Three essays on investments and time series econometrics

Abstract

This dissertation includes three essays on investments and time series econometrics. This work gives new insight into the behavior of implied marginal tax rates, implied volatility, and option pricing models. The first essay examines the movement of implied marginal tax rates. A body of research points to the existence of implied marginal tax rates that can be extracted from security or derivative prices. We use the LIBOR-based interest rate swap curve and the MSI-based interest rate swap curve to examine changes in the implied tax rate. We document multiple statistically and economically significant structural breaks in the long-run implied marginal tax rate that are not exclusively located in the financial crisis (one as recent as October, 2010). These breaks represent persistent divergence from long run averages and indicate that mean reversion models may not accurately describe the stochastic processes of implied marginal tax rates. In the second essay, I develop an asymmetric time series model of the VIX. I show that the VIX and realized volatility display significant nonlinear effects which I approximate with a smooth-transition autoregressive model. I find that under certain regimes the VIX depends almost exclusively on previous realized volatility. Under other regimes, I find that the VIX depends on both its lags and previous realized volatility. Since the VIX has become a popular hedging instrument, this finding has important implications for risk managers who elect to use the VIX and its related investment vehicles. It also has implications for the use of implied volatility in value-at-risk forecasting. The third essay presents a new model for option pricing model selection. There is a significant performativity issue intrinsic in much of the option pricing literature. Once an option-pricing model (OPM) gains widespread acceptance, volatilities tend to move so that the OPM fits well with observed prices. This often leads to systematic mispricing based purely on model results. A number of systematic issues such as volatility smile are present in OPMs. To remedy this issue, I propose a new method for ranking OPMs based on one step ahead forecasts. This model transforms the data to build a distribution of the stochastic term present in OPM. This sample distribution is then tested for normality so that OPMs can be ranked in a Bayesian-like framework by their closeness to a normal distribution.