Short Interest Rate Research Articles

The Valuation of Callable Bonds with Floored CMS-spread Coupons

A new type of structured bond has recently been introduced with enormous success - primarily among private investors - in many countries in Europe. The bonds are medium term and with fixed and very high initial coupons. The remaining coupons are determined as a constant multiplier times the spread between a long and a short swap interest rate. These coupons are floored at or near zero, and the bond investment can thus be seen as a bet on the steepening of future term structure curves. However, if the term structure becomes too steep, the bonds may be called by the issuer. The paper studies the pricing and the optimal call strategy of these highly exotic bonds in a stochastic interest rate framework. We implement two versions of the LIBOR Market Model as well as a Gaussian two-factor short rate model. We show how to adapt the Least-Squares Monte Carlo procedure to handle the callability of the product in a numerically efficient manner. We also calculate lower bounds for the product as well as delta and vega ratios.

Stock Return Predictability in a Monetary Economy

In an economy where agents hold money, the short interest rate determines the trade-off between money holdings and consumption. Building on this idea, we develop a theoretical model that shows the transmission mechanism through which the short rate finds its way to stock-return predictability regressions. We construct a cointegration relation that links share prices and dividends to the short interest rate when we investigate empirically the main implications of our model. This relationship, that we denote the pdR-ratio, strongly predict stock returns and excess returns, even when the statistical significance of long-horizon return predictability is evaluated using Hodrick (1992) t-statistics. The result that stock returns and excess returns are predictable at long horizons is different from recent findings reported by Ang & Bekaert (2006). We differ from Ang & Bekaert (2006) by explicitly accounting for the non-stationarity of the predictors in a cointegration framework. Our theoretical model also suggests that aggregate output might be better suited as a scaling variable than dividends. As a consequence, we also build a cointegration variable that relates share prices, output, and the interest rate in a cointegration framework. We denote this variable the pyR-ratio. We show that the pyR-ratio strongly predicts stock returns and excess returns at long horizons. The pyR-ratio is also found to have some predictive power for dividend growth which the pdR-ratio does not. Neither the pyR-ratio nor the pdR-ratio have predictive power for output growth and the interest rate.

A NEW FINITE ELEMENT METHOD FOR PRICING OF BOND OPTIONS UNDER TIME INHOMOGENEOUS AFFINE TERM STRUCTURE MODELS OF INTEREST RATES

In this paper we propose a new finite element method for pricing of bond options under time inhomogeneous one-factor affine models of short interest rates: the Hull–White model and the extended CIR model. The stability and weak convergence are established. Numerical results are presented to examine the method and to compare the calibrated models.

Using Irregularly Spaced Returns to Estimate Multi-factor Models: Application to Brazilian Equity Data

Multi-factor models are useful tools to explain cross-sectional covariance in equities returns. In this paper a new estimation method is proposed that makes use of irregularly spaced returns and an empirical example is provided with the 389 most liquid equities in the Brazilian Market. The market index shows itself capable of explaining equity returns while the US$/Brazilian real exchange rate and the Brazilian short interest rate do not. The example shows the usefulness of the estimation method in further using the model to fill in missing values and to provide interval forecasts.

Arbitrage, Covered Interest Parity and Long-Term Dependence Between the US Dollar and the Yen

Using a daily time series from 1983 to 2005 of currency prices in spot and forward USD/Yen markets and matching equivalent maturity short term US and Japanese interest rates, we investigate the sensitivity over the sample period of the difference between actual prices in forward markets to those calculated from short term interest rates. According to a fundamental theorem in financial economics termed covered interest parity (CIP) the actual and estimated prices should be identical once transaction and other costs are accommodated. The paper presents four important findings: First, we find evidence of considerable variation in CIP deviations from equilibrium that tends to be one way and favours those market participants with the ability to borrow US dollars (and subsequently lend yen). Second, these deviations have diminished significantly and by 2000 have been almost eliminated. We attribute this to the effects of electronic trading and pricing systems. Third, regression analysis reveals that interday negative changes in spot exchange rates, positive changes in US interest rates and negative changes in yen interest rates generally affect the deviation from CIP more than changes in interday volatility. Finally, the presence of long-term dependence in the CIP deviations over time is investigated to provide an insight into the equilibrium dynamics. Using a local Hurst exponent - a statistic used in fractal geometry - we find episodes of both positive and negative dependence over the various sample periods, which appear to be linked to episodes of dollar decline/yen appreciation, or vice versa. The presence of negative dependence is consistent with the actions of arbitrageurs successfully maintaining the long-term CIP equilibrium. Given the time varying nature of the deviations from equilibrium the sample period under investigation remains a critical issue when investigating the presence of longterm dependence.

