| This dissertation includes 3 papers in empirical finance. In chapter 1, since theory suggests a relationship between both volatility of volatility, variance risk premium, and the equity risk premium; we empirically investigate the relationship between volatility of volatility and the equity risk premium, and the relationship between the variance risk premium and the equity risk premium; we find that volatility of volatility alone explains 5 to 10% of the total variation of equity risk premium, and together with VIX data, it explains more than 20% of the total variation of equity premium; and we fail to find a significant relationship between volatility of volatility and the variance risk premium; we also use six measures of volatility of volatility based on non-parametric models, a GARCH model and VVIX data.;In chapter 2, we proposes a new way to measure the variance risk premium by applying a fractional cointegration relationship between implied variance and realized variance. To find the fractional cointegration coefficient between implied variance and realized variance, we develop a search method based on minimization of the score test statistic proposed by Robinson(1994). We use daily, weekly and monthly data of five stock market indexes (S&P500, S&P100, DJIA, NASDAQ100 and Russell2000) and their volatility indexes from the CBOE. We find our new measure improves the return prediction power of the variance risk premium both in-sample statically and out-of-sample dynamically, and the result is robust for the monthly data among all five indexes.;In chapter 3, by using submortgage data, we found that investors are being charged with a significant risk premium over owner occupants; besides that, they are also facing a more restricted loan; with the market getting hotter, this risk premium and restrictions are getting even worse. Being treated like that, our findings show that investors were actually not more risky than owner occupants in terms of both prepayment and default. We suspect the reason for this puzzle is that when the market getting hotter, there are more speculative investors who commit occupancy fraud to get a more favorable loan. And these speculative investors were actually recorded as owner occupants on loan documents, which increased our estimation of the hazard of owner occupants group. And our information asymmetry test actually reaffirmed our suspect. Therefore, this paper, for the first time, give statistical evidence on occupancy fraud, and we also proposed a statistical scanning way to reduce to potential occupancy fraud. |
