From the reviews:
This book brings together recent advances in the theory of implied volatility and refined semiparametric estimation strategies and dimension reduction methods for functional surfaces. The theory of implied and local volatility is presented. The smile-consistent modeling approaches are discussed in detail. ... This book is for readers with a preknowledge of stochastic processes and interest in financial derivatives, as for example plain vanilla or exotic options. (Klaus Ehemann, Zentralblatt MATH, Vol. 1084, 2006)
The parameter that measures volatility has long caused many problems in financial modeling. ... Fengler has written a research monograph. ... Concepts are presented in detail, elegantly connecting the past and current research, mathematical presentation, and numerical output (graphics). ... The appendices serve primarily for presentation of proofs and some results from stochastic calculus. This book is suitable for researchers, graduate students, and finance professionals. (Ita Cirovic Donev, MathDL, March, 2006)
This short book addresses one of the most ... fundamental questions in financial mathematics and derivatives trading, namely, volatility modeling and management. ... the author does a good job in presenting the local volatility models, their implementation, and the problem in using this approach for hedging. ... It is an admirable attempt at the daunting task of modeling the dynamics of the IVS. (Andrew Carter and Jean-Pierre Fouque, SIAM Review, Vol. 49 (1), 2007)
