Exponential-affine diffusion term structure models : dimension, time-homogeneity, and stochastic volatility

The object of study in this thesis is the most general affine term structure model characterized by Duffie and Kan (1996), which nests, as special cases, many of the interest rate models previously formulated in the literature. The purpose of the dissertation is two-fold: to derive fast and accurate pricing solutions for the general term structure framework under analysis, which enable the effective use of model’ specifications yet unexplored due to their analytical intractability, and, to implement a simple and robust model’ estimation methodology that enhances the model' fit to the market interest rates covariance surface. \n \nConcerning the first (theoretical) goal, analytical exact pricing solutions, for several interest rate derivatives, are first derived under a (simpler and) nested Gaussian affine specification Then, and as the main contribution of the present dissertation, such Gaussian formulae are transformed into first order approximate closed-form pricing solutions for the most general stochastic volatility model’ formulation. These approximate solutions arc shown to be both extremely fast to implement and accurate, which make them an effective alternative to the existing numerical pricing methods available. \n \nRelated to second thesis’ (empirical) goal, and in order to enable the model’ estimation from a panel-data of interest rate contingent claims’ prices, a general equilibrium model’ specification is derived under non-severc preferences’ assumptions and in the context of a monetary economy. The corresponding state-space model’ specification is estimated through a non-linear Kalman filter and using a panel-data of not only swap rates (as it is usual in the Finance literature) but also (for the first time) of caps and European swaptions prices It is shown that although the model' fit to the level of the yield curve is extremely good, short-term caps and swaptions are systematically mispriced. Finally, a time-inhomogeneous HJM formulation is proposed, and the model’ fit to the market interest rates covariance matrix is substantially improved \n