Main Field of Study and progress level:
Mathematics: Second cycle, has only first-cycle course/s as entry requirements
Computational Science and Engineering: Second cycle, has only first-cycle course/s as entry requirements
Mathematical Statistics: Second cycle, has only first-cycle course/s as entry requirements
Grading scale: Pass with distinction, Pass with merit, Pass, Pass with distinction, Pass, Fail
Responsible department: Department of Mathematics and Mathematical Statistics
Established by: Faculty Board of Science and Technology, 2018-03-16
Contents
The course covers the basic mathematical theory for modeling and pricing of financial instruments in continuous time.The focus in the course is on modeling stocks and pricing of stock options in the Black Scholes model, built on geometric Brownian motion. The course also covers the theory of interests and pricing of different interest instruments.
Expected learning outcomes
For a passing grade, the student must be able to
Knowledge and understanding
define stochastic differential equations
explain the notions self-financing portfolio and arbitrage
thoroughly account for commonly occuring instruments for interest and models for short interests
Skills and abilities
independently apply the theory for price setting of financial derivatives in discrete and continuous time
critically apply the Black-Scholes equation for price setting of European buy- and sell options
apply the theory for price setting of barrier options
solve simpler partial and stochastic differential equations
derive and apply the put-call parity
calculate and interpret the sensitivities for european buy- and sell options
Required Knowledge
The course requires 90 ECTS including a course in Multivariable Calculus and Differential Equations and a basic course in Mathematical Statistics, minimum 6 ECTS. Proficiency in English equivalent to Swedish upper secondary course English 5/A. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish to the level required for basic eligibility for higher studies.
Form of instruction
The teaching takes the form of lectures.
Examination modes
The course is assessed through written examinations in the form of two tests. From the first test students can award bonus points that can be added to the result on the mandatory final test. The bonus points are only valid on the ordinary final exam and on the first re-exam connected to the course occasion on which the bonus points were awarded. For the whole course, one of the following grades is assigned: Fail (U), Pass (3), Pass with merit (4) or Pass with distinction (5). The grade is only set once all compulsory elements have been assessed.
A student who has been awarded a passing grade for the course cannot be reassessed for a higher grade. Students who do not pass a test or examination on the original date are given another date to retake the examination. A student who has sat two examinations for a course or a part of a course, without passing either examination, has the right to have another examiner appointed, provided there are no specific reasons for not doing so (Chapter 6, Section 22, HEO). The request for a new examiner is made to the Head of the Department of Mathematics and Mathematical Statistics. Examinations based on this course syllabus are guaranteed to be offered for two years after the date of the student's first registration for the course.
Credit transfer All students have the right to have their previous education or equivalent, and their working life experience evaluated for possible consideration in the corresponding education at Umeå university. Application forms should be adressed to Student services/Degree evaluation office. More information regarding credit transfer can be found on the student web pages of Umeå university, http://www.student.umu.se, and in the Higher Education Ordinance (chapter 6). If denied, the application can be appealed (as per the Higher Education Ordinance, chapter 12) to Överklagandenämnden för högskolan. This includes partially denied applications
Other regulations
In a degree, this course may not be included together with another course with a similar content. If unsure, students should ask the Director of Studies in Mathematics and Mathematical Statistics. The course can also be included in the subject area of computational science and engineering.
Björk Tomas Arbitrage theory in continuous time Fourth edition. : Oxford : Oxford University Press : 2019 : xxi, 561 sider : ISBN: 9780198851615 Mandatory Search the University Library catalogue
Björk Tomas Arbitrage theory in continuous time 3rd ed. : Oxford : Oxford University Press : 2009 : xx, 525 p. : ISBN: 978-0-19-957474-2 (hbk.) Mandatory Search the University Library catalogue
