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Graduate courses

Departments' graduate courses for PhD-students.

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Syllabus for

Academic year
TMA285 - Financial derivatives and partial differential equations  
Finansiella derivat och partiella differentialekvationer
 
Syllabus adopted 2016-02-15 by Head of Programme (or corresponding)
Owner: MPENM
7,5 Credits
Grading: TH - Five, Four, Three, Fail
Education cycle: Second-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English
Open for exchange students: Yes

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0101 Examination 7,5 c Grading: TH   7,5 c   19 Mar 2019 am SB   11 Jun 2019 am M   30 Aug 2019 pm SB  

In programs

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)

Examiner:

Simone Calogero


  Go to Course Homepage

Eligibility:


In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

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 martingale methods to option pricing


- explain risk-neutral pricing and market completeness

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

- calibrate simple interest rate models

- compute numerically the price of European and American options


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 and finite element methods.

Organisation

Three lectures every week plus one problem session.

Literature

Calogero, S.: Introduction to stochastic calculus and financial derivatives, compendium (free available on the course homepage)

Shreve, S.: Stochastic Calculus for Finance II

Examination including compulsory elements

Written exam, and hand-ins for extra credit.


Page manager Published: Thu 04 Feb 2021.