An implementation of the HJM model with application to Japanese interest futures

In this paper, we propose a new specification of the forward rate model of Heath, Jarrow and Morton [5] and apply it to the Japanese 3 month interest rate futures. Our empirical result shows that the model we propose can capture the forward interest rate movement.     

American bond option pricing in one-factor dynamic term structure models

Arbitrage-tree pricing of American options on bonds in one-factor dynamic term structure models is investigated. We re-derive a general decomposition result which states that the American bond option premium can be split into the value of an otherwise equivalent European option and anearly exercise premium. This extends earlier work on American equity options by e.g. Kim (1990), Jamshidian (1992) and Carr, Jarrow, and Myneni (1992) and parallels recent work by Jamshidian (1991, 1992, 1993) and Chesney, Elliott, and Gibson (1993). We examine a Gaussian class of special cases in some detail and provide a variety of numerical valuation results.An earlier version of the paper was entitled American Bond Option Pricing in One-Factor Spot Interest Rate Models.I am grateful for many helpful comments from two anonymous referees, the participants of the Second Nordic Symposium on Contingent Claims Analysis in Finance held in Bergen, Norway in May of 1994 and from the participants of the EIASM Doctoral Tutorial held in connection with the 1994 EFA annual meeting in Bruxelles. I am particularly indebted to Krishna Ramaswamy for his help and advice during my stay as visiting doctoral fellow at the Wharton School of the University of Pennsylvania. Financial support from the Aarhus University Research Foundation (Grants # E-1994-SAM-1-1-72 & E-1995-SAM-1-59), the Danish Social Science Research Council, and the Danish Research Academy is gratefully acknowledged. All errors and omissions are my own.     

On the use of measure-valued strategies in bond markets

We propose here a theory of cylindrical stochastic integration, recently developed by Mikulevicius and Rozovskii, as mathematical background to the theory of bond markets. In this theory, since there is a continuum of securities, it seems natural to define a portfolio as a measure on maturities. However, it turns out that this set of strategies is not complete, and the theory of cylindrical integration allows one to overcome this difficulty. Our approach generalizes the measure-valued strategies: this explains some known results, such as approximate completeness, but at the same time it also shows that either the optimal strategy is based on a finite number of bonds or it is not necessarily a measure-valued process.Received: November 2002, Mathematics Subject Classification: 60H05, 60G60, 90A09JEL Classification: G10, E43The first author gratefully acknowledges financial support from the CNR Strategic Project Modellizzazione matematica di fenomeni economici. We thank professors A. Bagchi, R. Douady and J. Zabczyk for helpful discussions. A special thanks goes to professors T. Björk, Y. Kabanov and W. Schachermayer for comments and suggestions which contributed to improve the final version of this paper.     

Selecting a Bond-Pricing Model for Trading: Benchmarking, Pooling, and Other Issues

Abstract:  Does one make money trading on the deviations between observed bond prices and values proposed by bond-pricing models? We extend Sercu and Wu's (1997) work to more models and more data, but we especially refine the methodology. In particular, we provide a normal-return benchmark that markedly improves upon the Sercu-Wu ones in terms of noisiness and bias, and we demonstrate that model errors contribute more to the variance of residuals—actual minus fitted prices—than pricing errors made by the market. Trading on the basis of deemed mispricing is profitable indeed no matter what model one uses. But there is remarkably little difference across models, at least when one re-estimates and trades daily; and with pooling and/or longer holding periods the results seem to be all over the place, without any relation to various measures of fit in the estimation stage. We also derive and implement an estimator of how much of the typical deviation consists of mispricing and how much is model mis-estimation or mis-specification. Lastly, we find that pooled time-series and cross-sectional estimation, as applied by e.g., De Munnik and Schotman (1994) , does help in stabilizing the parameter, but; hardly improves the trader's profits.     

