Objectives and competences
Students:
1. Familiarize themselves with fundamental mathematical tools of asset pricing.
2. Gain in-depth and systematic knowledge of mathematical models of discrete-time and continuous time asset pricing
3. Develop the ability to apply specific mathematical tools and theoretical research-based knowledge at the forefront of their academic discipline (financial engineering).
4. Make critical judgements based on a sound theoretical base.
5. Gain the ability to apply their theoretical knowledge in business and economic practice, especially for hedging purposes.
Content (Syllabus outline)
1. Mathematical fundations of asset pricing
a) Risk-free assets
b) Risky assets
Partial and stochastic differential equations, random walk, Wiener process, Itô’s lemma
2. Discrete time market models
3. Pricing forward and futures contracts
4. Option pricing
a) Properties
b) Option pricing in the binomial tree model, Cox-Ross-Rubinstein formula
c) Transition to continuous time: Brownian motion, Black-Scholes formula, Girsanov’s theorem
5. Hedging, case study, analysis of delta and gamma hedging
6. Stochastic interest rates
7. Functional analisys and applications in financial mathematics
Learning and teaching methods
Lecturing.
Case studies.
Active research work, discussion.
Intended learning outcomes - knowledge and understanding
Knowledge and understanding:
- fundamental theoretical knowledge and
practical skills of financial engineering
- capacity to learn and create cognitions and novelties, including innovations
- identify and use of adequate analytical concepts and instruments
- capacity for analysis of complex problems and searching for the most effective solutions.
Cognitive and intellectual skills:
- with critical awareness, can undertake analysis
- managing complexity, incompleteness of data or potential contradictions which may appear in practice
- can act independently and with originality in problem solving
- can synthesise new approaches, in a manner that can contribute to the development of understanding or methodology in financial engineering.
Transferable/key skills and other attributes:
- capability of understanding and application of knowledge in praxis
- ability of additional learning and individual study of new methods of financial engineering
- capacity for generating new ideas
- capacity to adapt to new situations
- decision-making
- ethical commitment.
Readings
Obvezna študijska literature (Compulsory textbooks):
Capinski M., Zastawniak T. (2003). Mathematics for finance, an introduction to financial engineering, Springer-Verlag, London.
Dodatna študijska literature (Additonal textbooks):
1. Raziskovalnin članki v revijah: The Journal of Derivatives, The Journal of Finance, Journal of Futures Markets, Journal of Mathematical Analysis and Applications, Linear Algebra and its Applications
2. Shreve S. E. (2004). Stochastic calculus for Finance I, The binomial asset pricing model, Springer-Verlag, New York.
3. Shreve S. E. (2004). Stochastic calculus for Finance II, Continuous-time models, Springer, New York.
4. Björk T. (2009). Arbitrage theory in continuous time, Oxford University Press, New York.
5. Hull J. (2008). Options, futures, and other derivative securities, Prentice-Hall, Englewood Cliffs, New Jersey.
6. Marovt J, Breznik K. (2014). Praktikum iz poslovno-finančne matematike, FNM, Maribor.
Additional information on implementation and assessment Seminar work 60
Written examination.40
Student passes the exam, when each part of the examination is evaluated as positiv.
