Course syllabus adopted 2019-02-22 by Head of Programme (or corresponding).
Overview
- Swedish nameOptioner och matematik
- CodeMVE095
- Credits7.5 Credits
- OwnerMPENM
- Education cycleSecond-cycle
- Main field of studyMathematics
- DepartmentMATHEMATICAL SCIENCES
- GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Course round 1
- Teaching language English
- Application code 20148
- Open for exchange studentsYes
Credit distribution
Module | Sp1 | Sp2 | Sp3 | Sp4 | Summer | Not Sp | Examination dates |
|---|---|---|---|---|---|---|---|
| 0106 Examination 7.5 c Grading: TH | 7.5 c |
|
In programmes
- MPCAS - COMPLEX ADAPTIVE SYSTEMS, MSC PROGR, Year 1 (compulsory elective)
- MPCAS - COMPLEX ADAPTIVE SYSTEMS, MSC PROGR, Year 2 (elective)
- MPENM - ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory elective)
- MPENM - ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 2 (elective)
- TKIEK - INDUSTRIAL ENGINEERING AND MANAGEMENT - Financial mathematics, Year 2 (compulsory)
- TKITE - SOFTWARE ENGINEERING, Year 3 (elective)
- TKTEM - ENGINEERING MATHEMATICS, Year 3 (elective)
Examiner
Simone Calogero- Professor, Analysis and Probability Theory, Mathematical Sciences
Eligibility
General entry requirements for Master's level (second cycle)Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Specific entry requirements
English 6 (or by other approved means with the equivalent proficiency level)Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Course specific prerequisites
One variable calculus, linear algebra, probability theory/statistics.
Aim
The course deals with the options pricing theory within the binomial model and the Black-Scholes model.
Learning outcomes (after completion of the course the student should be able to)
(a) Describe financial derivatives of European, American and Asian type
(b) Explain the concept of arbitrage
(c) Describe algorithms for pricing and hedging financial derivatives in the binomial model
(d) Compute numerically the price of American puts in the binomial model
(e) Derive the Black-Scholes model as limit of the binomial model
(f) Compute the Black-Scholes price of call and put options
(g) Price call and put options when the underlying stock pays a dividend
(h) Treat currency options in the Black Scholes model
(i) Treat options on the maximum and minimum of the price of two stocks in the Black-Scholes model
(f) Treat elementary Portfolio theory
Content
The Dominance Principle. Binomial model. Self-Financing Portfolios. Probability theory and Brownian Motion. Black-Scholes Model. Black-Scholes formula. Call and Put options. Exotic Options. Dividends. Currency Derivatives. Elementary portfolio theory.
Organisation
The course comprises approximately 50 lecture hours.
Literature
Calogero, S.: Introduction to options pricing theory, compendium (freely available online at the course homepage)
Borell, C.: Introduction to the Black-Scholes Model, compendium (freely available online at the course homepage)
Examination including compulsory elements
Assignments. Written examination.
The course syllabus contains changes
- Changes to examination:
- 2021-04-14: Exam date Exam date changed by Elisabeth Eriksson
[33228, 53867, 3], New exam for academic_year 2020/2021, ordinal 3 (not discontinued course) - 2021-01-27: Exam date Exam date changed by E Eriksson
[33228, 53867, 2], New exam for academic_year 2020/2021, ordinal 2 (not discontinued course) - 2020-09-30: Grade raising No longer grade raising by GRULG
- 2021-04-14: Exam date Exam date changed by Elisabeth Eriksson