Option valuation under stochastic volatility II. With Mathematica code. The monograph continues previous work of the author in [Option valuation under stochastic volatility. With Mathematica code. Newport Beach, CA: Finance Press (2000; Zbl 0937.91060)]. Through a collection of published and unpublished results, it emphasizes the mathematical and computational aspects of finance for an audience in academia and industry. Volume I treated derivatives of securities with stochastic volatility particularly two dimensional diffusions. Volume II investigates several models for various options with jump diffusion. However, the material ranges from volatility smile to discrete dividends to statistical inference for time series. Examples are grounded in data such as US Short Term Treasury Interest Rate and the CBOE Volatility Index. While transform and spectral methods are common tools, they are supplemented by numerics in Mathematica and C/C++ code including a discussion of the NDSolve package.