Gäller från och med: Autumn 2020
Beslutad av: Professor Thomas Johansson
Datum för fastställande: 2020-05-19
Avdelning: Mathematical Statistics
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskod: FMSN25
Undervisningsspråk: English
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.
Kunskap och förståelse
För godkänd kurs skall doktoranden
Färdighet och förmåga
För godkänd kurs skall doktoranden
Värderingsförmåga och förhållningssätt
För godkänd kurs skall doktoranden
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.
Undervisningsformer: Föreläsningar, laborationer, övningar
Examinationsformer: Skriftlig tentamen, inlämningsuppgifter
Betygsskala: Underkänd, godkänd
Examinator:
Förkunskapskrav: FMSF10 Stationary Stochastic Processes or FMSF15 Markov Processes. Knowledge corresponding to FMSF05 Probability Theory helps.
Kursansvarig: Magnus Wiktorsson <magnus.wiktorsson@matstat.lu.se>
Hemsida: www.maths.lth.se/matstat/kurser/fmsn25/