Cover -- Title Page -- Copyright -- Contents -- Foreword -- Acknowledgments (Second Edition) -- Acknowledgments (First Edition) -- Introduction (Second Edition) -- Introduction (First Edition) -- Summary -- Contributions and Further Research -- Data and Programs -- Chapter 1 The Volatility Problem -- Introduction -- The Stock Market -- The Stock Price Process -- Historic Volatility -- The Derivatives Market -- The Black-Scholes Approach -- The Cox Ross Rubinstein Approach -- Jump Diffusion and Level-Dependent Volatility -- Jump Diffusion -- Level-Dependent Volatility -- Local Volatility -- The Dupire Approach -- The Derman Kani Approach -- Stability Issues -- Calibration Frequency -- Stochastic Volatility -- Stochastic Volatility Processes -- GARCH and Diffusion Limits -- The Pricing PDE under Stochastic Volatility -- The Market Price of Volatility Risk -- The Two-Factor PDE -- The Generalized Fourier Transform -- The Transform Technique -- Special Cases -- The Mixing Solution -- The Romano Touzi Approach -- A One-Factor Monte-Carlo Technique -- The Long-Term Asymptotic Case -- The Deterministic Case -- The Stochastic Case -- A Series Expansion on Volatility-of-Volatility -- Local Volatility Stochastic Volatility Models -- Stochastic Implied Volatility -- Joint SPX and VIX Dynamics -- Pure-Jump Models -- Variance Gamma -- Variance Gamma with Stochastic Arrival -- Variance Gamma with Gamma Arrival Rate -- Chapter 2 The Inference Problem -- Introduction -- Using Option Prices -- Conjugate Gradient (Fletcher-Reeves-Polak-Ribiere) Method -- Levenberg-Marquardt (LM) Method -- Direction Set (Powell) Method -- Numeric Tests -- The Distribution of the Errors -- Using Stock Prices -- The Likelihood Function -- Filtering -- The Simple and Extended Kalman Filters -- The Unscented Kalman Filter -- Kushner's Nonlinear Filter -- Parameter Learning.
