This book is a sequel to the author's well-received "Option Valuation under Stochastic Volatility". It extends that work to jump-diffusions and many related topics in quantitative finance. Topics include spectral theory for jump-diffusions, boundary behavior for short-term interest rate models, modelling VIX options, inference theory, discrete dividends, and more. It provides approximately 750 pages of original research in 26 chapters, with 165 illustrations, Mathematica, and some C/C++ codes. The first 12 chapters (550 pages) are completely new. Also included are reprints of selected previous publications of the author for convenient reference. The book should interest both researchers and quantitatively-oriented investors and traders.
First 12 chapters: Slow Reflection, Jump-Returns, & Short-term Interest Rates | Spectral Theory for Jump-diffusions | Joint Time Series Modelling of SPX and VIX | Modelling VIX Options (and Futures) under Stochastic Volatility | Stochastic Volatility as a Hidden Markov Model | Continuous-time Inference: Mathematical Methods and Worked Examples | A Closer Look at the Square-root and 3/2-model | A Closer Look at the SABR Model | Back to Basics: An Update on the Discrete Dividend Problem | PDE Numerics without the Pain | Exact Solution to Double Barrier Problems under a Class of Processes | Advanced Smile Asymptotics: Geometry, Geodesics, and All That
"In this sequel to his already classic volume on option pricing with stochastic volatility, Alan Lewis treats a wide range of important topics, including VIX options, SABR, smile asymptotics, jumps, discrete dividends, and much more, with a treasure-trove of methodologies, from spectral theory to geometric asymptotics to PDE numerics. This rigorous, yet accessible, presentation will be of great interest to both academics and practitioners. Highly recommended”. ̶-Prof. Vadim Linetsky, Northwestern University
"The highly regarded first volume in this series used diffusion processes to model the underlying's price and its volatility. This highly anticipated second volume throws jumps into this heady mix. While the main impact on option prices will be felt on the short end, the payoff for the reader will definitely be long term." ̶-Peter Carr, Ph.D, Executive Director of NYU Courant Math Finance Program
"Alan Lewis’s long-awaited sequel to his earlier “Option Valuation under Stochastic Volatility” is destined to become another cult classic. The author’s unique and original insights into models and computation, many presented here for the first time, will delight and inspire the reader. I highly recommend this book to all serious students of quantitative finance, whether practitioner or academic." ̶-Jim Gatheral, author of “The Volatility Surface: A Practitioner's Guide”, and Presidential Professor at Baruch College, CUNY
