Practitioners and researchers who have handled financial market data know that asset returns do not behave according to the bell-shaped curve associated with the Gaussian or normal distribution. Indeed, the use of Gaussian models when the asset return distributions are not normal could lead to a wrong choice of portfolio, the underestimation of extreme losses, or mispriced derivative products. Consequently, non-Gaussian models and models based on processes with jumps are gaining popularity among financial market practitioners. Non-Gaussian distributions are the key theme of this book, which addresses the causes and consequences of non-normality and time dependency in both asset returns and option prices. One of the main aims is to bridge the gap between the theoretical developments and the practical implementations of what many users and researchers perceive as sophisticated models.