The paper derives a general form of the term structure of interest rates. The following assumptions are made: (A.1) The instantaneous (spot) interest rate follows a diffusion process; (A.2) the price of a discount bond depends only on the spot rate over its term; and (A.3) the market is efficient. Under these assumptions, it is shown by means of an arbitrage argument that the expected rate of return on any bond in excess of the spot rate is proportional to its standard deviation. This property is then used to derive a partial differential equation for bond prices. The solution to that equation is given in the form of a stochastic integral representation. An interpretation of the bond pricing formula is provided. The model is illustrated on a specific case.

The paper investigates the term structure of interest rates imposed by equilibrium in a production economy consisting of participants with heterogeneous preferences. Consumption is restricted to an arbitrary number of discrete times. The paper contains an exact solution to market equilibrium and provides an explicit constructive algorithm for determining the state price density process. The convergence of the algorithm is proven. Interest rates and their behavior are given as a function of economic variables.

The paper looks at the behavior of investors in an economy consisting of a production process controlled by a state variable representing the state of technology. The participants in the economy maximize their individual utilities of consumption. Each participant has a constant relative risk aversion. The degrees of risk aversion, as well as the time preference functions, differ across participants. The participants may lend and borrow among themselves, either at a floating short rate, or by issuing or buying term bonds. We derive conditions under which such an economy is in equilibrium, and obtain equations determining interest rates.

ABSTRACT 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‐of‐horizon 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.