MAT9740 – 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.
In addition to the final exam, each PhD student is expected to give an oral presentation on a topic of relevance (chosen in cooperation with the lecturer). The presentation has to be approved by the lecturer for the student to be admitted to the final exam.
Admission to the course
PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.
If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.
PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.
Recommended previous knowledge
MAT4720 – Stochastic Analysis and Stochastic Differential Equations (MAT4701 – Stochastic analysis with applications (continued))
Overlapping courses
- 10 credits overlap with MAT4740 – 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
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.
In addition, each PhD candidate is expected to give an oral presentation on a topic of relevance chosen in cooperation with the lecturer. The presentation has to be approved by the lecturer for the student to be admitted to the final exam.
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: MAT4740 – 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 pass/fail scale. 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.