Essays on risk and volatility

In this work, we begin with an investigation into the temporal correlation in default risk. We first establish a link between the dynamics of house price changes and the dynamics of default rates in the Gaussian copula framework by specifying a time series model for a common risk factor. We show that the serial correlation propagates from the common risk factor to default rates. In the second essay, we specify a model where the default correlation is stochastic. We find the distribution of expected value of cash flows received by securitized investment vehicles is distorted by the dynamics of default correlation. The third essay provides an empirical study on variance risk premium, which is defined as the difference between implied variance and ex post realized variance. We show that an individual stock\u27s variance risk premium and its two components can be used to predict future equity premium. In the fourth essay, we derive asymptotic properties of the quasi maximum likelihood estimator of smooth transition regressions. We show that the estimator converges at the usual ãT-rate and has an asymptotically normal distribution