This paper develops a two-step estimation methodology that allows us to apply catastrophe theory to stock market returns with time-varying volatility and to model stock market crashes. In the first step, we utilize high-frequency data to estimate daily realized volatility from returns. Then, we...

We estimate a non-linear diffusion model to capture the dynamics of the VIX index. The model is estimated under the risk neutral and the objective probability measures. The risk neutral dynamics are captured through a novel estimation method applied to futures prices. We find that non-linearity...

We propose a new adequacy test and a graphical evaluation tool for nonlinear dynamic models. The proposed techniques can be applied in any setup where parametric conditional distribution of the data is specified, in particular to models involving conditional volatility, conditional higher...

This paper develops tests for selection of competing non-linear dynamic models. The null hypothesis is that the models are equally close the Data Generating Process (DGP), according to a certain measure of closeness. The alternative is that one model is closer to the DGP. The models can be...

Modern economies have been subjected to a number of shocks during the past several years such as the burst of the Internet bubble, terrorist attacks, corporate scandals, the war in Iraq, the uncertainty about energy prices, and the recent subprime mortgage crisis. In particular, during the last...

This paper shows that the latest generation of asset pricing models with long-run risk exhibits economically significant nonlinearities, and thus the ubiquitous Campbell--Shiller log-linearization can generate large numerical errors. These errors in turn translate to considerable errors in the...