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.     

Yield curve modeling and forecasting using semiparametric factor dynamics

Using a dynamic semiparametric factor model (DSFM) we investigate the term structure of interest rates. The proposed methodology is applied to monthly interest rates for four southern European countries: Greece, Italy, Portugal and Spain from the introduction of the Euro to the recent European sovereign-debt crisis. Analyzing this extraordinary period, we compare our approach with the standard market method – dynamic Nelson–Siegel model. Our findings show that two nonparametric factors capture the spatial structure of the yield curve for each of the bond markets separately. We attributed both factors to the slope of the yield curve. For panel term structure data, three nonparametric factors are necessary to explain 95% variation. The estimated factor loadings are unit root processes and reveal high persistency. In comparison with the benchmark model, the DSFM technique shows superior short-term forecasting in times of financial distress.     

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.     

Testing for rational bubbles in the presence of structural breaks: Evidence from nonstationary panels

This paper presents new results on the rational bubbles hypothesis for a panel of 18 OECD countries using the model developed by Campbell (2000). We provide an analysis of international data that exploits increased power deriving from the panel unit root and cointegration methodology, together with the flexibility of allowing explicitly for multiple endogenous structural breaks in the individual series. Differently from the time series methodology, the panel data approach allows for a global analysis of the financial crashes that are related to rational bubbles. We find strong evidence in favor of bubbles phenomena.     

Predicting bankruptcy using the discrete-time semiparametric hazard model

The usual bankruptcy prediction models are based on single-period data from firms. These models ignore the fact that the characteristics of firms change through time, and thus they may suffer from a loss of predictive power. In recent years, a discrete-time parametric hazard model has been proposed for bankruptcy prediction using panel data from firms. This model has been demonstrated by many examples to be more powerful than the traditional models. In this paper, we propose an extension of this approach allowing for a more flexible choice of hazard function. The new method does not require the assumption of a parametric model for the hazard function. In addition, it also provides a tool for checking the adequacy of the parametric model, if necessary. We use real panel datasets to illustrate the proposed method. The empirical results confirm that the new model compares favorably with the well-known discrete-time parametric hazard model.     

Pricing the term structure with linear regressions

We show how to price the time series and cross section of the term structure of interest rates using a three-step linear regression approach. Our method allows computationally fast estimation of term structure models with a large number of pricing factors. We present specification tests favoring a model using five principal components of yields as factors. We demonstrate that this model outperforms the Cochrane and Piazzesi (2008) four-factor specification in out-of-sample exercises but generates similar in-sample term premium dynamics. Our regression approach can also incorporate unspanned factors and allows estimation of term structure models without observing a zero-coupon yield curve.     

Corporate credit default models: a mixed logit approach

The popular logit model is extended to allow for varying stochastic parameters (mixed logit) and non-linearities of regressor variables while analysing a cross-sectional sample of German corporate credit defaults. With respect to economic interpretability and goodness of probability forecasts according to disriminatory power and calibration, empirical results favor the extended specifications. The mixed logit model is particularly useful with respect to interpretability. However, probability forecasts based on the mixed logit model are not distinctively preferred to extended logit models allowing for non-linearities in variables. Further potential improvements with the help of the mixed logit approach for panel data are shown in a Monte Carlo study.     

Efficient Factor Models For Yield Curve Dynamics

Abstract

This paper derives a class of efficient factor models that bridge a gap between factor models and Heath-Jarrow-Morton models. These efficient factor models provide arbitrage-free dynamics for the yield curve, can be readily extended to fit the current yield curve, and have closed-form formulas for pricing default-free zero-coupon bonds. The short rate is a state variable in these efficient factor models. There are no restrictions imposed on the functional form of the volatility of the short rate except for certain technical conditions to ensure the solvability of the associated stochastic differential equations. The stochastic volatility of the short rate can be one of the state variables. The paper also presents a closed-form solution for default-free discount bond prices in the Malkiel model and provides a new method to derive the Ritchken-Sankarasubramanian model.     

Bayesian approach to yield curve modelling with application to the simulation of EMU environments: generating scenarios by modelling yield curve movements

A Bayesian approach to yield curve modelling is developed where information on the current and recent yield curves is used to generate yield curve scenarios, and a model is proposed that generates return distribution for bonds. The predictive power of the model is developed by comparing out-of-sample lagged realized yields with forecast yields, and it is demonstrated that the returns generated by this scenario approach and those generated using the standard time series approach are consistent. The model is applied to pre-EMU and post-EMU environments. This paper assesses the implications of different assumptions on the early post-EMU environment for international bond portfolio selection, as well as the immediate short-term effect of EMU on risk and return.     

Non-Linear Predictive Models for Intra-Day Foreign Exchange Trading

Artificial neural networks were used to search for non-linear relations in high- frequency foreign exchange time series. Three years (1985-7) tick-by-tick bid prices for the Swiss franc to the US dollar exchange rate were used in this study as training data to specify predictive models for intra-day trading, which was then tested on the same exchange rate time series in the following year (1988). A simple trading rule was adopted to evaluate the models, which showed statistically significant trading profit under moderate transaction costs. In contrast, a standard linear model did not produce profit with the same training and test data and under the same trading rule and transaction cost assumption. This provides evidence for the non-linear nature of the foreign exchange time series under study.     

