Course syllabus for Financial derivatives and stochastic analysis

Course syllabus adopted 2026-02-26 by Head of Programme (or corresponding).

Overview

  • Swedish nameFinansiella derivat och stokastisk analys
  • CodeTMA285
  • Credits7.5 Credits
  • OwnerMPENM
  • 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 20154
  • Open for exchange studentsYes

Credit distribution

0101 Examination 7.5 c
Grading: TH		 7.5 c

In programmes

Examiner

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

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

Course specific prerequisites

General entry requirements and an equivalent of the course MVE095 Options and Mathematics or in all 90 higher education credits in Mathematics and Mathematical statistics.

Aim

The course deals with financial derivatives using stochastic calculus and partial differential equations.

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

On successful completion of the course the student will be able to:
  • master applications of the Ito‐Doeblin and Feynman‐Kac formulas to option pricing,
  • account for risk‐neutral pricing,
  • derive the Black‐Scholes differential equation for the price of a simple European derivative when there are several underlying stocks,
  • price European barrier options in the Black‐Scholes model,
  • use domestic and foreign risk neutral measures to price derivatives on currencies

Content

  • Probability and measure theory,
  • Brownian motion and stochastic calculus,
  • The Ito‐Doeblin and Feynman‐Kac formulas,
  • Girsanovʹs theorem,
  • Risk‐neutral pricing,
  • Self‐financing portfolio strategies and arbitrage,
  • Martingale representation and complete markets,
  • The Black‐Scholes model,
  • Puts and calls,
  • Several underlying assets,
  • Path‐dependent options,
  • Forward and futures contracts,
  • Barrier options,
  • Up-and-out call,
  • Change of numeraire,
  • Foreign and domestic risk-neutral measures,
  • Forward measures.

Organisation

Lectures and problem sessions.

Literature

Shreve, S.: Stochastic Calculus for Finance II

Calogero, S.: Stochastic calculus, financial derivatives and PDE’s. Compendium (freely available on the course homepage)

Examination including compulsory elements

The assessment consists of a written exam at the end of the course. During the course, there may be optional assignments that give bonus points on the exam. Examples of such assignments are small written tests, labs, and oral or written presentations. Information about this is found on the course home page.

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 about disability study support.