An equilibrium characterization of the term structure
TL;DR: In this article, the authors derived a general form of the term structure of interest rates and showed that the expected rate of return on any bond in excess of the spot rate is proportional to its standard deviation.
About: This article is published in Journal of Financial Economics.The article was published on 1977-11-01. It has received 6160 citations till now. The article focuses on the topics: Affine term structure model & Bond valuation.
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TL;DR: In this paper, the authors use an intertemporal general equilibrium asset pricing model to study the term structure of interest rates and find that anticipations, risk aversion, investment alternatives, and preferences about the timing of consumption all play a role in determining bond prices.
Abstract: 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
7,014 citations
Cites methods from "An equilibrium characterization of ..."
...An arbitrage approach to bond pricing was developed in a series of papers by Brennan and Schwartz [3], Dothan [10], Garman [14], Richard [28], and Vasicek [37]....
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Posted Content•
TL;DR: In this article, a unifying theory for valuing contingent claims under a stochastic term structure of interest rates is presented, based on the equivalent martingale measure technique.
Abstract: 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.
2,799 citations
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01 Jan 1979
TL;DR: In this paper, the authors propose extension theorems, Martingales, and Compactness, as well as the non-unique case of the Martingale problem, and some estimates on the transition probability functions.
Abstract: Preliminary Material: Extension Theorems, Martingales, and Compactness.- Markov Processes, Regularity of Their Sample Paths, and the Wiener Measure.- Parabolic Partial Differential Equations.- The Stochastic Calculus of Diffusion Theory.- Stochastic Differential Equations.- The Martingale Formulation.- Uniqueness.- Ito's Uniqueness and Uniqueness to the Martingale Problem.- Some Estimates on the Transition Probability Functions.- Explosion.- Limit Theorems.- The Non-Unique Case
2,626 citations
TL;DR: In this paper, a new approach for approximating the value of American options by simulation is presented, using least squares to estimate the conditional expected payoff to the optionholder from continuation.
Abstract: This article presents a simple yet powerful new approach for approximating the value of American options by simulation. The key to this approach is the use of least squares to estimate the conditional expected payoff to the optionholder from continuation. This makes this approach readily applicable in path-dependent and multifactor situations where traditional finite difference techniques cannot be used. We illustrate this technique with several realistic examples including valuing an option when the underlying asset follows a jump-diffusion process and valuing an American swaption in a 20-factor string model of the term structure.
2,612 citations
09 May 2001
TL;DR: In this article, a simple yet powerful new approach for approximating the value of American options by simulation is presented, based on the use of least squares to estimate the conditional expected payoff to the optionholder from continuation.
Abstract: This article presents a simple yet powerful new approach for approximating the value of American options by simulation. The key to this approach is the use of least squares to estimate the conditional expected payoff to the optionholder from continuation. This makes this approach readily applicable in path-dependent and multifactor situations where traditional finite difference techniqes cannot be used. We illustrate this technique with several realistic examples including valuing an option when the underlying asset follows a jump-diffusion process and valuing an American swaption in a 20-factor string model of the term structure.
2,602 citations
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TL;DR: In this paper, a theoretical valuation formula for options is derived, based on the assumption that options are correctly priced in the market and it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks.
Abstract: If options are correctly priced in the market, it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks. Using this principle, a theoretical valuation formula for options is derived. Since almost all corporate liabilities can be viewed as combinations of options, the formula and the analysis that led to it are also applicable to corporate liabilities such as common stock, corporate bonds, and warrants. In particular, the formula can be used to derive the discount that should be applied to a corporate bond because of the possibility of default.
28,434 citations
"An equilibrium characterization of ..." refers methods in this paper
...The development of the model is based on an arbitrage argument similar to that of Black and Scholes (1973) for option pricing....
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TL;DR: In this article, the American Finance Association Meeting, New York, December 1973, presented an abstract of a paper entitled "The Future of Finance: A Review of the State of the Art".
Abstract: Presented at the American Finance Association Meeting, New York, December 1973.(This abstract was borrowed from another version of this item.)
11,225 citations
"An equilibrium characterization of ..." refers background in this paper
...The most notable exceptions are the works of Roll (1970, 1971), Merton (1973, 1974), and Long (1974)....