Euro and FIBOR interest rates: A continuous time modelling analysis

The introduction of the Euro in January 1999 and the new reference interest rate EURIBOR® which is widely used as the underlying interest rate for Euro denominated derivative contracts have opened up a new area of research in international financial markets. In this paper we estimate single factor models using daily EURIBOR® and FIBOR interest rate data. We also estimate a model allowing a level-GARCH specification and a two factor model. We find evidence of level-volatility effects in both rates.     

Reduced-form Models with Regime Switching: An Empirical Analysis for Corporate Bonds

Empirical evidence shows that there is a close link between regime shifts and business cycle fluctuations. A standard term structure of interest rates, such as the Cox et al. (1985 Econometrica, 53, 385–407; CIR) model, is sharply rejected in the Treasury bond data. Only Markov regime-switching models on the entire yield curve of the Treasury bond data can account for the observed behavior of the yield curve. In this paper, we examine the impact of regime shifts on AAA-rated and BBB-rated corporate bonds through the use of a reduced-form model. The model is estimated by the Efficient Method of Moments (EMM). Our empirical results suggest that regime-switching risk has significant implications for corporate bond prices and hence has a material impact on the entire corporate bond yield curve, providing evidence for the approach of rating through the cycle employed by rating agencies.     

Models of the yield curve and the curvature of the implied forward rate function

We examine several alternative models of the UK gilt yield curve using daily data for the period 12 July 1996-10 February 2010. We select the best models according to two criteria: low out of sample errors in pricing bonds and low curvature of the implied forward rate curve function. We suggest additions to some of the models that significantly improve their performance. Some of the new models out perform those typically used by the central banks. In particular this paper suggests that the model used by the Canadian Central Bank which both outperforms other models and is particularly easy to estimate, is well suited to the UK gilt market.     

INTEREST RATE PARITY AND THE BEHAVIOR OF THE BID-ASK SPREAD

We use a stochastic frontier regression model to test interest rate parity (IRP) with bid- ask spreads for the Belgian franc, the Deutschmark, and the Swiss franc. The forward markets tested have become efficient in the sense that IRP holds well. The bounds provided by IRP do not appear to be binding, however. We provide evidence that in spite of the overall goodness of fit of the model, the arbitrage margins are sometimes violated, implying possible arbitrage opportunities. The percentage bid-ask spread is consistently higher for the Belgian franc than for the Deutschmark and the Swiss franc. Spreads are increasing functions of the time to maturity and volatility. Spread-size clustering is more severe than price-level clustering and appears to be inversely related to volatility and positively related to the trading volume. We find no evidence of significant calendar-day effects on spread size.     

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.     

Explosion in the quasi-Gaussian HJM model

We study the explosion of the solutions of the SDE in the quasi-Gaussian HJM model with a CEV-type volatility. The quasi-Gaussian HJM models are a popular approach for modeling the dynamics of the yield curve. This is due to their low-dimensional Markovian representation which simplifies their numerical implementation and simulation. We show rigorously that the short rate in these models explodes in finite time with positive probability, under certain assumptions for the model parameters, and that the explosion occurs in finite time with probability one under some stronger assumptions. We discuss the implications of these results for the pricing of the zero coupon bonds and Eurodollar futures under this model.     

面板数据下的线性混合模型及其在车险费率厘定中的应用

精算师在进行车险净保费信度厘定时可采用关于面板数据的线性混合模型,本文采用每次交通事故平均损失额和事故发生频率作为车险净保费的计算指标。利用2008~2012年31个省、市、自治区5年的数据,建立面板数据下的线性混合模型,选取人均地区生产总值、每平方公里人口数、民用汽车拥有量作为解释变量,得到每次交通事故平均损失额和事故发生频率的估计模型,进而得到纯保费估计。这一研究可为车险费率市场化提供一定的理论支持和参考。     

MODELING THE TERM STRUCTURE FROM THE ON‐THE‐RUN TREASURY YIELD CURVE

We propose a new model to estimate the term structure of interest rates using observed on‐the‐run Treasury yields. The new model is an improvement over models that require a priori knowledge of the shape of the yield curve to estimate the term structure. The general form of the model is an exponential function that depends on the estimation of four parameters fit by nonlinear least squares and has straightforward interpretations. In comparing the proposed model with current yield‐curve‐smoothing models, we find that, for the data used, the proposed model does best overall in terms of pricing accuracy both in sample and out of sample. JEL classification: E43, G12     

AN ANALYTICAL MODEL OF RISKY YIELD CURVES

This paper proposes a multiperiod certainty equivalent model of present valuation that takes a dynamic approach to valuation, as opposed to a recursive approach employed traditionally in financial economics. Assuming a flat basic, or riskless, yield curve and risk-averse investors, the model is used to examine the potential effects of default risk on the shape of the yield curve. The shape of the yield curve is shown to be directly related to the level and time pattern of default probabilities.