This thesis examines the Leverage Effect in stocks, stock indices and stock options. The Leverage Effect refers to the observed negative correlation between an asset’s return and its volatility. Part I presents an examination of the Leverage Effect at the stock level. The research provides the first investigation of stock returns, volatility and trading volumes from an information theoretic perspective. It finds support for trading volumes as an explanation for the stock level Leverage Effect and shows that index returns are also an important factor. It also analyses how trading behaviour is influenced by an investor’s risk preference and how this relates to return-volume correlation. Predictions of an analytical model of trading behaviour are verified empirically using a range of stocks and institutional trades in S&P500 stocks. Part II examines the Leverage Effect at the index level. The research supports previous findings that the Leverage Effect is far larger at the index level and decays more quickly. Again using an information theoretic analysis, it shows that it is driven by a combination of trading volumes and an asymmetric relationship between index returns and stock return correlations. Part III examines the time variation of the Leverage Effect at the stock and index levels. It shows that they are both time dependent and discusses the relationship between the stock and index levels. It also documents changes in market behaviour since the 2008 financial crisis. Part IV examines the Leverage Effect in stock options by developing a descriptive statistical model of implied volatility using multivariate q-Gaussian distributions. This is the first research to show that implied volatility can be modelled using q-Gaussian distributions and provides a tool for trading and risk management. It also shows how the multivariate q-Gaussian distribution could be used to generate virtual data for scenario testing and option pricing using a simple Markov Chain or Auto-regressive process. Finally PartV presents the conclusions of the thesis and avenues for future research.