Stochastic volatility is the main concept used in the fields of financial economics and mathematical finance to deal with time-varying volatility in financial markets. This book brings together some of the main papers that have influenced this exciting new field, and shows that the development of this subject has been highly multidisciplinary, and has helped to produce methods and models for the realistic pricing of options, efficient asset allocation, and accurate risk assessment. A lengthy introduction by the editor, a leader in the field, connects the papers with the literature.