The volatility of the instantaneous spot interest rate implied by arbitrage pricing—A dynamic Bayesian approach

This paper considers the estimation of the volatility of the instantaneous short interest rate from a new perspective. Rather than using discretely compounded market rates as a proxy for the instantaneous short rate of interest, we derive a relationship between observed LIBOR rates and certain unobserved instantaneous forward rates. We determine the stochastic dynamics for these rates under the risk-neutral measure and propose a filtering estimation algorithm for a time-discretised version of the resulting interest rate dynamics based on dynamic Bayesian updating in order to estimate the volatility function. Our time discretisation can be justified by the fact that data are observed discretely in time. The method is applied to US Treasury rates of various maturities to compute a (posterior) distribution for the parameters of the volatility specification.

Instability of return prediction models

This study examines evidence of instability in models of ex post predictable components in stock returns related to structural breaks in the coefficients of state variables such as the lagged dividend yield, short interest rate, term spread and default premium. We estimate linear models of excess returns for a set of international equity indices and test for stability of the estimated regression parameters. There is evidence of instability for the vast majority of countries. Breaks do not generally appear to be uniform in time: different countries experience breaks at different times. For the majority of international indices, the predictable component in stock returns appears to have diminished following the most recent break. We assess the adequacy of the break tests and model selection procedures in a set of Monte Carlo experiments.

Commentary: The Savings-Investment Balance: Is there a UK investment shortfall?

In the first half of this decade, the world experienced a period of low short and long-term interest rates. Shortterm rates have risen from these low levels, first in Canada and the United Kingdom, then in the United States and finally in the Euro Area. Long-term rates, by contrast, remained low, suggesting that holders of longterm debt expected the rise in short-term rates to be only temporary. Only in the past few months has the apparently anomalous pricing of long-term debt started to disappear. But with interest rates on long-term debt similar to short-term market rates internationally, the market does not yet show that the traditional upwardsloping yield curve and, on this basis, long rates remain depressed. They are also markedly below the levels of two to three years ago.

Remarks on some short rate term structure models

Some widely used short interest rate termstructure models are discussed. By establishing certain estimateson the solutions of stochastic differential inequalities, we foundthat the interest rate processes obtained from these models do nothave enough integrability which leads to some defects in severalapplications.

The Term Structure of Interest Rates in a DSGE Model

The paper evaluates the implications of the Smets and Wouters (2004) DSGE model for the US yield curve. Bond prices are modelled in a way that is consistent with the macro model and the resulting risk premium in long term bonds is a function of the macro model parameters exclusively. When the model is estimated under the restriction that the implied average 10-year term premium matches the observed premium, it turns out that risk aversion and habit only need to rise slightly, while the increase in the term premium is achieved by a drop in the monetary policy parameter that governs the aggressiveness of the monetary policy rule. A less aggressive policy increases the persistence of the reaction of inflation and the short interest rate to any shock, reinforces the covariance between the marginal rate of substitution of consumption and bond prices, turns positive the contribution of the inflation premium and drives the term premium up. The paper concludes that by generating persistent inflation the presence of nominal rigidities can help in reconciling the macro model with the yield curve data.

Financial Integration: A New Methodology And An Illustration

This paper develops a simple new methodology to test for asset integration and applies it within and between American stock markets. Our technique is tightly based on a general intertemporal asset-pricing model, and relies on estimating and comparing expected risk-free rates across assets. Expected risk-free rates are allowed to vary freely over time, constrained only by the fact that they are equal across (risk-adjusted) assets. Assets are allowed to have general risk characteristics, and are constrained only by a factor model of covariances over short time periods. The technique is undemanding in terms of both data and estimation. We find that expected risk-free rates vary dramatically over time, unlike short interest rates. Further, the S&P 500 market seems to be well integrated, and the NASDAQ is generally (but not always) integrated. However, the NASDAQ is poorly integrated with the S&P 500.

Instability of Return Prediction Models

This study examines evidence of instability in models of ex post predictable components in stock returns related to structural breaks in the coefficients of state variables such as the lagged dividend yield, short interest rate, term spread and default premium. We estimate linear models of excess returns for a set of international equity indices and test for stability of the estimated regression parameters. There is evidence of instability for the vast majority of countries. We then attempt to characterize the timing and nature of the breaks. Breaks do not generally appear to be uniform in time: different countries experience breaks at different times. We do identify a contemporaneous break for the US and UK indices in 1974. There is also some evidence of a break for a cluster of European nations during the 1978-1982 period. These breaks may relate to the oil price shock of 1974 and the formation of the European Monetary System in 1979. For the majority of intenational indices, the predictable component in stock returns appears to have diminished following the most recent break. We assess the adequecy of the break tests and model selection procedures in a set of Monte Carlo experiments.

A note on nonlinear dynamics in the Spanish term structure of interest rates

This note applies the methodology to test for threshold cointegration recently proposed by Hansen and Seo (2002) [Hansen, B. E. & Seo, B., (2002). Testing for two-regime threshold cointegration in vector error-correction models. Journal of Econometrics, 110, 293–318] to the Spanish term structure of interest rates during the period 1980:1–2002:12. The evidence suggests that nonlinear cointegration between long and short interest rates is clearly rejected, so that a linear cointegration model would provide an adequate empirical description for the Spanish term structure of interest rate.

