MAT4740 – Malliavin Calculus and Applications to Finance

Schedule, syllabus and examination date

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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

Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.

Prerequisites

Recommended previous knowledge

Overlapping courses

10 credits overlap with MAT9740 – Malliavin Calculus and Applications to Finance

*The information about overlaps for discontinued courses may not be complete. If you have questions, please contact the Department. 

Teaching

4 hours lectures/exercises per week.

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 oral or written examination. 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.

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.

Explanations and appeals

Resit an examination

Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.

Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

Evaluation

The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

Facts about this course

Credits

10

Level

Master

Teaching

Taught according to demand and resources. Contact studieinfo@math.uio.no if you are interested in this course.

Examination

The same semester as taught.

Teaching language

English

The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.