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: 1. Slow Reflection, Jump-Returns, & Short-term Interest Rates 2. Spectral Theory for Jump-diffusions 3. Joint Time Series Modelling of SPX and VIX 4. Modelling VIX Options (and Futures) under Stochastic Volatility 5. Stochastic Volatility as a Hidden Markov Model 6. Continuous-time Inference: Mathematical Methods and Worked Examples 7. A Closer Look at the Square-root and 3/2-model 8. A Closer Look at the SABR Model 9. Back to Basics: An Update on the Discrete Dividend Problem 10. PDE Numerics without the Pain 11. Exact Solution to Double Barrier Problems under a Class of Processes 12. Advanced Smile Asymptotics: Geometry, Geodesics, and All That