Syllabus academic year 2011/2012
(Created 2011-09-01.)
Credits: 7,5. Grading scale: TH. Cycle: A (Second Cycle). Main field: Technology. Language of instruction: The course will be given in English on demand. FMSN25 overlaps following cours/es: FMS170 and MASM19. Optional for: F5, F5fm, I4, I5fir, Pi5, Pi5fm. Course coordinator: Director of studies, Anna Lindgren,, Mathematical Statistics. Recommended prerequisits: A course in stochastic processes, e.g. Markov proceses or Stationary stochastic processes and an additional course in probability theory corresponding to FMSF05 or equivalent. The course might be cancelled if the number of applicants is less than 16. Assessment: Written exam, laboratory work, and home assignments. The course grade is based on the exam grade. Parts: 2. Further information: The course is also given at the faculty of science. Home page:

The student should get a thorough understanding and insight in the economical and mathematical considerations which underlie the valuation of derivatives on financial markets. The student should get knowledge about and ability to handle the models and mathematical tools that are used in financial mathematics. The student should also get a thorough overview concerning the most important types of financial contracts used on the stock- and the interest rate markets and moreover get a solid base for understanding contracts that have not been explicitely treated in the course.

Knowledge and understanding
For a passing grade the student must

Skills and abilities
For a passing grade the student must

Judgement and approach
For a passing grade the student must

The course consists of two related parts. In the first part we will look at option theory in discrete time. The purpose is to quickly introduce fundamental concepts of financial markets such as free of arbitrage and completeness as well as martingales and martingale measures. We will use tree structures to model time dynamics of stock prices and information flows.

In the second part we will study models formulated in continuous time. The models we focus on are formulated as stochastic differential equations (SDE:s). The theories behind Brownian motion, stochastic integrals, Ito-'s formula, measures changes and numeraires are presented and applied to option theory both for the stock and the interest rate markets. We derive e.g. the Black-Scholes formula and how to create a replicating portfolio for a derivative contract.

Björk, T.: Arbitrage Theory in Continuous Time, 2nd Ed., 2004.
Rasmus, S.: Derivative Pricing, Avd. Matematisk Statistik, 2006.


Code: 0111. Name: Written Examination.
Higher education credits: 6. Grading scale: TH. Assessment: Written examination.

Code: 0211. Name: Laboratory Work and Home Assignments.
Higher education credits: 1,5. Grading scale: UG. Assessment: Laboratory work and home assignments.