Uncertain volatility models -- theory and application
The book is devoted to the study of uncertain volatility models that evaluate option portfolios under worst- and best-case scenarios when the volatility coefficient of the pricing model can not be determined exactly, and the user defines only subjective volatility constraints: within those constraints, extremal prices are computed. Two types of constraints are studied in this book: (1) volatility bands with upper and lower bounds; (2) shock scenarios with short periods of extreme volatility, but unknown timing. The author's approach is based on the uncertain volatility model developed by \textit{M. Avellaneda} and \textit{A. Parás} [Appl. Math. Finance 3, 21-52 (1996; Zbl 1097.91514)]. Uncertain volatility models are nonlinear, and this book explores algorithmic issues that arise due to linearity. The author travels in this book the entire road from innovative mathematical finance to a working software system, which he calls Mtg (for ``Martingale''). The theory, numerical methods, combinatorial algorithms, software architecture and user interface are discussed. The software, contained on the accompanying CD for most Windows platforms, can be used through a command-line interface, as C++ library, through Mathematica, and over the Web. The software on the accompanying CD consists of 81500 lines of C++ code and 11500 lines of Java code. The book contains 13 Chapters and three sections with The Network Application MtgClt/MtgSvr, The Scripting Language MtgScript and Mathematica Extensions. Practicioners and students who need to build analytic software libraries may benefit from reading this book and studying the software. This book is also for graduate students and researchers who wish to study advanced aspects of volatility risk in portfolios of vanilla and exotic options.
scientific article; zbMATH DE number 1761221