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Syllabus for

Academic year
MVE095 - Options and mathematics
Optioner och matematik
 
Syllabus adopted 2019-02-22 by Head of Programme (or corresponding)
Owner: MPENM
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: Second-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English
Application code: 20148
Open for exchange students: Yes

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0106 Examination 7,5c Grading: TH   7,5c   09 Jan 2021 am J

In programs

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 2 (elective)
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory 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

  Go to Course Homepage


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.


Published: Mon 28 Nov 2016.