MSc with Thesis in Financial Mathematics
- Compulsory Courses
Credit: 0(0-0); ECTS: 50.0The Program of research leading to M.S. degree arranged between the student and a faculty member. Students register to this course in all semesters while the research program or write up of thesis is in progress. Student must start registering to this course no later than the second semester of his/her M.S. study.
Credit: 3(3-0); ECTS: 8.0Introduction to Derivative and Financial Markets. The Structure of Options Markets. Principles of Option Pricing. Option Pricing Models. Basic Option Strategies. Advanced Option Strategies. The Structure of Forward and Futures Markets. Principles of Spot Pricing. Principles of Forward and Futures Pricing. Futures Hedging Strategies. Advanced Futures Strategies. Options on Futures. Foreign Currency Derivatives. Swaps and Other Interest Rate Agreements.
Credit: 3(3-0); ECTS: 8.0The objective of this course is an introduction to the probabilistic techniques required for understanding the most widely used financial models. In the last few decades, financial quantitative analysts have used sophisticated mathematical concepts in order to describe the behavior of markets and derive computing methods. The course presents the martingales, the Brownian motion, the rules of stochastic calculus and the stochastic differential equations with their applications to finance. Outline of Topics: Discrete time models, Martingales and arbitrage opportunities, complete markets, European options, option pricing, stopping times, the Snell envelope, American options. Continuous time models: Brownian motion, stochastic integral with respect to the Brownian motion, the Itô Calculus, stochastic differential equations, change of probability, representation of martingales; pricing and hedging in the Black-Scholes model, American options in the Black-Scholes model; option pricing and partial differential equations; interest rate models; asset models with jumps.
Credit: 3(3-0); ECTS: 8.0The focus of this course is on asset pricing. The topics that will be discussed can be summarized as follows: Individual investment decisions under uncertainty are analyzed and the optimal portfolio theory is discussed using both static and dynamic approach. Then the theory of capital market equilibrium and asset valuation is introduced. In this context several equilibrium models of asset markets are presented. These include the Arrow-Debreu model of complete markets, the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT). Besides mutual fund separation and aggregation theorems are analyzed. Finally, the financial decisions of firms are considered and the Modigliani-Miller theorems are analyzed.
Credit: 3(3-0); ECTS: 8.0Probability spaces. Independence. Conditional probability. Product probability spaces. Random variables and their distributions. Distribution functions. Mathematical expectation (Integration with respect to a probability measure.) Lp-spaces. Moments and generating functions. Conditional expectation. Linear estimation. Gaussian vectors. Various convergence concepts. Central Limit Theorem. Laws of large numbers.
4 Elective Courses (Total 24 credits)
See IAM Catalogue for possible elective courses.Back