On the estimation and comparison of short-rate models using the generalised method of moments

Subsequent to the influential paper of [Chan, K.C., Karolyi, G.A., Longstaff, F.A., Sanders, A.B., 1992. An empirical comparison of alternative models of the short-term interest rate. Journal of Finance 47, 1209-1227], the generalised method of moments (GMM) has been a popular technique for estimation and inference relating to continuous-time models of the short-term interest rate. GMM has been widely employed to estimate model parameters and to assess the goodness-of-fit of competing short-rate specifications. The current paper conducts a series of simulation experiments to document the bias and precision of GMM estimates of short-rate parameters, as well as the size and power of [Hansen, L.P., 1982. Large sample properties of generalised method of moments estimators. Econometrica 50, 1029-1054], J-test of over-identifying restrictions. While the J-test appears to have appropriate size and good power in sample sizes commonly encountered in the short-rate literature, GMM estimates of the speed of mean reversion are shown to be severely biased. Consequently, it is dangerous to draw strong conclusions about the strength of mean reversion using GMM. In contrast, the parameter capturing the levels effect, which is important in differentiating between competing short-rate specifications, is estimated with little bias. (c) 2006 Elsevier B.V. All rights reserved.

Are there non-linearities 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.

An empirical investigation of the level effect in Australian interest rates

An extensive literature examines the dynamics of interest rates, with particular attention given to the positive relationship between interest-rate volatility and the level of interest rates—the so-called level effect. This paper examines the interaction between the estimated level effect and competing parameterisations of interest-rate volatility for the Australian yield curve. We adopt a new methodology that estimates elasticity in a multivariate setting that explicitly accommodates the correlations that exist between various yield factors. Results show that significant correlations exist between the residuals of yield factors and that such correlations do indeed impact on model estimates. Within the multivariate setting, the level of the short rate is shown to be a crucial determinant of the conditional volatility of all three yield factors. Measures of model fit suggest that, in addition to the usual level effect, the incorporation of GARCH effects and possible regime shifts is important

Yield-factor volatility models

The term structure of interest rates is often summarized using a handful of yield factors that capture shifts in the shape of the yield curve. In this paper, we develop a comprehensive model for volatility dynamics in the level, slope, and curvature of the yield curve that simultaneously includes level and GARCH effects along with regime shifts. We show that the level of the short rate is useful in modeling the volatility of the three yield factors and that there are significant GARCH effects present even after including a level effect. Further, we find that allowing for regime shifts in the factor volatilities dramatically improves the model’s fit and strengthens the level effect. We also show that a regime-switching model with level and GARCH effects provides the best out-of-sample forecasting performance of yield volatility. We argue that the auxiliary models often used to estimate term structure models with simulation-based estimation techniques should be consistent with the main features of the yield curve that are identified by our model.

Jackknife for bias reduction in predictive regressions

One of the fundamental econometric models in finance is predictive regression. The standard least squares method produces biased coefficient estimates when the regressor is persistent and its innovations are correlated with those of the dependent variable. This article proposes a general and convenient method based on the jackknife technique to tackle the estimation problem. The proposed method reduces the bias for both single- and multiple-regressor models and for both short- and long-horizon regressions. The effectiveness of the proposed method is demonstrated by simulations. An empirical application to equity premium prediction using the dividend yield and the short rate highlights the differences between the results by the standard approach and those by the bias-reduced estimator. The significant predictive variables under the ordinary least squares become insignificant after adjusting for the finite-sample bias. These discrepancies suggest that bias reduction in predictive regressions is important in practical applications.

A Non-Parametric Dimension Test of the Term Structure

Published as an article in: Studies in Nonlinear Dynamics & Econometrics, 2004, vol. 8, issue 3, article 6.

Switching Regimes in the Term Structure of Interest Rates During U.S. Post-War: A case for the Lucas proof equilibrium?

Published as an article in: Studies in Nonlinear Dynamics & Econometrics, 2004, vol. 8, issue 1, pages 5.

