Recommended prerequisite for participation in the module

The module builds on knowledge and skills obtained in the module Stochastic Analysis. Experience with programming in R is expected. Previous knowledge of models in financial mathematics is helpful but not necessary.

Content, progress and pedagogy of the module

Students who have completed the module will gain knowledge of the theoretical background for stochastic integration as well as its application to finance.

Learning objectives

Knowledge

• Know about stochastic integration with respect to continuous semimartingales
• Know about the quadratic variation of stochastic integrals
• Know about Itô’s formula
• Know about change of measures via Girsanov’s Theorem with special emphasis on its use in arbitrage theory
• Know about Stochastic Differential Equations (SDE’s) and its relevance in the modelling of asset prices
• Know how to solve SDE’s numerically

Skills

• Are able to apply basic computation rules and calculi associated to stochastic integrals
• Are able to apply Itô’s formula
• Are able to conduct a change of measure via Girsanov’s Theorem
• Can apply basic methods of stochastic calculus to the modelling of financial markets
• Are able to solve SDE’s theoretically and numerically

Competences

• Are able to read, understand, criticize and make use of advanced literature on stochastic calculus
• Are able to connect, formulate, and analyze scientific problems with the basic theory of stochastic integration

Type of instruction

As described in §17 in the curriculum. 

Extent and expected workload

This is a 5 ECTS project module and the work load is expected to be 150 hours for the student.

Exam

Exams

Name of exam	Stochastic Calculus and Its Applications
Type of exam	Written or oral exam
ECTS	5
Assessment	Passed/Not Passed
Type of grading	Internal examination
Criteria of assessment	The criteria of assessment are stated in the Examination Policies and Procedures