1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2022/2023
4. Mathematics - pierwszego stopnia z tyt. licencjata
5. Introduction to Mathematical Finance

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Introduction to Mathematical Finance - opis przedmiotu

Cel przedmiotu

The aim of the course is to teach students to use basic tools for money time-value analysis; securities pricing and risk analysis of various financial instruments; ability to evaluate and compare investment projects, loans and retirement plans.

Wymagania wstępne

Zapisz zmiany

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

Zakres tematyczny

Lecture:

1. Simple, compound and continuous interest and discounting. Nominal and effective rates, continuous interest and discount rate.
2. Cash flows – present value and future value for a fixed and floating discount rate; internal rate of return, modified internal rate of return.
3. Annuities and perpetuities; annuities-due, immediate annuities, perpetuities-due, immediate perpetuities. Equal payments, standard increasing and standard decreasing payments.
4. Difference and differential equations of capital formation.
5. Cash flow analysis in investment projects and project evaluation.
6. Repayment of a debt – the repayment schedule, remaining/current debt. Short term debts and simple interest. Medium and long term debts and compound interest.
7. Linear depreciation, linearly decreasing depreciation allowanes, depreciation with a constant rate, accelerated depreciation, redemption fund method.
8. Elements of securities pricing theory (for bills of exchange, treasury bills, bonds, stocks). Term structure of interest rates.
9. Forward and futures contracts, options - information on the pricing of derivative financial instruments.
10. Basics of securities portfolio theory.

Laboratory:

1. Determining present value and future value of payment in case of simple, discrete and continuously compound interest and discounting. Using financial functions to determine nominal and effective interest rates. Equivalence of interest and discount rate.
2. The use of financial functions to calculate present and future value of cash flow streams for constant and varying rates; internal rate of return  and modified internal rate of return. 
3. Using financial functions to determine the present and future value of a stream of equal payments (annuities-due and immediate annuities).
4. Cash flow analysis in investment projects and project evaluation - using financial functions that allow to determine net present value, profitability index, internal rate of return and  modified internal rate of return for a given cash flow.
5. Determining a debt repayment plan. Calculation of payments of a debt with use of financial functions. Comparison of various debt repayment schedules.
6. Forward and futures contracts, options - basic option strategies, pricing of derivative financial instruments in spreadsheet.

Metody kształcenia

Lectures – with conversation and online usage of financial and insurance data.
Laboratory – individual solving tasks with real data using a spreadsheet, preceded by a discussion on the necessary theoretical tools; individual development of solutions to selected tasks in the form of project reports.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

The condition for passing the course is obtaining positive grades in the lecture and laboratory. The final grade for the course will be determined on the basis of the grade from the lecture and the grade from the laboratory, as the rounding of the weighted arithmetic mean of these two grades to the grade from the grading scale specified in the study regulations. The weight of the lecture grade will be 0.6 and the weight of the laboratory grade will be 0.4.

Literatura podstawowa

1. D. Lovelock, M. Mendel, A.L. Wright, An Introduction to the Mathematics of Money, Springer, 2007.
2. A.O. Peters, X. Dong, An Introduction to Mathematical Finance with Applications, Springer, 2016.

Literatura uzupełniająca

 

1. M. Capiński, T. Zastawniak, Mathematics for Finance, Springer, 2003.
2. P. Brandimarte, Numerical Methods in Finanace, John Wiley & Sons, New York, 2002.

Uwagi

The description has been prepared by dr hab. Longin Rybiński, prof. UZ, and modified by dr Dorota Głazowska.

Zmodyfikowane przez dr Dorota Głazowska (ostatnia modyfikacja: 03-03-2024 20:25)