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Syllabus for

Academic year
TMA285 - Financial derivatives and stochastic analysis  
 
Syllabus adopted 2014-02-17 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
0101 Examination 7,5c Grading: TH   7,5c   12 Jan 2016 pm H,  08 Apr 2016 am EKL   16 Aug 2016 am SB  

In programs

TKIEK INDUSTRIAL ENGINEERING AND MANAGEMENT - Financial mathematics, Year 3 (elective)
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 2 (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

The course "Options and mathematics" is recommended.

Aim

To treat financial derivates by means of stochastic differential and integral calculus.

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

to understand both applied and theoretical aspects of financial derivative pricing theory.

Content

Some of the concepts that will be discussed in the course are Measure theory, probability theory; Brownian motion an Stochastic Integration. Ito's, and Feynman-Kac's formulas. The connection between Brownian motion and PDEs. Stochastic differential equations. Self financed portfolio strategies and arbitrage. Black-Scholes' model, and stability analysis of that model. Wiener measures and Cameron-Martin's Theorem. Martingale representation. Complete capital markets. Financial derivative depending on multiple stocks. Currency depending options. Exotic options. Bonds- and interest models. Option price in Gaussian interest models. The course has 56 hours of lecturing or teaching.

Organisation

Three lectures every week plus one problem session.

Literature

Steven Shreve's Stochastic Calculus for Finance II.

Examination

Written exam, and hand-ins for extra credit.


Page manager Published: Mon 28 Nov 2016.