Course syllabus for Financial derivatives and partial differential equations

The course syllabus contains changes
See changes

Course syllabus adopted 2021-02-12 by Head of Programme (or corresponding).

Overview

  • Swedish nameFinansiella derivat och partiella differentialekvationer
  • 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 20131
  • Open for exchange studentsYes

Credit distribution

0101 Examination 7.5 c
Grading: TH		 7.5 c
  • 14 Mar 2023 am J
  • 09 Jun 2023 pm J
  • 25 Aug 2023 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

General entry requirements and the equivalent of the course MVE095 Options and Mathematics or in all 90 higher education credits in Mathematics and Mathematical statistics. The equivalent of the course TMS165 Stochastic Calculus is also required.

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 stochastic calculus and partial differential equations to option pricing

- explain the concepts of risk-neutral pricing and market completeness

- derive the partial differential equation for the price of European derivatives when the underlying stock has stochastic volatility

- compute numerically the price of European and Asian options in markets with stochastic volatility

- compute  numerically the yield curve of coupon bonds implied one factor interest rate models



Content

Concepts from stochastic calculus reviewed in the course:

- Brownian motion, Ito's calculus, stochastic differential equations

- Change of measure, Girsanov theorem

Topics in financial derivatives pricing theory include:

- Self-financing portfolio strategies and arbitrage

- Black-Scholes model

- Stochastic volatility models and interest rate models

- Asian options

- Forwards and futures contracts

- Financial derivatives depending on multiple stocks

Connection with partial differential equations:

- Parabolic and hypoelliptic PDEs for option prices

- Initial and boundary value problems

- Numerical computation of option prices by finite difference methods.

Organisation

Three lectures every week plus one problem session.

Literature

Calogero, S.: Stochastic calculus, financial derivativesand PDE’s. Compendium (free available on the course homepage)

Shreve, S.: Stochastic Calculus for Finance II

Examination including compulsory elements

Exercises assignments, numerical project. Oral exam for extra credit

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.

The course syllabus contains changes

  • Changes to examination:
    • 2023-03-20: Exam date Exam date 2023-08-25 added by Elisabeth Eriksson
      [35925, 58170, 3], New exam for academic_year 2022/2023, ordinal 3 (not discontinued course)
    • 2023-01-10: Exam date Exam date 2023-06-09 added by Elisabeth Eriksson
      [35925, 58170, 2], New exam for academic_year 2022/2023, ordinal 2 (not discontinued course)