Option markets have become among the most heavily transacted financial markets in the world. Option pricing models are used to price the options transacted on these markets. These models have been described as amongst the most accurate in the social sciences. Despite this outstanding success, claims that the conventional option pricing models are failing are appearing with increasing frequency. These anomalies represent a serious problem for option markets because they imply that the conventional option pricing approaches are flawed.A flawed option pricing model represents a serious problem for the global financial system as a whole. Options are the mechanism in which financial participants may transfer risk between each other. Clearly, if the best conventional option pricing models are sub-optimal (i.e. mis-specified), this risk transfer is sub-optimal also. Powerful desktop computing and abundant, extremely accurate intra-day transactions data, has led many researchers to pursue modern statistical approaches for pricing options. In this book we use various such approaches and show that they lead to improved option pricing.