Course syllabus for Options and mathematics

Course syllabus adopted 2023-02-08 by Head of Programme (or corresponding).

Overview

  • Swedish nameOptioner och matematik
  • CodeMVE690
  • Credits7.5 Credits
  • OwnerTKIEK
  • Education cycleSecond-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language English
  • Application code 51137
  • Block schedule
  • Open for exchange studentsYes
  • Only students with the course round in the programme overview.

Credit distribution

0123 Examination 7.5 c
Grading: TH		7.5 c
  • 30 Okt 2024 am J
  • 07 Jan 2025 am J
  • 27 Aug 2025 pm J

In programmes

Examiner

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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

Borell, C. Introduction to the Black-Scholes Theory

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.