MAT9740 – 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.

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

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.

Prerequisites

Recommended previous knowledge

Overlapping courses

10 credits overlap with MAT4740 – Malliavin Calculus and Applications to Finance

*Please note that information regarding overlapping courses is not complete. For more information, please contact The Department of Mathematics.

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

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.

In addition, 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.

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.

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

PhD

Teaching

Spring 2018

Spring 2014

Spring 2013

Spring 2010

Spring 2008

Spring. Taught according to demand and resources. If you want to attend the course, please send an e-mail to studieinfo@math.uio.no.

Examination

Spring 2018

Spring 2014

Spring 2013

Spring 2010

Spring 2008

Spring. According to demand and resources.

Teaching language

English

The course is given in English. If no students have asked for the course in English within the first lecture, it may be given in Norwegian.