In modern derivatives trading, Black-Scholes theory is only a starting point. Asset volatilities are not constant, but change with market conditions. Large price moves are associated with periods of market turbulence and this leads to a smile shaped curve of the volatility implied from market prices. Smile Pricing Explained provides a clear and thorough explanation of the concepts of smile modelling that are at the forefront of modern derivatives pricing. The key models used in practice are covered, together with numerical techniques and calibration. Dr Austing guides the reader from the principle of no arbitrage and Black-Scholes, through local and stochastic volatility models, to arrive at a deep understanding of the state of the art of smile modelling. Along the way, practical introductions to the Monte Carlo and finite difference numerical approaches are provided, with user friendly guidance to the deep mathematics underlying the pricing theory. Smile Pricing Explained provides a much-needed guide to the concepts and complexities of smile modelling. Written in particularly accessible style, topics are presented succinctly, and unnecessary complexity is carefully avoided. Intuition is provided before mathematics so that readers may enjoy the book without necessarily following every technical detail. This book will prove a popular resource for both new and established quantitative practitioners as well as graduate students who wish to understand the realities of the area.