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Syllabus for

Academic year
MVE095 - Options and mathematics  
 
Syllabus adopted 2014-02-13 by Head of Programme (or corresponding)
Owner: MPENM
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: Second-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English
Open for exchange students

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0106 Examination 7,5 c Grading: TH   7,5 c   02 Jun 2016 pm H   05 Apr 2016 pm EKL   17 Aug 2016 am SB  

In programs

TKIEK INDUSTRIAL ENGINEERING AND MANAGEMENT - Financial mathematics, Year 2 (compulsory)
TKTEM ENGINEERING MATHEMATICS, Year 2 (elective)
MPCAS COMPLEX ADAPTIVE SYSTEMS, MSC PROGR, Year 2 (elective)
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (elective)

Examiner:

Docent  Simone Calogero



  Go to Course Homepage

Eligibility:


In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

Course specific prerequisites

Standard courses in Real Analysis (including several variables), Linear Algebra, and Probability (or Statistics). No previos knowledge in Lebeque Integration or Stocastic Calculus is required.

Aim

The purpose is to present arbitrage theory and its applications to pricing problems of financial derivatives in the binomial model. In the limit the Black-Scholes differential equation and option prices are obtained.

Learning outcomes (after completion of the course the student should be able to)

see aim above

Content

The Dominance Principle. Gaussian Processes and Brownian Motion. The Central Limit Theorem. The Binomial Model and Black-Scholes Model. Self-Financing Portfolios. The Black-Scholes Differential Equation. Calls and Puts. Path-Dependent Options. Dividends. Currency Derivatives. Elementary portfolio theory.

Organisation

The course comprises approximately 50 lecture hours.

Literature

Borell, C.: Introduction to the Black-Scholes Model, compendium (freely available online at www.math.chalmer.se/~borell)

Steven E. Shreve: Stochastic Calculus for Finance I: The Binomial Asset Pricing Model. Springer

Examination

Assignments. Written examination.


Page manager Published: Mon 28 Nov 2016.