This ebook contains a set of slides that can be used to present lectures in a graduate course or in a research seminar in mathematical finance.

The ebook is divided in three chapter, each chapter is divided in three sections, each section contains a set of slides that can be used to present a lecture. The lectures are independent one from the others.

The lectures discuss the results of the research in mathematical finance of the authors during the years 2007-2012. The results presented are concerned with the study of stochastic volatility models (Heston, SABR models and their generalizations), and in particular with the option pricing and calibration problems relative to these models.These results have been published in papers appeared in academic journals. The papers are complemented with multimedia material and mathematical software available on the web.

The book is published under the Creative Commons Attribution 4.0 International (CC BY 4.0) License. This license allows readers to copy and redistribute the material in any medium or format, and to remix, transform, or build upon the material, including for commercial use, providing the original author is credited. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

Copyright on any open access book published by Science Publishing Group is retained by the author(s). Authors grant Science Publishing Group a license to publish the book and identify itself as the original publisher. Authors also grant any third party the right to use the book freely as long as its original authors, citation details and publisher are identified.

Lorella Fatone, Dipartimento di Matematica e Fisica, Università di Camerino, Camerino, Italy.
Francesca Mariani, Dipartimento di Scienze Economiche, Università di Verona, Verona, Italy.
Maria Cristina Recchioni, Dipartimento di Management, Università Politecnica delle Marche, Ancona, Italy.
Francesco Zirilli, Dipartimento di Matematica "G. Castelnuovo", Università di Roma "La Sapienza", Roma, Italy.