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by Peter Schotman In this paper we propose and implement a Bayesian procedure for the empirical valuation of bond options given the observed term structure of interest rates, and given assumptions about the time series behavior of the instantaneous spot rate. The Bayesian approach is motivated by the extreme multicollinearity in the cross-sectional data. The multicollinearity is caused by some local identification problems in the likelihood function. These same singularities motivate the choice of prior. The proposed method is applied to a dataset of Dutch bond prices.
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by Andrew D. Sanford and Gael Martin 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 indexed by the level effect parameter for the volatility in the short rate process. The inferential approach adopted is Bayesian, with estimation of the models proceeding via a Markov Chain Monte Carlo simulation scheme. Discrimination between the alternative models is based on Bayes factors, estimated from the simulation output using the Savage-Dickey density ratio. 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 the nested models. Keywords: Interest Rate Models, Markov Chain Monte Carlo, Data Augmentation, Bayes Factors. Discuss this paper
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by Min Li This paper presents a case study of interest rate term structure estimation of U.S. Treasury bonds and AT&T corporate bonds from April 1994 to December 1995. We first adopt a Bayesian regression spline model to estimate the term structure of risk-free Treasury bonds where the number and location of the spline knots are adaptively selected using the reversible jump Markov chain Monte Carlo algorithm. We then develop a hierarchical Bayesian approach to estimate the corporate term structure, Discuss this paper
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by Philip Gray Estimating continuous-time short-rate models is challenging since the likelihood function for most popular models is unknown. While approximate likelihood functions are often used, this practice induces bias into the estimation process. This paper explores a Bayesian method of estimating short-rate models. While the approach also employs an approximate likelihood, data augmentation is utilised to mitigate discretisation bias. The results suggest that Bayesian estimates of posterior densities for model parameters closely resemble true posterior densities. While non-essential for point estimation, a small degree of data augmentation is useful in recovering accurate posterior densities and reducing the bias in estimates of bond price. These findings are encouraging for the many cases where exact likelihood-based estimation is impossible and approximations must be relied upon
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Jesper Lund Part II: GMM for diffusion processes Nonparametric estimation for diffusions Reviews of GMM and kernel estimators Discuss this paper
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