Are there nonlinearities in short‐term interest rates?

The present paper investigates the characteristics of short‐term interest rates in several countries. We examine the importance of nonlinearities in the mean reversion and volatility of short‐term interest rates. We examine various models that allow the conditional mean (drift) and conditional variance (diffusion) to be functions of the current short rate. We find that different markets require different models. In particular, we find evidence of nonlinear mean reversion in some of the countries that we examine, linear mean reversion in others and no mean reversion in some countries. For all countries we examine, there is strong evidence of the need for the volatility of interest rate changes to be highly sensitive to the level of the short‐term interest rate. Out‐of‐sample forecasting performance of one‐factor short rate models is poor, stemming from the inability of the models to accommodate jumps and discontinuities in the time series data.     

Calibration of Gaussian heath, Jarrow and Morton and random field interest rate term structure models

We show how the recently introduced Gaussian random field interest rate term structure models can be calibrated accurately and quickly to market caps and swaptions prices. We show how the calibrated random field model can be approximated arbitrarily closely with a multi-factor Gaussian Heath, Jarrow and Morton model. We argue that the Gaussian random field model is easier to calibrate and can be used as an indirect way to calibrate multi-factor Gaussian Heath, Jarrow and Morton interest rate models.This work was carried out when the author was at the Financial Options Research Centre, Warwick Business School, University of Warwick. I wish to thank Stewart Hodges for many helpful discussions and comments and Martin Cooper of Tokai Bank, Europe, for supplying the data used in this paper. I also wish to thank the Economic and Social Research Council and FORC for funding. An earlier version of this paper entitled Multi-Factor Gaussian HJM Approximation to Kennedy and Calibration to Caps and Swaptions Prices was presented at the 9th Annual Conference, FORC., Warwick Business School, September 1996. Another version also appears in the author's Ph.D. thesis. I am grateful to the helpful comments provided by Marti Subrahmanyam and the two anonymous referees. All errors are my own and the views expressed in no way reflect the opinion of my employer.     

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.     

Modelling the term structure of interest rates in a small emerging market economy

This paper investigates the term structure of interest rates in a small emerging market economy – the Dominican Republic. The modelling finds a significant dynamic link amongst the day-to-day interbank interest rate and a representative banking system interest rate. But the interbank rate's forecasting power breaks down in the aftermath of the 2003 banking crisis. This episode illustrates how the monetary authorities' credibility with the public and market expectations affect the term structure's reliability.     

On a general class of one-factor models for the term structure of interest rates

We propose a general one-factor model for the term structure of interest rates which based upon a model for the short rate. The dynamics of the short rate is described by an appropriate function of a time-changed Wiener process. The model allows for perfect fitting of given term structure of interest rates and volatilities, as well as for mean reversion. Moreover, every type of distribution of the short rate can be achieved, in particular, the distribution can be concentrated on an interval. The model includes several popular models such as the generalized Vasicek (or Hull-White) model, the Black-Derman-Toy, Black-Karasinski model, and others. There is a unified numerical approach to the general model based on a simple lattice approximation which, in particular, can be chosen as a binomial or -nomial lattice with branching probabilities .     

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.     

A preference free partial differential equation for the term structure of interest rates

The objectives of this paper are two-fold: the first is the reconciliation of the differences between the Vasicek and the Heath-Jarrow-Morton approaches to the modelling of term structure of interest rates. We demonstrate that under certain (not empirically unreasonable) assumptions prices of interest-rate sensitive claims within the Heath-Jarrow-Morton framework can be expressed as a partial differential equation which both is preference-free and matches the currently observed yield curve. This partial differential equation is shown to be equivalent to the extended Vasicek model of Hull and White. The second is the pricing of interest rate claims in this framework. The preference free partial differential equation that we obtain has the added advantage that it allows us to bring to bear on the problem of evaluating American style contingent claims in a stochastic interest rate environment the various numerical techniques for solving free boundary value problems which have been developed in recent years such as the method of lines.     

Negative real interest rates

Standard textbook general equilibrium term structure models such as that developed by Cox, Ingersoll, and Ross [1985b. “A Theory of the Term Structure of Interest Rates.” Econometrica 53 (2): 385–407], do not accommodate negative real interest rates. Given this, the Cox, Ingersoll, and Ross [1985b. “A Theory of the Term Structure of Interest Rates.” Econometrica 53 (2): 385–407] ‘technological uncertainty variable’ is formulated in terms of the Pearson Type IV probability density. The Pearson Type IV encompasses mean-reverting sample paths, time-varying volatility and also allows for negative real interest rates. The Fokker–Planck (i.e. the Chapman–Kolmogorov) equation is then used to determine the conditional moments of the instantaneous real rate of interest. These enable one to determine the mean and variance of the accumulated (i.e. integrated) real rate of interest on a bank (or loan) account when interest accumulates at the instantaneous real rate of interest defined by the Pearson Type IV probability density. A pricing formula for pure discount bonds is also developed. Our empirical analysis of short-dated Treasury bills shows that real interest rates in the UK and the USA are strongly compatible with a general equilibrium term structure model based on the Pearson Type IV probability density.     

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.     

Macroeconomic releases and the interest rate term structure

We extract two systematic economic factors from a wide array of noisy and sparsely observed macroeconomic releases, and link the dynamics and market prices of the two factors to the interest rate term structure. The two factors predict 77.9–82.1% of the daily variation in LIBOR and swap rates from one month to 10 years. Shocks on inflation-related releases have large, positive impacts on interest rates of all maturities, leading to parallel shifts of the yield curve, but shocks on output-related releases have larger impacts on the short rate than on the long rate, thus generating a slope effect.     

On the Information in the Interest Rate Term Structure and Option Prices

We examine whether the information in cap and swaption prices is consistent with realized movements of the interest rate term structure. To extract an option-implied interest rate covariance matrix from cap and swaption prices, we use Libor market models as a modelling framework. We propose a flexible parameterization of the interest rate covariance matrix, which cannot be generated by standard low-factor term structure models. The empirical analysis, based on US data from 1995 to 1999, shows that option prices imply an interest rate covariance matrix that is significantly different from the covariance matrix estimated from interest rate data. If one uses the latter covariance matrix to price caps and swaptions, one significantly underprices these options. We discuss and analyze several explanations for our findings.     

Do Investors Expect Mean Reversion in Asset Prices?

We investigate the existence and source of equilibrium mean reversion in UK non-financial and financial asset prices over the period 6 April, 1981, through 31 October, 1995. Our results indicate substantial expected transitory components in commodity and metals markets but report expected mean reversion for financial assets only at the near to maturity horizons. Implied cash flow yields appear to have a role in driving the mean reverting process particularly at short horizons while the role of interest rate movements varied across assets and across maturities. Our results reject the existence of a common risk premium across market term structures.     

Deviations from daily uncovered interest rate parity and the role of intervention

This paper considers the relationship between daily deviations from uncovered interest rate parity and US and German central bank intervention. The study uses daily overnight Eurocurrency deposit rates with a maturity time of 1 day, which exactly matches the sampling interval of the data. The intervention data are the official net daily purchases and sales of dollars vis-à-vis the German mark by the Federal Reserve System and the Bundesbank. The model uses FIGARCH innovations to represent the degree of long-term dependence in the volatility process. Some support is found for the intervention variables affecting the risk premium as predicted by theory. The impact of intervention in the 2 years immediately following the meltdown of the equity markets in October 1987 and Louvre Accord is particularly strong.