This thesis consists of four empirical essays on historical volatility models, implied volatility and the efficiency of options markets. The first essay examines the 'asymmetric volatility' phenomenon in index returns from the perspective of the 'diversification effect'. Changes in the average realized correlation among the Dow Jones's constituents are found to drive changes in the index's realized volatility and to be negatively and asymmetrically correlated with index returns. In line with the 'diversification hypothesis', it is shown that accounting for correlation dynamics in a GARCH specification reduces the level of asymmetry in index returns, with conditional correlation changes absorbing part of the past returns' explanatory power over changes in the conditional variance, while the returns' sign remains highly significant. The second essay examines volatility asymmetry from the perspective of the 'down-market effect', and reports that individual stocks' volatilities respond asymmetrically to lagged market returns and that the respective degree of asymmetry is comparable to the one exhibited by the index. The third essay explores the possibility of an option-implied measure of the exchange rate's future variance having an impact on the validity of the Uncovered Interest Parity condition. The results suggest that accounting for the above Jensen's Inequality Term significantly increases the proportion of forward unbiasedness regressions that are in line with theoretical parity predictions. Finally, the fourth essay focuses on the efficiency of the emerging Greek options market in terms of options' returns that are commensurate with the underlying risk. Based on a set of commonly used market efficiency measures, the hypothesis that the developing Greek options market exhibits a degree of efficiency that is comparable to those of the developed US and UK markets cannot be rejected.