1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2018/2019
4. Mathematics - pierwszego stopnia z tyt. licencjata
5. Wstęp do matematyki finansowej

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Wstęp do matematyki finansowej - opis przedmiotu

Cel przedmiotu

The student should accomplish basic tools for money time-value analysis, investment analysis, asset pricing and risk analysis, comparing and building investment strategies with derivatives.

Wymagania wstępne

Zapisz zmiany

Calculus 1, 2, Linear Algebra 1, Probability Theory.

Zakres tematyczny

Lecture:
1. Simple, compound and continuous interest. Nominal and effective rates.
2. Mathematical models for varying rates.
3. Standard and nonstandard annuities and perpetuities.
4. Cash flows – present value, future value, internal rate of return, modified internal rate of return; investment cash flows.
5. Payment of a debt – schedule for a short term and long term debts; actual percentage rate.
6. Term structure of interest rates and yield curves. Bonds – zero-coupon bonds and coupon bonds; duration and convexity; immunization and matching assets and liabilities.
7. Pricing derivative securities – Black Scholes formula and Cox-Ross_Rubinstein formula.
8. Basics of portfolio theory; Capital Asset Pricing Model and Arbitrage Pricing Theory.
9. Von Neumann–Morgenstern expected utility.

Laboratory:
1. Present value and future value of payment in case of simple, discrete and continuously compound interest. Equivalence of nomianal and effective rate, equivalence of interest and discount rate.
2. Calculating present and future value of cash flow for constant and varying rates; annuities and perpetuities.

3. Internal rate of return (numerical aspects and spreadsheet calculation) and modified internal rate of return.
4. Tools for investment analysis: cash flow net present value, internal rate of return, profitability index, playback period. Solving practical problems.
5. Debt repayment plans. Calculation of payments and IRR based comparison of various debt repayment schedules.
6. Derivative securities (futur es, european and american and options) and basic option strategies – pricing in spreadsheet.

Metody kształcenia

Lectures – with conversation and online usage of financial and insurance data.
Laboratory – the use of spreadsheet functions, individual problem solving, individual project report.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

Assessment of written test, ongoing review of laboratory work, project assessment. The final grade is a weighted mean of lecture grade (60%) and laboratory grade (40%).

Literatura podstawowa

1. M. Dobija, E. Smaga, Podstawy matematyki finansowej i ubezpieczeniowej, PWN, Warszawa, 1995.
2. E. Nowak (red.), Matematyka i statystyka finansowa, Fundacja Rozwoju Rach., Finanse, Warszawa, 1994.
3. M. Podgórska, J. Klimkowska, Matematyka finansowa, PWN, Warszawa, 2005.
4. Piasecki K., Modele matematyki finansowej, PWN, Warszawa, 2007.

Literatura uzupełniająca

1. A. Weron, R. Weron, Inżynieria finansowa, WNT, Warszawa, 1998.
2. Capiński M., Zastawniak T., Mathematics for Finance, Springer, 2003.
3. P. Brandimarte, Numerical Methods in Finanace, John Wiley & Sons, New York, 2002.

Uwagi

Zmodyfikowane przez dr Alina Szelecka (ostatnia modyfikacja: 07-07-2018 12:08)