Asset price processes with jumps have been advocated as a tool to overcome some of the empirical deficiencies of models based on Brownian motion such as the Black Scholes model.

This lecture gives an introduction to the theory of stochastic processes with jumps with a view towards applications in finance. We will cover basic jump processes, Levy processes and their mathematical construction and elements of stochastic calculus for jump processes. Armed with these results we will study the pricing and the hedging of derivatives in financial models with jumps using probabilistic methods and partial integro-differential equations.

Full attendance is compulsory. This means that students should attend at least 80% of all lectures, at most one lecture can be missed.

The first part of the course (approx 6 units) consist of lectures of the instructor. This is followed by student presentations where various applications of jump processes in financial mathematics are discussed.

Presentation during the course 30%, final exam 60%, active class participationm 10%.

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Lectures Continuous Time Finance I and II from the MSc Qfin or equivalent. In case of doubt please contact the instructor.

ruediger.frey@wu.ac.at