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Syllabus for

Academic year
MVE095 - Options and mathematics  
Optioner och matematik
 
Syllabus adopted 2021-02-12 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
Main field of study: Mathematics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English
Application code: 20132
Open for exchange students: Yes

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0106 Examination 7,5 c Grading: TH   7,5 c   13 Jan 2022 am J,  13 Apr 2022 am J   23 Aug 2022 am J  

In programs

MPDSC DATA SCIENCE AND AI, MSC PROGR, Year 1 (compulsory elective)
MPDSC DATA SCIENCE AND AI, MSC PROGR, Year 2 (elective)
TKITE SOFTWARE ENGINEERING, Year 3 (elective)
TKIEK INDUSTRIAL ENGINEERING AND MANAGEMENT - Financial mathematics, Year 2 (compulsory)
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 2 (elective)
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory elective)
MPCAS COMPLEX ADAPTIVE SYSTEMS, MSC PROGR, Year 1 (compulsory elective)
MPCAS COMPLEX ADAPTIVE SYSTEMS, MSC PROGR, Year 2 (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 and European options in the binomial model

(e) Derive the Black-Scholes model as limit of the binomial model

(f) Compute the Black-Scholes price of European options

(g) Use the Monte Carlo method to compute the Black-Scholes price of Asian options

(h) Compute the Black-Scholes price of European options when the underlying stock pays a dividend

(i) Derive the value of coupon bonds in the Vasicek interest rate model 


Content

The Arbitrage-free Principle. Binomial model. Self-Financing Portfolios. Probability theory and Brownian Motion. Black-Scholes Model. Black-Scholes formula. Call and Put options. Exotic Options. Monte Carlo method. Dividends. Coupon bonds. Yield curve  

Organisation

The course comprises approximately 50 lecture hours.

Literature

Calogero, S.: A first course in options pricing theory, compendium (freely available online at the course homepage)



Examination including compulsory elements

Assignments. Written examination.



The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.


Page manager Published: Mon 28 Nov 2016.