MCMC methods for random field and latent factor models in finance

This dissertation consists of three chapters that develop Markov Chain Monte Carlo (MCMC) estimation methods for random field and latent factor models. Chapter 1 develops a state-space framework for MCMC estimation of dynamic term structure models using a panel of observed forward rates. This framework is rich enough to handle traditional factor models as well as more recently developed random field models of the term structure. The chapter concludes with an empirical application, which finds that affine factor models are unable to explain the patterns of volatility and correlation in a historical sample of U.S. Treasury forward rates. By contrast, random field models fit these aspects of the data nearly perfectly.;Chapter 2 extends the estimation framework proposed in Chapter 1 to data sets that include prices of coupon bonds and fixed income derivatives. In traditional factor models, bond prices are exponential-affine in the state vector, and derivatives prices may be computed using a Fourier inversion approach. For random field models, an estimation approach is proposed where points on the forward rate curve and volatilities of forward rates are treated as a latent state vector, and the forward rate curve is approximated by series interpolation. Under this approximation, bond prices are exponential-affine in the state, and the same transform approach to derivatives pricing may be applied to random field models.;Chapter 3 employs a similar state space framework for MCMC estimation of stochastic volatility models. Using a historical sample of equity returns, both multifactor models and models with jumps are shown to be significant improvements over a single continuous volatility factor.