Recent spikes in oil prices have thrown light on how stock market may be impacted by oil price shocks. The task in this book is to try to find approaches which can explain the main basic characteristics of stock market returns and/or CO prices thereby appropriately analyze the relationship between them. This book conducts three empirical analyzes of the oil-stock relationship for five developed countries using distinct novel approaches. In the first chapter, we test for the existence of this underlying relationship based on a new wavelet approach. The second chapter assesses the impact of nonlinear oil price increases to the stock market returns in presence of structural changes using an MS-EGARCH model. In the final chapter, we combine the wavelet with a trivariate BEKK-MSG model to examine whether there exists a transmission of shocks and/or volatility from real CO changes to real stock market returns.