Long memory in the U.S. interest rate

In this article, we examine the order of integration of the U.S. long-term interest rate by means of using fractionally integrated techniques. Using annual data for the time period 1940-2000, the results based on the univariate tests of Robinson [Journal of American Statistical Association 84 (1994) 1420] support the hypothesis of a unit root. However, using a much longer span of the data (1798-2000), the order of integration seems to be smaller than one if the disturbances are white noise, while the unit root cannot be rejected if they are weakly autocorrelated.     

A chaotic approach to interest rate modelling

This paper presents a new approach to interest rate dynamics. We consider the general family of arbitrage-free positive interest rate models, valid on all time horizons, in the case of a discount bond system driven by a Brownian motion of one or more dimensions. We show that the space of such models admits a canonical mapping to the space of square-integrable Wiener functionals. This is achieved by means of a conditional variance representation for the state price density. The Wiener chaos expansion technique is then used to formulate a systematic analysis of the structure and classification of interest rate models. We show that the specification of a first-chaos model is equivalent to the specification of an admissible initial yield curve. A comprehensive development of the second-chaos interest rate theory is presented in the case of a single Brownian factor, and we show that there is a natural methodology for calibrating the model to at-the-money-forward caplet prices. The factorisable second-chaos models are particularly tractable, and lead to closed-form expressions for options on bonds and for swaptions. In conclusion we outline a general international model for interest rates and foreign exchange, for which each currency admits an associated family of discount bonds, and show that the entire system can be generated by a vector of Wiener functionals.Received: March 2004, Mathematics Subject Classification (2000): 91B28, 91B30, 91B50, 60H07JEL Classification: E43We are grateful to J. Boland, D. Brody, P. Carr, M. Davis, F. Delbaen, D. Filipovi, R. Jarrow, M. Grasselli, P. Hunt, T. Hurd, D. Madan, P. Malliavin, H. Rasmussen and M. Zervos for stimulating discussions. We thank D. Brody, M. Grasselli, T. Hurd and M. Zervos, in particular, for suggesting a number of improvements in the arguments presented here. We are grateful for helpful comments by participants at the Frontiéres en Finance seminar, Paris, May 2002, the Mathematics in Finance conference, Kruger Park, RSA, August 2002, the Imperial College finance seminar, February 2003, the 13th annual Derivative Securities Conference, New York, April 2003, the Analysis of Random Markets Workshop, Banach Center, Warsaw, October 2003 and the Quantitative Methods in Finance Conference, Sydney, December 2003, where this work was presented. LPH acknowledges the hospitality of the Institute for Advanced Study, Princeton, where part of this work was carried out. AR acknowledges financial support from the Department of Mathematics, Kings College London.     

Uncovered interest parity, monetary policy and time-varying risk premia

In a recent paper, McCallum argued that monetary-policy behavior can be responsible for the apparent empirical failure of uncovered interest parity (UIP). The present paper investigates whether optimizing policy behavior can account for the observed regime-dependence of UIP evidence. The main result is that the tradeoff between interest-rate and exchange-rate stability is a potential candidate for the explanation of the apparent failure of UIP and that the consideration of policy reactions can explain why deviations from UIP differ systematically by the exchange-rate regime.     

Liquidity provision,interest rates,and unemployment

The effective liquidity supply of the economy—the weighted-sum of all assets that serve as media of exchange—matters for interest rates and unemployment. We formalize this idea by adding an over-the-counter market with collateralized trades to the Mortensen–Pissarides model. An increase in public liquidity through a higher supply of real government bonds raises the real interest rate, crowding out private liquidity and increasing unemployment. If unemployment is inefficiently high, keeping liquidity scarce can be socially optimal. A liquidity crisis affecting the acceptability of private assets as collateral widens the rate-of-return difference between private and public liquidity, also increasing unemployment.     

U.S. real exchange rate fluctuations and relative price fluctuations

Traditional theory attributes fluctuations in real exchange rates to changes in the relative price of nontraded goods. This paper studies the relation between the United States’ bilateral real exchange rate and the associated bilateral relative price of nontraded goods for five of its most important trade relationships. We find that this relation depends crucially on the choice of price series used to measure relative prices and on the choice of trade partner. The relation is stronger when we measure relative prices using producer prices rather than consumer prices. The relation is stronger the more important is the trade relationship between the United States and a trade partner. Even in cases where there is a strong relation between the real exchange rate and the relative price of nontraded goods, however, a large fraction of real exchange rate fluctuations is due to deviations from the law of one price for traded goods.     

