MAT4740 – Malliavin Calculus and Applications to Finance
Course description
Schedule, syllabus and examination date
Course content
The course provides an introduction to Malliavin calculus for Lévy processes. The Malliavin derivative and Skorohod integral will be introduced for the Brownian motion and the pure jump Lévy processes, using the chaos expansion approach. The basic calculus rules will be introduced and the relationship with the Ito integral will be detailed. Several applications will be presented. These include the use of the Clark-Ocone formula for an explicit martingale representation and for hedging in finance, the use of the chain rule to study the parameter sensitivity of stochastic differential equations and its application to risk management.
Learning outcome
After completing the course you will:
- be familiar with Lévy processes and Lévy-Ito decomposition, Gaussian and Poisson random measures;
- know about integral representations, iterated Ito integrals and chaos expansions;
- know about the operators Malliavin derivative and Skorohod integral and the associated calculus rules;
- understand the relationship among the Malliavin calculus, the Ito calculus, and other stochastic integrals e.g. forward integral;
- use the methods of Malliavin calculus in financial applications: hedging and sensitivity analysis;
- understand how the methods can be used in the study of properties of stochastic differential equations.
Admission to the course
Students admitted at UiO must apply for courses in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.
Nordic citizens and applicants residing in the Nordic countries may apply to take this course as a single course student.
If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.
Recommended previous knowledge
emne: MAT4720 (emne: MAT4701)
Overlapping courses
- 10 credits overlap with MAT9740 – Malliavin Calculus and Applications to Finance.
Teaching
4 hours lectures/exercises per week.
The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.
Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.
Examination
No mandatory assignments.
Final written exam or final oral exam, which counts 100 % towards the final grade. The form of examination will be announced by the teaching staff by 15 October/15 March for the autumn semester and the spring semester respectively.
It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses: MAT9740 – Malliavin Calculus and Applications to Finance
Examination support material
No examination support material is allowed.
Language of examination
Subjects taught in English will only offer the exam paper in English. You may write your examination paper in Norwegian, Swedish, Danish or English.
Grading scale
Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.
Resit an examination
This course offers both postponed and resit of examination. Read more:
More about examinations at UiO
- Use of sources and citations
- Special exam arrangements due to individual needs
- Withdrawal from an exam
- Illness at exams / postponed exams
- Explanation of grades and appeals
- Resitting an exam
- Cheating/attempted cheating
You will find further guides and resources at the web page on examinations at UiO.