Investigating the Role of Systematic and Firm‐Specific Factors in Default Risk: Lessons from Empirically Evaluating Credit Risk Models*

This paper proposes and empirically investigates a family of credit risk models driven by a two‐factor structure for the short interest rate and an additional factor for firm‐specific distress. The firm‐specific distress factors include leverage, book‐to‐market, profitability, equity‐volatility, and distance‐to‐default. Our estimation approach and performance yardsticks show that interest rate risk is of first‐order importance for explaining variations in single‐name defaultable bond yields. When applied to low‐grade bonds, a credit risk model that takes leverage into consideration reduces absolute yield mispricing by as much as 30%. A strategy relying on Treasury instruments is effective in dynamically hedging credit exposures.

Issues in Money Demand: The Case of Europe

AbstractThis article establishes a co‐integration analysis for the euro area (sample period: 1983–2000), identifying three co‐integrating vectors: one which can be labelled money demand (in which real M3 money balances are related to output, with unit elasticity, and the long rate of interest); another pertaining to the spread between the short and long rate of interest; and a third which is an output (IS) relationship in which output is related to the real rate of interest. Currency substitution terms affect the adjustment of real money balances though they do not enter the co‐integration space. We use the aggregation procedure for historical Euroland data advocated by Beyer, Doornik and Hendry for application to aggregation of money, GDP and prices when exchange rates were varying. We make use of the German short‐ and long‐term interest rates as benchmarks for own rate and opportunity cost variables.

Calibration of Structural Credit Risk Models: Implied Sensitivities and Liquidity Discounts

Empirical tests of structural credit risk models typically ignore bond prices when estimating parameters. In this paper we depart from this, examining a calibration of the Collin-Dufresne & Goldstein (2001) model to bond prices. Using alternative specifications of a liquidity discount we evaluate the model based on fit to yield spreads and sensitivities to underlying fundamentals, producing a novel approach to evaluating the fit of a credit risk model. When augmenting with a liquidity discount we obtain a very good fit and outperform a two-factor reduced form model. Generally we understate the sensitivity towards changes in the leverage ratio and to a larger degree changes in the short interest rate. For investment grade bonds the model attributes 40% of the yield spread at 5 years of maturity to credit risk, in some agreement with the literature.

Monetary Policy after Bubbles Burst: The Zero Lower Bound, the Liquidity Trap and the Credit Deadlock

The current widespread use of models of monetary policy that link expenditure to interest rates, while by-passing interaction of the supply and demand for money in the transmission mechanism, fails to illuminate several important policy issues, and is beginning to create a professional memory loss in some of these areas. This claim is illustrated with reference to recent discussions of the conduct of monetary policy in the wake of financial crises, particularly when short interest rates are close to zero, as they have recently been in Japan.

A comparison of estimation methods in non-stationary ARFIMA processes

This paper reports an extensive Monte Carlo simulation study based on six estimators for the long memory fractional parameter when the time series is non-stationary, i.e., ARFIMA(p, d, q) process for d > 0.5. Parametric and semiparametric methods are compared. In addition, the effect of the parameter estimation is investigated for small and large sample sizes and non-Gaussian error innovations. The methodology is applied to a well known data set, the so-called UK short interest rates.

Financial Integration: A New Methodology and an Illustration

This Paper develops a simple new methodology to test for asset integration and applies it within and between American stock markets. Our technique is tightly based on a general intertemporal asset-pricing model, and relies on estimating and comparing expected risk-free rates across assets. Expected risk-free rates are allowed to vary freely over time, constrained only by the fact that they are equal across (risk-adjusted) assets. Assets are allowed to have general risk characteristics, and are constrained only by a factor model of covariances over short time periods. The technique is undemanding in terms of both data and estimation. We find that expected risk-free rates vary dramatically over time, unlike short interest rates. Further, the S&P 500 market seems to be well integrated, and the NASDAQ is generally (but not always) integrated. The NASDAQ, however, is poorly integrated with the S&P 500.

Financial Integration: A New Methodology and An Illustration

This paper develops a simple methodology to test for asset integration, and applies it within and between American stock markets. Our technique relies on estimating and comparing expected risk-free rates across assets. Expected risk-free rates are allowed to vary freely over time, constrained only by the fact that they must be equal across (risk-adjusted) assets in well integrated markets. Assets are allowed to have standard risk characteristics, and are constrained by a factor model of covariances over short time periods. We find that implied expected risk-free rates vary dramatically over time, unlike short interest rates. Further, internal integration in the S&P 500 market is never rejected and is generally not rejected in the NASDAQ. Integration between the NASDAQ and the S&P, however, is always rejected dramatically.