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.     

A statistical comparison of the short-term interest rate models for Japan,U.S., and Germany

We propose a simple and practical model selection method for continuous time models. We apply the method to several continuous time short-term interest rate models using discrete time series data of Japan, U.S. and Germany. All the models can be easily estimated from discrete observations, and their performances can be evaluated in a uniform statistical framework. The models that allow dependence of volatility on the level of interest rates tend to perform well empirically. The degree of volatility dependence on the interest rate levels seems to be different across the countries. For the German data, we observe that a model with nonlinear drift performs better than the best linear drift model.     

The analysis and valuation of interest rate options

This paper provides a simple, alternative model for the valuation of European-style interest rate options. The assumption that drives the hedging argument in the model is that the forward prices of bonds follow an arbitrary two-state process. Later, this assumption is made more specific by postulating that the discount on a zero-coupon bond follows a multiplicative binomial process. In contrast to the Black-Scholes assumption applied to zero-coupon bonds, the limiting distribution of this process has the attractive features that the zero-bond price has a natural barrier at unity (thus precluding negative interest rates), and that the bond price is negatively skewed. The model is used to price interest rate options in general, and interest rate caps and floors in particular. The model is then generalized and applied to European-style options on bonds. A relationship is established between options on swaps and options on coupon bonds. The generalized model then provides a computationally simple formula, closely related to the Black-Scholes formula, for the valuation of European-style options on swaps.     

Nonparametric density estimation and tests of continuous time interest rate models

I study the finite sample distribution of one of Ait-Sahalia's(1996c) nonparametric tests of continuous-time models of theshort-term riskless rate. The test rejects true models too oftenbecause interest rate data are highly persistent but the asymptoticdistribution of the test (and of the kernel density estimatoron which the test is based) treats the data as if it were independentlyand identically distributed. To attain the accuracy of the kerneldensity estimator implied by its asymptotic distribution with22 years of data generated from the Vasicek model in fact requires2755 years of data.     

Determinants of interest rate swap spreads

This study argues that an interest rate swap, as a non-redundant security, creates surplus which will be shared by swap counterparties to compensate their risks in swaps. This action in turns affects swap spreads. Analyzing the time series impacts of the changes of risks of swap counterparties on swap spreads, we conclude that both lower and higher rating bond spreads have positive impacts on swap spreads. We also derive a risk–spread relation to test if swap counterparties are firms with differential credit ratings. Since the risk allocation between swap counterparties varies over business cycles, hence this factor needs to be controlled. We conclude that (1) similar results hold if the business cycle factor is controlled and (2) swap spreads contain procyclical element and are less cyclical than lower credit rating bond spreads.     

Further evidence on the rationality of interest rate expectations

This paper extends the limited work on interest rate expectations to a previously unexploited data set that covers a broad range of EMS and non-EMS foreign currency deposits. We corroborate the earlier finding in the literature that interest rate forecasts are not rational and that agents do not use all available information in an efficient manner; this finding applies to the post-1990 period, thus questioning the assertion of Frankel and Froot [Frankel, J.F., Froot, K.A., 1987a. Using survey data to test standard propositions regarding exchange rate expectations. American Economic Review 77, 151] that “the nature of the rejection of rational expectations strongly depends on the sample period”. Although forecast errors on EMS rates are smaller and less volatile than errors on non-EMS rates, expectations on EMS rates are nevertheless biased.     

Sterilization of short-term capital inflows—through lower interest rates?

Reductions in international interest rates are a major cause of capital flows to emerging economies. Increases in domestic interest rates are a frequent policy response to the resulting price increases. This is often unsuccessful. The paper suggests a theoretical explanation based on distinctive features of emerging financial markets, including imperfect asset substitutability and imperfect capital mobility for some sectors of the economy. It concludes that the appropriate policy response to capital inflows may be lower interest rates.     

Bayesian comparison of several continuous time models of the Australian short rate

This paper provides an empirical analysis of a range of alternative single‐factor continuous time models for the Australian short‐term interest rate. The models are nested in a general single‐factor diffusion process for the short rate, with each alternative model indexed by the level effect parameter for the volatility. The inferential approach adopted is Bayesian, with estimation of the models proceeding through a Markov chain Monte Carlo simulation scheme. Discrimination between the alternative models is based on Bayes factors. A data augmentation approach is used to improve the accuracy of the discrete time approximation of the continuous time models. An empirical investigation is conducted using weekly observations on the Australian 90 day interest rate from January 1990 to July 2000. The Bayes factors indicate that the square root diffusion model has the highest posterior probability of all models considered.     

