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Option valuation under stochastic volatility II. With Mathematica code. (English) Zbl 1391.91001
Newport Beach, CA: Finance Press (ISBN 978-0-9676372-1-1/pbk). viii, 737 p. (2016).
The monograph continues previous work of the author in Volume I [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 Through a collection of published and unpublished results, it emphasizes the mathematical and computational aspects of finance for an audience in academia and industry.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.

MSC:
91-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to game theory, economics, and finance
91G20 Derivative securities (option pricing, hedging, etc.)
91G60 Numerical methods (including Monte Carlo methods)
91-04 Software, source code, etc. for problems pertaining to game theory, economics, and finance
60H30 Applications of stochastic analysis (to PDEs, etc.)
60J75 Jump processes (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
Software:
Mathematica; NDSolve
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