of the stochastic process driving interest rates, and deduct a characterization of the term structure implied by these assumptions in an efficiently operating market. The resulting spot rate curves have a specific functional form dependent only on a few parameters. Unfortunately, the spot rate curves derived by these models (at least in the instances when it was possible to obtain explicit formulas) do not conform well to the observed data on bond yields and prices. Typically, actual yield curves exhibit more varied shapes than those justified by the equilibrium models. It is undoubtedly a question of time until a sufficiently rich theoretical model is proposed that provides a good fit to the data. For the time being, however, empirical fitting of the term structure is very much an unrelated task to investigations of equilibrium bond markets. The objective in empirical estimation of the term structure is to fit a spot rate curve (or any other equivalent description of the term structure, such as the discount function) that (1) fits the data sufficiently well, and (2) is a sufficiently smooth function. The second requirement, being less quantifiable than the fiLrst,

https://www.jstor.org/stable/pdfplus/2327333.pdf

Term Structure Modeling Using Exponential Splines

Consider a fixed-income portfolio whose duration is equal to the length of a given investment horizon. It is shown that there is a lower limit on the change in the end-ofhorizon value of the portfolio resulting from any given change in the structure of interest rates. This lower limit is the product of two terms, of which one is a function of the interest rate change only, and the other depends only on the structure of the portfolio. Consequently, this second term provides a measure of immunization risk. If this measure is minimized, the exposure of the portfolio to any interest rate change is the lowest. THE TRADITIONAL THEORY OF immunization as formalized by Fisher and Weil [6] defines the conditions under which the value of an investment in a bond portfolio is protected against changes in the level of interest rates. The specific assumptions of this theory are that the portfolio is valued at a fixed horizon date, that there are no cash inflows or outflows within the horizon, and that interest rates change only by a parallel shift in the forward rates. Under these assumptions, a portfolio is said to be immunized if its value at the end of the horizon does not fall below the target value, where the target value is defined as the portfolio value at the horizon date under the scenario of no change in the forward rates. The main result of this theory is that immunization is achieved if the duration of the portfolio is equal to the length of the horizon. The assumption that interest rates can only change by a parallel shift (that is, by the same amount for all maturities) has been the subject of considerable concern. Bierwag [1, 2], Bierwag and Kaufman [3], Khang [7], and others have postulated alternative models of interest rate behaviors. Each of these specifications implies a different measure of duration, with immunization attained if this duration measure is equal to the horizon length. A limitation of this approach is that the portfolio is protected only against the particular type of interest rate change assumed. In a more recent development, Cox et al. [5], Brennan and Schwartz [4], and others have investigated immunization conditions when interest rates are governed by a continuous process consistent with a market equilibrium. Depending on the specilfication of the interest rate process, there is a duration-like measure (possibly multidimensional, as in Brennan and Schwartz) such that the portfolio is immunized if a proper value of this measure is maintained. This assumes a continuous rebalancing of the portfolio. Again, immunization is achieved only if interest rate changes conform to the specific process assumed. In this paper, we wish to pursue a different approach. If it turned out that the

Oldrich A Vasicek

Papers

An equilibrium characterization of the term structure

A Test for Normality Based on Sample Entropy

A note on using cross-sectional information in bayesian estimation of security betas

Term Structure Modeling Using Exponential Splines

A Risk Minimizing Strategy for Portfolio Immunization