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Hidden Markov model of risky term structure: An application to Brazil Open Access

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This dissertation proposes a close-form solution, arbitrage free model of risky term structure, in a hidden Markov model framework. A Bayesian methodology for the estimation of this model is proposed and it is applied to Brazilian term structure data. This work is divided into three chapters.The first chapter presents the rationale for the study as well as a literature review of interest models, regime switching models and their intersection. A theoretical model for credit risky term structure in a hidden Markov framework is presented both in continuous and discrete time. A closed form solution is proposed given a set of simplifying assumptions.The second chapter reviews classical methods of estimating affine term structure models and presents their Bayesian equivalent. Bayesian methodologies for a risk free hiddenMarkov model of the structure and for the risky term structure model of Chapter 1 are proposed. A step by step MCMC algorithm is given as well as a short review of useful tools such as the Metropolis-Hastings and Gibbs algorithms.The third chapter applies the proposed model to Brazilian term structure data collected from January 1998 to April 2007. The fit of the term structure, the market prices of default determinants and regime switching risk are discussed. The model is contrasted to two alternatives in the ATSM family. I find that Brazilian term structure exhibits a high mean and a high volatility regime as well as a low mean and a low volatility regime. The high regime is associated with the Brazilian exchange rate crisis from 1998 to 1999 and with US recession from 2002 to 2004. The proposed model is superior to its single regime counterpart, but is not significantly different from hidden Markov ATSMs that do not differentiate between risk free and risky term structure.

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