"The concept of local volatility as well as the local volatility model are one of the classical topics of mathematical … volatility function; b) construction of parametric or non-parametric regression of the local volatility surface suitable for fast … calibration; c) no-arbitrage interpolation and extrapolation of the local and implied volatility surfaces; d) extension of the …

processes and polynomial semimartingales and by showing how efficient calibration of local stochastic volatility models is … volatility models to financial data. We show how this computationally challenging problem can be efficiently solved by applying …

This book presents a factor-based model of the stochastic evolution of the implied volatility surface. The model allows … volatility derivatives. In the first part, the book develops a unifying theory for the analysis of contingent claims under both … the real-world measure and the risk-neutral measure in an environment of stochastic implied volatility. On the basis of …