Dynamic Models of Asset Returns and Mortgage Default

This dissertation consists of three chapters. The first chapter builds a new series of dynamic copula models and studies the influence of macro variables on the dependence between assets. The second chapter develops a dynamic logistics regression model and investigates how systematic risk affects mortgage default. The third chapter uses the frailty model developed in chapter 2 to explore spatial dependence between commercial and residential mortgage risk. In all three chapters, we extend the generalized autoregressive score (GAS) models proposed in Creal, Koopman and Lucas (2013a). In the first chapter, we propose a series of dynamic copula models with a short- and long run component specification, inspired by the mixed data sampling (MIDAS) component structure applied to univariate GARCH models in Engle, Ghysels and Sohn (2013) and multivariate GARCH models in Colacito, Engle and Ghysels (2011). In particular, we extend the framework of MIDAS to dynamic copulas. In the framework of GAS models, we combine macro variables of low frequency with asset returns of high frequency, and investigate the influence of low frequency macro variables on the dependence between asset returns. Our data consists of stock portfolios and a bond. We assess the new class of models with these data and find that an extra component enhances the model with more volatility. Moreover, the macro variables with MIDAS work as a proxy for the market condition, and allow that the macro environment affects how dependence parameter reacts to innovations. With these two flexibilities, the model performance is consistently improved through our empirical applications. In the second chapter, we design a new dynamic logistic regression model to track systematic risk of mortgages. Specifically, we match default rates in multiple dimensions by extending the GAS models. Our data consists of commercial mortgages in the U.S. retail market from 1997 to 2013. An empirical analysis of these data suggests the influence of origination month and the originator preference on default rates. To model the effects of these variables, we group mortgages by these two variables and allow latent factors to vary by groups. Compared with GAS models using a single factor, our multi-factor models feature improved empirical fits. To the best of our knowledge, this is the first attempt that uses observation-driven models to predict mortgage defaults. We show that the new class of models has better tractability compared with parameter-driven models. For instance, although our dataset has more than two million records, and our most complex model incorporates up to 15 frailty factors, the estimation process only takes two minutes using a standard desktop computer. In the third chapter, we use the frailty model developed in chapter 2 to explore spatial dependence between commercial and residential mortgage risk. Our dataset contains 1.6 million records of commercial mortgages and 140 million records of residential mortgages in the U.S. market. The time range of these records is between January 1999 and March 2016. Our empirical analysis demonstrates strong spatial dependence between commercial defaults and residential default in multiple respects. First, we apply Granger causality tests to the empirical default rates of commercial mortgages and residential mortgages in 10 main MSA areas, and the test results in 9 areas reveal a significant lead and lag relationship of the two mortgage markets. Second, we test the causal relation among the frailty factors that explain systematic risk of commercial mortgage and residential mortgage, and provide strong evidence on the close correlations between the residential and commercial mortgage markets. Last but not least, we show that residential PD is a good explanatory variable in predicting default of commercial mortgages in adjacent areas, and this prediction power also implies that local residential market drives the commercial market. To the best of our knowledge, this is the first paper exploring the spatial dependence between commercial mortgage default and residential mortgage default.Doctor of Philosoph