MA020 Financial Computing

Faculty of Informatics
Autumn 2009
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
Karel Zikan, PhD. (lecturer)
Guaranteed by
prof. Ing. Jiří Sochor, CSc.
Department of Visual Computing – Faculty of Informatics
Contact Person: prof. Ing. Jiří Sochor, CSc.
Timetable
Fri 10:00–11:50 B204
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 25 student(s).
Current registration and enrolment status: enrolled: 0/25, only registered: 0/25, only registered with preference (fields directly associated with the programme): 0/25
fields of study / plans the course is directly associated with
Course objectives
The purpose of these lectures is to build foundations of computational finance; to open the possibility of a career in private or governmental finance institutions. Another purpose, and possibly a more important purpose, is to prepare students for a life-long 'side career' of sophisticated investing and of building personal- and family wealth. In terms of mathematics involved, this course is a complement of and an extension of the lectures in Concrete Mathematics. While the lectures of Concrete Mathematics focus on the analysis of complicated, but deterministic recurrences, many real-life problems (even some some key real-life problems) are in their very essence recurrences that are stochastic in their nature. That means that each step of the recurrence is fundamentally a transformation randomly chosen from a nontrivial population of transformations. Despite of this random nature of stochastic recurrences, we need to uncover key relationships that govern their behavior and made critical inferences. In this cycle of lectures, we examine tools for solving problems of stochastic recurrences associated with investing and during financial transactions. (Similar problems arise, for instance, also in population dynamics, that is in the problem of survival and extinction of species, but we touch on those only occasionally.) The course is built around the text: John C. Hull, "Options, Futures, and Other Derivatives." Ancillary materials are listed with the Concrete Mathematics course. Integral part of the course is also introduction of key jargon of financial mathematics.
Syllabus
  • (1) Mathematical tools for stochastical recurrences -- introduction and overview (2) Derivatives, derivative markets -- introduction and overview (3) Modern portfolio theory -- alpha, beta, pareto-optimality, Sharpe, calmar, zeta... (4) Volatility -- gambler's ruin, VAR, critical time, rate of growth, leveraging, gearing (5) Forward contracts, Futures, Swaps, -- hedging, credit risk (6) Interest rates, risk-free rates -- LIBOR, Eurodollar, diffusion processes (Weiner), Ito Calculus, arbitrage principles (7) Options -- European options and Black Sholes-Merton, American options and dynamic programming (Bellman Equations), options stategies (covered puts, strangles, butterflies, ...), Greeks, volatility smiles, GARCH(1,1) (8) Swaps -- Credit ratings (9) Exotic derivatives
Language of instruction
Czech
Further Comments
Study Materials
The course is taught only once.
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