Essays on Bayesian inference with financial applications

This thesis is composed of two main research lines. The first line, developed in chapters 2 to 4, deals with frequentist and Bayesian estimation of regime-switching GARCH models and its application to risk management on energy markets, while the second part, which corresponds to chapter 5, focuses on forecast rationality testing within a Bayesian framework. Chapter 2 presents a unified mathematical framework for characterizing the class of MS-GARCH models based on collapsing the regimes in order to eliminate the usual path dependence problem. Within this framework, two new models (identified as Basic model and Simplified Klaassen model) are proposed as alternative specifications of the MS-GARCH model. Using Maximum Likelihood Estimation, we estimate the parameters of the different models within this family and compare their performance on both simulation and empirical exercises. Chapter 3 proposes new efficient Monte Carlo simulation techniques based on multiple proposal Metropolis. The application to approximated inference for regime-switching GARCH models is there discussed. In Chapter 4, we provide an extension of our efficient Monte Carlo simulation algorithm to a multi-chain Markov switching multivariate GARCH model and apply it to risk management in commodity market. More specifically we focus on futures commodity market and suggest a dynamic and robust minimum variance hedging strategy which accounts for model parameter uncertainty. In chapter 5, we propose a new Bayesian inference procedure for testing the monotonicity properties of second moment bounds across several horizons presented in Patton and Timmermann [2012].