This book introduces Uncertain Volatility Models in mathematical finance. Uncertain Volatility Models evaluate option portfolios under worst- and best-case scenarios when the volatility coefficient of the pricing model cannot be determined exactly. The user defines subjective volatility constraints; within those constraints, extremal prices are computed. This book studies two types of constraints: volatility bands with upper and lower bounds, and shock scenarios with short periods of extreme volatility, but unkown timing.

Uncertain Volatility Models are nonlinear. Worst- and best-case scenarios applied to isolated option positions do not always lead to the same extremal volatility. When applied to an options portfolio, a diversification effect reduces the overall exposure to volatility fluctuations within the subjective constraints. This book explores algorithmic issues that arise due to nonlinearity.

Because Uncertain Volatility Models must be applied to option portfolios as a whole, they are difficult to implement on a computer if the portfolio contains barrier or American options. The accompanying CD contains a C++ implementation of Uncertain Volatility Models in source code. The software prices portfolios of vanilla, barrier and American options.

This book is for graduate students, researchers and practitioners who wish to study advanced aspects of volatility risk in portfolios of vanilla and exotic options.