Three essays on the term structure of interest rates

A PhD Dissertation, presented as part of the requirements for the Degree of Doctor of Philosophy from the NOVA - School of Business and Economics

Testing the expectations theory of the term structure in threshold models

We test the expectations theory of the term structure of U.S. interest rates in nonlinear systems. These models allow the response of the change in short rates to past values of the spread to depend upon the level of the spread. The nonlinear system is tested against a linear system, and the results of testing the expectations theory in both models are contrasted. We find that the results of tests of the implications of the expectations theory depend on the size and sign of the spread. The long maturity spread predicts future changes of the short rate only when it is high.

Stochastic growth and monetary policy: the impacts on the term structure of interest rates

This paper builds a simple, empirically-verifiable rational expectations model for term structure of nominal interest rates analysis. It solves an stochastic growth model with investment costs and sticky inflation, susceptible to the intervention of the monetary authority following a policy rule. The model predicts several patterns of the term structure which are in accordance to observed empirical facts: (i) pro-cyclical pattern of the level of nominal interest rates; (ii) countercyclical pattern of the term spread; (iii) pro-cyclical pattern of the curvature of the yield curve; (iv) lower predictability of the slope of the middle of the term structure; and (v) negative correlation of changes in real rates and expected inflation at short horizons.

Pricing the option adjust spread of Brazilian Eurobonds

This paper presents results of a pricing system to compute the option adjusted spread ("DAS") of Eurobonds issued by Brazilian firms. The system computes the "DAS" over US treasury rates taktng imo account the embedded options present on these bonds. These options can be calls ("callable bond"), puts ("putable bond") or combinations ("callable and putable bond"). The pricing model takes into account the evolution of the term structure along time, is compatible with the observable market term structure and is able to compute risk measures such as duration and convexity, and pricing and hedging of options on these bonds. Examples show the ejJects of the embedded options on the spread and risk measures as well as the ejJects on the spread due to variations on the volatility parameters ofthe short rate.

Affine processes, arbitrage-Free Term structures of legendre polynomials,and option pricing

Multivariate Affine term structure models have been increasingly used for pricing derivatives in fixed income markets. In these models, uncertainty of the term structure is driven by a state vector, while the short rate is an affine function of this vector. The model is characterized by a specific form for the stochastic differential equation (SDE) for the evolution of the state vector. This SDE presents restrictions on its drift term which rule out arbitrages in the market. In this paper we solve the following inverse problem: Suppose the term structure of interest rates is modeled by a linear combination of Legendre polynomials with random coefficients. Is there any SDE for these coefficients which rules out arbitrages? This problem is of particular empirical interest because the Legendre model is an example of factor model with clear interpretation for each factor, in which regards movements of the term structure. Moreover, the Affine structure of the Legendre model implies knowledge of its conditional characteristic function. From the econometric perspective, we propose arbitrage-free Legendre models to describe the evolution of the term structure. From the pricing perspective, we follow Duffie et al. (2000) in exploring Legendre conditional characteristic functions to obtain a computational tractable method to price fixed income derivatives. Closing the article, the empirical section presents precise evidence on the reward of implementing arbitrage-free parametric term structure models: The ability of obtaining a good approximation for the state vector by simply using cross sectional data.

Pricing in stochastic-local volatility models with default

In recent years is becoming increasingly important to handle credit risk. Credit risk is the risk associated with the possibility of bankruptcy. More precisely, if a derivative provides for a payment at cert time T but before that time the counterparty defaults, at maturity the payment cannot be effectively performed, so the owner of the contract loses it entirely or a part of it. It means that the payoff of the derivative, and consequently its price, depends on the underlying of the basic derivative and on the risk of bankruptcy of the counterparty. To value and to hedge credit risk in a consistent way, one needs to develop a quantitative model. We have studied analytical approximation formulas and numerical methods such as Monte Carlo method in order to calculate the price of a bond. We have illustrated how to obtain fast and accurate pricing approximations by expanding the drift and diffusion as a Taylor series and we have compared the second and third order approximation of the Bond and Call price with an accurate Monte Carlo simulation. We have analysed JDCEV model with constant or stochastic interest rate. We have provided numerical examples that illustrate the effectiveness and versatility of our methods. We have used Wolfram Mathematica and Matlab.