Decreasing Yield Curves in a Model with an Unknown Constant Growth Rate

The effect of incomplete information on the term structure ofinterest rates is examined in the framework of a pure exchangeeconomy under uncertainty where aggregate output grows at aconstant rate. If the growth rate is known, the term structure isflat. In contrast, the term structure is a decreasing curve whenagents do not know the growth rate. Long term yields are less thanthe short rate and the yield of long term bonds is determined bythe worst possible realizations of future short rates.     

利率期限结构理论研究综述

本文主要对利率期限结构的理论研究做综述,以20世纪70年代初和90年代末为分界线,70年代以前称为传统的利率期限结构,主要以描述性研究为主;70年代以后称为现代利率期限结构,主要以随机模型研究为主;从20世纪90年代末,开始了两极分化发展。本文分为三个部分：第一部分对20世纪70年代之前传统利率期限结构的描述性理论作了概括;第二部分是现代利率期限结构的定量模型,包括均衡模型和无套利模型;第三部分则主要介绍20世纪90年代末以来的一些最新研究进展,包括市场模型和宏观金融模型等。     

Monetary policy with signal extraction from the bond market

Monetary policy is conducted in an environment of uncertainty. This paper presents a model where the central bank uses real time data from the bond market together with standard macroeconomic indicators to infer the current state of the economy more efficiently, while taking into account that its own actions influence the bond market and therefore what it observes. That the central bank uses the information in the term structure to set policy creates a link between the bond market and the macroeconomy that is novel to the literature. The estimated model suggests that there is some information in US yields of maturities of less than 1 year that can help the Federal Reserve to identify shocks to the economy on a timely basis.     

On the Economic Link Between Asset Prices and Real Activity

Abstract:  This paper presents a model linking two financial markets (stocks and bonds) with real business cycle, in the framework of the Consumption Capital Asset Pricing Model with Generalized Isoelastic Preferences. Besides interest rate term spread, the model includes a new variable to forecast economic activity: stock market term spread. This is the slope of expected stock market returns. The empirical evidence documented in this paper suggests systematic relationships between business cycle's state and the shapes of two yield curves (interest rates and expected stock returns). Results are robust to changes in measures of economic growth, stock prices, interest rates and expectations generating mechanisms.     

A Complete Markovian Stochastic Volatility Model in the HJM Framework

This paper considers a stochastic volatility version of the Heath, Jarrow and and Morton (1992) term structure model. Market completeness is obtained by adapting the Hobson and Rogers (1998) complete stochastic volatility stock market model to the interest rate setting. Numerical simulation for a special case is used to compare the stochastic volatility model against the traditional Vasicek (1977) model.     

Multi-Factor Cox-Ingersoll-Ross Models of the Term Structure: Estimates and Tests from a Kalman Filter Model

This paper presents a method for estimating multi-factor versions of the Cox-Ingersoll-Ross (1985b) model of the term structure of interest rates. The fixed parameters in one, two, and three factor models are estimated by applying an approximate maximum likelihood estimator in a state-space model using data for the U.S. treasury market. A nonlinear Kalman filter is used to estimate the unobservable factors. Multi-factor models are necessary to characterize the changing shape of the yield curve over time, and the statistical tests support the case for two and three factor models. A three factor model would be able to incorporate random variation in short term interest rates, long term rates, and interest rate volatility.     

Stochastic duration and fast coupon bond option pricing in multi-factor models

Generalizing Cox, Ingersoll, and Ross (1979), this paper defines the stochastic duration of a bond in a general multi-factor diffusion model as the time to maturity of the zero-coupon bond with the same relative volatility as the bond. Important general properties of the stochastic duration measure are derived analytically, and the stochastic duration is studied in detail in various well-known models. It is also demonstrated by analytical arguments and numerical examples that the price of a European option on a coupon bond (and, hence, of a European swaption) can be approximated very accurately by a multiple of the price of a European option on a zero-coupon bond with a time to maturity equal to the stochastic duration of the coupon bond. This revised version was published online in June 2006 with corrections to the Cover Date.     

