Course syllabus adopted 2023-02-14 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
Module | Sp1 | Sp2 | Sp3 | Sp4 | Summer | Not Sp | Examination dates |
|---|---|---|---|---|---|---|---|
| 0101 Examination 7.5 c Grading: TH | 7.5 c |
In programmes
- MPCAS - COMPLEX ADAPTIVE SYSTEMS, MSC PROGR, Year 1 (compulsory elective)
- MPENM - ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory elective)
Examiner
Moritz Schauer- Senior Lecturer, Applied Mathematics and Statistics, Mathematical Sciences
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 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 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
Lectures and problem sessions.
Literature
Calogero, S.: Stochastic calculus, financial derivativesand PDEs. Compendium (free available on the course homepage)
Shreve, S.: Stochastic Calculus for Finance II
Examination including compulsory elements
Examination includes assignments and a written exam. Some of the assignments require knowledge of Python or Matlab.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.