1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2022/2023
4. Mathematics - drugiego stopnia z tyt. magistra
5. Financial Engineering

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Financial Engineering - opis przedmiotu

Cel przedmiotu

The course covers selected topics related to financial engineering. The objective of the classes is to familiarize students with fundamental concepts related to capital markets and methods of valuing financial instruments traded on these markets, based on stochastic analysis methods.

Wymagania wstępne

Zapisz zmiany

Knowledge of basic courses in mathematical analysis, probability calculus, stochastic processes, and fundamentals of financial mathematics.

Zakres tematyczny

The course covers fundamental financial instruments such as forward and futures contracts, options, and explores the valuation of forward and futures contracts. It also delves into financial arbitrage, the use of currency futures contracts for exchange rate risk hedging, the Black-Scholes market model, and the arbitrage theory. Strategies that are self-financing and replicate derivative instruments are discussed, along with the Black-Scholes equation and the pricing of standard options. The Feynman-Kac formula and its application to option valuation, options on futures contracts, Girsanov's theorem, and martingale pricing of financial instruments are also part of the curriculum. The course extends to the valuation of selected exotic options, the pricing of Unit-Linked insurance, and includes practical exercises and laboratory work.

Practical exercises and laboratory work cover topics such as calculating profit/loss for futures contracts, the role of arbitrage, and the value of contracts. Options and option strategies are explored with a focus on determining profit/loss functions and their relationships with futures contracts. Self-financing strategies, the calculation of option prices using the Black-Scholes model, options on futures contracts, and estimating model parameters using historical volatility are included in the exercises.

Metody kształcenia

The lecture will be supplemented with illustrative accounting examples to demonstrate the discussed concepts. Exercises will involve individual solving of theoretical and computational tasks, preceded by a theoretical introduction to the analyzed problems.

The laboratory component will include computer simulations of price processes and statistical analysis of market data using computer software packages. Students will engage in hands-on activities, applying theoretical concepts to real-world scenarios through the use of computational tools. The goal is to enhance practical skills in financial analysis, data interpretation, and the application of mathematical models to simulate and understand market dynamics.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

The assessment for the course is composed of three components: exercises (30%), laboratory work (30%), and the exam (40%). A prerequisite for taking the exam is a positive evaluation of the exercises. To pass the course, students must receive a positive assessment for exercises, laboratory work, and the exam. The overall performance in each of these elements contributes to the final grade, with the exam carrying the highest weight in the overall evaluation.

Literatura podstawowa

1. A. N. Shiryaev, Essentials of Stochastic Finance, World Scientific, 1999.
2. M. Musiela, M. Rutkowski, Martingale Methods in Financial Modelling, Springer, 1997.
3. R.S. Lipcer, A.N. Shiryaev, Statistics of Random Processes, Springer, 2001.

Literatura uzupełniająca

Uwagi

Zmodyfikowane przez dr hab. Mariusz Michta, prof. UZ (ostatnia modyfikacja: 29-12-2023 17:36)