Financial models based on jump processes are increasingly used in risk management and option pricing, resolving some of the shortcomings of the Black Scholes model and pointing to new theoretical, empirical, and computational issues. Providing an accessible overview of this strand of research, this book includes a self-contained presentation of the necessary mathematical background and gives a unified presentation of theoretical, numerical, and empirical issues related to the use of jump processes in applications to statistical modelling of financial time series and option pricing. The book demystifies technical difficulties so that readers can better understand the applications of financial modelling.