Syllabus academic year 2009/2010
(Created 2009-08-11.)

Higher education credits: 9. Grading scale: TH. Level: A (Second level). Language of instruction: The course will be given in English on demand. FMS170 overlap following cours/es: MAS232, MAS232, MASM19, MAS232, MASM19, MAS232 och MASM19. Optional for: F4, F4sfm, I4fi, L4fa, Pi4, Pi4fm. Course coordinator: Director of studies, Anna Lindgren,, Matematisk statistik. Recommended prerequisits: A course in stochastic processes, e.g., Stationary stochastic processes or Markov processes. Additional probability theory corresponding to FMSF05 helps. The course might be cancelled if the numer of applicants is less than 16. Assessment: Written exam, laboratory work, and home assignments. The course grade is based on the exam grade. Further information: The course is also given at the faculty of science with the code MASM19. 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 three 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 alternative models formulated in continuous time. The models we focus on are formulated as stochastic differential equations (SDE:s). Most of the second part is devoted to the probability theory required to understand the SDE models. This includes, e.g., Brownian motion, stochastic integrals and Itô's formula.

Finally, in the third part we study various applications of the theory from part two. Here we come back to option theory and derive, e.g., the Black-Scholes formula. After that we will study the bond market and interest rate derivatives.

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