Entry requirements

120 credit points including Financial Mathematics II, Measure Theory and Stochastic Integration, Partial Differential Equations with Applications to Finance

Learning outcomes

In order to pass the course (grade 3) the student should be able to

• construct models for pricing advanced financial derivatives;
• price complex financial derivatives with risk neutral valuation using methods from the theory of parabolic partial differential equations;
• present advanced financial models and pricing to various users of financial instruments;
• use measure theory, e.g. Girsanov's theorem and martingale theory for financial modelling;
• use Levy processes for financial modelling;
• use free boundary problems, integro-differential equations and non-linear parabolic differential equations for financial modelling.

Content

Applications of measure theory and Girsanov’s theorem. Optimal stopping time problems and free boundary problems with applications to options of American type. Levy processes and parabolic integro-differential equations with applications to modelling with jump processes. Hedging and super-hedging. Exotic financial derivatives.

Instruction

Lectures and problem solving sessions.

Assessment

Written examination at the end of the course. Moreover, assignments during the course.