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TL;DR: In this article, an intertemporal model for the capital market is deduced from portfolio selection behavior by an arbitrary number of investors who aot so as to maximize the expected utility of lifetime consumption and who can trade continuously in time.
Abstract: An intertemporal model for the capital market is deduced from the portfolio selection behavior by an arbitrary number of investors who aot so as to maximize the expected utility of lifetime consumption and who can trade continuously in time. Explicit demand functions for assets are derived, and it is shown that, unlike the one-period model, current demands are affected by the possibility of uncertain changes in future investment opportunities. After aggregating demands and requiring market clearing, the equilibrium relationships among expected returns are derived, and contrary to the classical capital asset pricing model, expected returns on risky assets may differ from the riskless rate even when they have no systematic or market risk. ONE OF THE MORE important developments in modern capital market theory is the Sharpe-Lintner-Mossin mean-variance equilibrium model of exchange, commonly called the capital asset pricing model.2 Although the model has been the basis for more than one hundred academic papers and has had significant impact on the non-academic financial community,' it is still subject to theoretical and empirical criticism. Because the model assumes that investors choose their portfolios according to the Markowitz [21] mean-variance criterion, it is subject to all the theoretical objections to this criterion, of which there are many.4 It has also been criticized for the additional assumptions required,5 especially homogeneous expectations and the single-period nature of the model. The proponents of the model who agree with the theoretical objections, but who argue that the capital market operates "as if" these assumptions were satisfied, are themselves not beyond criticism. While the model predicts that the expected excess return from holding an asset is proportional to the covariance of its return with the market
6,294 citations
"An equilibrium characterization of ..." refers background in this paper
...0 North-Holland Publishing Company AN EQUILIBRIUM CHARACTERIZATION OF THE TERM STRUCTURE Oldrich VASICEK* Wells Fargo Bank and University of California, Berkeley, CA, U.S.A. Received August 1976, revised version received August 1977 The paper derives a general form of the term structure of interest rates....
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...The most notable exceptions are the works of Roll (1970, 1971), Merton (1973, 1974), and Long (1974)....
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...…Publishing Company AN EQUILIBRIUM CHARACTERIZATION OF THE TERM STRUCTURE Oldrich VASICEK* Wells Fargo Bank and University of California, Berkeley, CA, U.S.A. Received August 1976, revised version received August 1977 The paper derives a general form of the term structure of interest rates....
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TL;DR: In this paper, the authors considered the continuous-time consumption-portfolio problem for an individual whose income is generated by capital gains on investments in assets with prices assumed to satisfy the geometric Brownian motion hypothesis, which implies that asset prices are stationary and lognormally distributed.
4,952 citations
01 Jan 1975
TL;DR: In this paper, the authors considered the continuous-time consumption-portfolio problem for an individual whose income is generated by capital gains on investments in assets with prices assumed to satisfy the geometric Brownian motion hypothesis, which implies that asset prices are stationary and lognormally distributed.
Abstract: Publisher Summary
A common hypothesis about the behavior of limited liability asset prices in perfect markets is the random walk of returns or in its continuous-time form the geometric Brownian motion hypothesis, which implies that asset prices are stationary and log-normally distributed. A number of investigators of the behavior of stock and commodity prices have questioned the accuracy of the hypothesis. In an earlier study described in the chapter, it was examined that the continuous-time consumption-portfolio problem for an individual whose income is generated by capital gains on investments in assets with prices assumed to satisfy the “geometric Brownian motion” hypothesis. Under the additional assumption of a constant relative or constant absolute risk-aversion utility function, explicit solutions for the optimal consumption and portfolio rules were derived. The changes in these optimal rules with respect to shifts in various parameters such as expected return, interest rates, and risk were examined by the technique of comparative statics. This chapter presents an extension of these results for more general utility functions, price behavior assumptions, and income generated also from noncapital gains sources. If the geometric Brownian motion hypothesis is accepted, then a general separation or mutual fund theorem can be proved such that, in this model, the classical Tobin mean-variance rules hold without the objectionable assumptions of quadratic utility or of normality of distributions for prices. Hence, when asset prices are generated by a geometric Brownian motion, the two-asset case can be worked on without loss of generality.
2,644 citations