Syllabus for |
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MVE095 - Options and mathematics
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| Syllabus adopted 2014-02-13 by Head of Programme (or corresponding) |
| Owner: MPENM |
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7,5 Credits |
| Grading: TH - Five, Four, Three, Not passed |
| Education cycle: Second-cycle |
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Major subject: Mathematics
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Department: 11 - MATHEMATICAL SCIENCES
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Teaching language: English
Open for exchange students
| Course module |
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Credit distribution |
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Examination dates |
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Sp1 |
Sp2 |
Sp3 |
Sp4 |
Summer course |
No Sp |
| 0106 |
Examination |
7,5 c |
Grading: TH |
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7,5 c
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02 Jun 2016 pm H
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05 Apr 2016 pm EKL
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17 Aug 2016 am SB
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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.