Banking market conditions and deposit interest rates

This paper shows that the impact of market structure on bank deposit interest rates is complex. Both market size structure and multimarket bank presence have independent effects on rates. There is evidence that mid-size banks were more aggressive competitors than other banks, but that the effect of market structure on deposit rates has evolved over time, with mega-banks recently becoming more aggressive competitors. This may be related to the growth of mega-banks in many markets. These findings have implications for existing theories of deposit pricing and, by extension, antitrust policy in banking.     

An alternative approach to the calibration of the Vasicek and CIR interest rate models via generating functions

We propose a new method to calibrate the Vasicek and Cox--Ingersoll--Ross interest rate models from bond prices. We define an appropriate generating function and derive recursive relations between the derivatives of the generating function and the bond prices. The parameters of the Vasicek and CIR models are then obtained by solving a system of linearly independent equations arising from the recursive relations. We include numerical results that show the method’s accuracy when bond prices generated from the exact formulas are used.     

Duration, factor sensitivities, and interest rate Greeks

In this paper, we introduce for interest rate sensitive assets the natural analogs of delta and gamma for equity options by considering the derivatives of asset prices with respect to the directions along which the forward rate curve may evolve. Macaulay duration and convexity, as well as stochastic duration considered in Cox et al. (J Business 52:51–61, 1979) and Munk (Rev Derivat Res 3:157–181, 1999), are easily obtained as special cases of these in which the derivatives are computed along parallel shifts and the direction of the forward rate volatilities, respectively. Moreover, we demonstrate using the example of the Ritchken and Sankarasubramanian (Math Financ 5:55–72, 1995) model that the hedging strategy based on these sensitivity measures provides a superior performance in comparison to the traditional duration based hedging approaches.      

International capital flows and U.S. interest rates

Foreign purchases of U.S. government bonds have an economically large and statistically significant impact on long-term interest rates. While the dramatic reductions in both long-term inflation expectations and the volatility of long rates contributed much to the decline of long rates in the 1990s, more recently foreign flows have become important. Controlling for various factors, we estimate that absent the substantial foreign inflows into U.S. government bonds the 10-year Treasury yield would be 80 basis points higher. Our results are robust to a number of alternative specifications.     

International interest rates and US monetary policy announcements: Evidence from Hong Kong and Singapore

This paper investigates the responses of market interest rates to US monetary policy announcements for the US and two emerging economies, Hong Kong and Singapore which are similar on many respects but have experienced opposite exchange rate regimes in the last twenty years. Our results, based on market expectations extracted from federal fund futures rates, document that FOMC announcements significantly affect the term structure of interest rate in the US and both Asian countries. Further, international interest rate differentials around FOMC meeting dates tend to be negative for short maturities with the impact gradually dissipating as bond maturity increases. Finally, for the case of Singapore, we find that domestic interest rates react to both external and domestic monetary policy announcements with a magnitude that is larger over the full bond maturity spectrum for domestic announcements. These results are robust to time-varying futures risk premia and alternative measures of interest rates expectations.     

Calibrating a market model with stochastic volatility to commodity and interest rate risk

Based on the multi-currency LIBOR Market Model, this paper constructs a hybrid commodity interest rate market model with a stochastic local volatility function allowing the model to simultaneously fit the implied volatility surfaces of commodity and interest rate options. Since liquid market prices are only available for options on commodity futures, rather than forwards, a convexity correction formula for the model is derived to account for the difference between forward and futures prices. A procedure for efficiently calibrating the model to interest rate and commodity volatility smiles is constructed. Finally, the model is fitted to an exogenously given correlation structure between forward interest rates and commodity prices (cross-correlation). When calibrating to options on forwards (rather than futures), the fitting of cross-correlation preserves the (separate) calibration in the two markets (interest rate and commodity options), while in the case of futures a (rapidly converging) iterative fitting procedure is presented. The fitting of cross-correlation is reduced to finding an optimal rotation of volatility vectors, which is shown to be an appropriately modified version of the ‘orthonormal Procrustes’ problem in linear algebra. The calibration approach is demonstrated in an application to market data for oil futures.