Yield curve shapes and the asymptotic short rate distribution in affine one-factor models

We consider a model for interest rates where the short rate is given under the risk-neutral measure by a time-homogeneous one-dimensional affine process in the sense of Duffie, Filipović, and Schachermayer. We show that in such a model yield curves can only be normal, inverse, or humped (i.e., endowed with a single local maximum). Each case can be characterized by simple conditions on the present short rate r _t . We give conditions under which the short rate process converges to a limit distribution and describe the risk-neutral limit distribution in terms of its cumulant generating function. We apply our results to the Vasiček model, the CIR model, a CIR model with added jumps, and a model of Ornstein–Uhlenbeck type. Supported by the Austrian Science Fund (FWF) through project P18022 and the START program Y328. Supported by the module M5 “Modeling of Fixed Income Markets” of the PRisMa Lab, financed by Bank Austria and the Republic of Austria through the Christian Doppler Research Association. Both authors would like to thank Josef Teichmann for most valuable discussions and encouragement. We also thank various proofreaders at FAM and the anonymous referee for their comments.     

Monetary policy,bond risk premia,and the economy

Within an affine model of the term structure of interest rates, where bond yields get driven by observable and unobservable macroeconomic factors, parameter restrictions help identify the effects of monetary policy and other structural disturbances on output, inflation, and interest rates and decompose movements in long-term rates into terms attributable to changing expected future short rates versus risk premia. When estimated, the model highlights a broad range of channels through which monetary policy affects risk premia and the economy, risk premia affect monetary policy and the economy, and the economy affects monetary policy and risk premia.     

Tax Clientele Effects in the Term Structure of UK Interest Rates

This paper tests for tax clientele effects in the term structure of UK interest rates. Five empirical models of the term structure of interest rates, incorporating tax effects, are estimated with daily data covering the period 31 March, 1995 to 3 August, 1995. In May 1995, the British government announced its intention to eliminate the tax exemption on capital gains from government bonds, but subsequently in July 1995 backtracked on some of its initial proposals. This period therefore forms the basis of a crude natural experiment in the sense that it provides an opportunity to examine tax clientele effects 'before' and 'after' an event which should have levelled greatly the taxing of government bonds. The empirical analysis suggests large tax clientele effects. However, there is little evidence of tax-specific term structures of interest rates.     

Beta Regimes for the Yield Curve

We propose an affine term structure model which accommodatesnonlinearities in the drift and volatility function of the short-terminterest rate. Such nonlinearities are a consequence of discretebeta-distributed regime shifts constructed on multiple thresholds.We derive iterative closed-form formula for the whole yieldcurve dynamics that can be estimated using a linearized Kalmanfilter. Fitting the model on US data, we collect empirical evidenceof its potential in estimating conditional volatility and correlationacross yields.     

On the robustness of short–term interest rate models

This paper investigates the robustness of a range of short–term interest rate models. We examine the robustness of these models over different data sets, time periods, sampling frequencies, and estimation techniques. We examine a range of popular one–factor models that allow the conditional mean (drift) and conditional variance (diffusion) to be functions of the current short rate. We find that parameter estimates are highly sensitive to all of these factors in the eight countries that we examine. Since parameter estimates are not robust, these models should be used with caution in practice.     

On the Nonlinear Specifications of Short-Term Interest Rate Behavior: Evidence from Euro-Currency Markets

This paper presents a coherent nonlinear interest rate model that incorporates the dynamics of the error correction specification into the traditional term structure model. The joint tests based on six Euro-Currency rates indicate that the linear specification should be rejected. The estimated equation suggests that the linear components—the change of the long-term interest rate and the error correcting term are highly significant. The nonlinear components involving the higher order of the independent variables, the cross products, the lagged error squares, and/or the ARCH effect also present significant explanatory power for predicting short-term Euro-Currency rate changes, confirming the non-linear specifications.