Book excerpt: "This thesis comprises three essays that explore several theoretical and empirical features of affine term structure models. In the first essay, we focus on the ability of continuous-time affine term structure models to capture time variability in the second conditional moment. Using data on US Treasury yields, we conclude that affine term structure models are much better at extracting time-series volatility from the cross-section of yields than argued in the literature. These models have nonetheless difficulty capturing volatility dynamics at the short end of the maturity spectrum, perhaps indicating some form of segmentation between long-maturity and short-maturity bonds. These results are robust to the choice of sample period, interpolation method and estimation method. In the second essay, we propose the use of the unscented Kalman filter technique for the estimation of affine term structure models using non-linear instruments. We focus on swap rates and show that the unscented Kalman filter leads to important reductions in bias and gains in precision. The use of the unscented Kalman filter results in substantial improvements in out-of-sample forecasts. Our findings suggest that the unscented Kalman filter may prove to be a good approach for a number of problems in fixed income pricing in which the relationship between the state vector and the observations is nonlinear, such as the estimation of term structure models using interest rate derivatives or coupon bonds, and the estimation of quadratic term structure models. The third essay provides a tractable framework for pricing defaultable securities with recovery risk. Pricing solutions are explored for a large family of discrete-time affine processes and a five-factor Gaussian model is estimated on BBB and B Standard and Poor's yield indices. This rich econometric setup allows the model to simultaneously capture two important stylized facts of defaultable securities: The positive correlation between the loss given default and the intensity of default, and the negative correlation between the intensity of default and the risk-free interest rate." --