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The implied volatility surface is a key financial variable for the pricing and the risk management of plain vanilla and exotic options portfolios alike. This book fills a gap in the financial literature by bringing together both recent advances in the theory of implied volatility and refined semiparametric estimation strategies and dimension reduction methods for functional surfaces: Part One of the book is devoted to smile-consistent pricing approaches. The theory of implied and local volatility is presented concisely, and vital smile-consistent modeling approaches such as implied trees, mixture diffusion, or stochastic implied volatility models are discussed in detail. The Part Two familiarizes the reader with estimation techniques that meet the challenges in implied volatility modeling, such as the rich functional structure of observed implied volatility surfaces and the necessity for dimension reduction: non- and semiparametric smoothing techniques.
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