Book Description

This dissertation consists of three essays on Bayesian inference in financial economics. The first essay explores the impact of discretization errors on the parametric estimation of continuous-time financial models. Euler and other discretization schemes cause discretization errors in solving stochastic differential equations. The empirical impact of these discretization errors on estimating two continuous-time financial models is investigated by using Monte Carlo experiments to compare the "exact" estimator and "Euler" estimator for the Euler scheme. The primary finding is that reducing the discretization interval to reduce the discretization error does not necessarily improve the performance of the estimators. This implies that discretization schemes may yield reliable results when the sampling interval is regularly small and shortening the discretization intervals or using data augmentation techniques may be redundant in practice. The second essay examines the identification problem in state-space models under the Bayesian framework. Underidentifiability causes no real difficulty in the Bayesian approach in that a legitimate posterior distribution might be achieved for unidentified parameters when appropriate priors are imposed. When estimating unidentified parameters, Markov chain Monte Carlo algorithms may yield misleading results even if the algorithms seem to converge successfully. In addition, the identification problem does really not matter when the prediction of state-space models instead of parameter estimation is concerned. The third essay extensively studies credit risk models using Bayesian inference. Bayesian inference is conducted and Markov chain Monte Carlo algorithms are developed for three popular credit risk models. Empirical results show that these three models in which the same PD (probability of default) can be estimated using different information may yield quite different results. Motivated by the empirical results about credit risk model uncertainty, I propose a "combined" Bayesian estimation method to incorporate information from different datasets and model structure for estimating the PD. This new approach provides an insight in dealing with two practical problems, model uncertainty and data insufficiency, in credit risk management.