Dynamic interest rate and credit risk models

Abstract

This thesis studies the pricing of Treasury bonds, the pricing of corporate bonds and the modelling of portfolios of defaultable debt. By drawing on the related literature, Chapter 1 provides economic background and motivation for the study of each of these topics. Chapter 2 studies the use of Gaussian affine dynamic term structure models (GDTSMs) for forming forecasts of Treasury yields and conditional decompositions of the yield curve into expectation and risk premium components. Specifically, it proposes market prices of risk that can generate bond price time series that are consistent with the important empirical result of Cochrane and Piazzesi (2005), that a linear combination of forward rates can forecast excess returns to bonds. Since the GDTSM here falls into the essentially affine class (Duffee (2002)), it is analytically tractable. Chapter 3 studies conditional risk premia in a commonly applied default intensity based model for pricing corporate bonds. Here, I refer to such models as completely affine defaultable dynamic term structure models (DDTSMs). There are two main contributions. First, I show that completely affine DDTSMs imply that the compensation for the risk associated with shocks to default intensities (the credit spread risk premium) is related to the volatility of default intensities. Second, I run regressions to show that this relationship holds in a set of corporate bond data. Finally, Chapter 4 proposes a new dynamic model for default rates in large debt port- folios. The model is similar in principle to Duffie, Saita, and Wang (2007) and Duffie, Eckner, Horel, and Saita (2009) in that the default intensity depends on the observed macroeconomic state and unobserved frailty variables. However, the model is designed for use with more commonly available aggregate, rather than individual, default data. Fitting the model to aggregate charge-off rates in US corporate, real-estate and non- mortgage retail sectors, it is found that interest rates, industrial production and unemployment rates have quantitatively plausible effects on aggregate default rates.