The student should accomplish basic tools for money time-value analysis, investment analysis, asset pricing and risk analysis, as well as the usage of lifetime tables for calculating single and periodic premium in life insurance policies.
Wymagania wstępne
Calculus 1, 2, Linear Algebra 1, Probability Theory.
Zakres tematyczny
Lecture:
Simple, compound and continuous interest. Nominal and effective rates.
Mathematical models for varying rates.
Standard and nonstandard annuities and perpetuities.
Cash flows – present value, future value, internal rate of return, modified internal rate of return; investment cash flows.
Payment of a debt – schedule for a short term and long term debts; actual percentage rate.
Term structure of interest rates and yield curves. Bonds – zero-coupon bonds and coupon bonds; duration and convexity; immunization and matching assets and liabilities.
Pricing derivative securities – Black Scholes formula and Cox-Ross-Rubinstein formula.
Basics of portfolio theory; Capital Asset Pricing Model and Arbitrage Pricing Theory.
Basic life insurance contracts and elementary life annuities.
The future lifetime, life tables.
Single net premium and annual net premiums of constant amount for whole life and term insurance.
Laboratory:
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.
Calculating present and future value of cash flow for constant and varying rates; annuities and perpetuities.
Internal rate of return (numerical aspects and spreadsheet calculation) and modified internal rate of return.
Tools for investment analysis: cash flow net present value, internal rate of return, profitability index, payback period. Solving practical problems.
Debt repayment plans. Calculation of payments and IRR based comparison of various debt repayment schedules.
Derivative securities (futures, european and american and options) and basic option strategies – pricing in spreadsheet.
Life tables. Single net premium and annual net premiums.
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
Capiński M., Zastawniak T., Mathematics for Finance, Springer, 2003.
H.U. Gerber, Life Insurance Mathematics, Springer, Berlin, 1990.
P. Brandimarte, Numerical Methods in Finance, John Wiley & Sons, New York 2002.
Lovelock D., Mendel M., Wright A.L., An Introduction to the Mathematics of Money, Springer 2007.
Petters A.O., Dong X., An Introduction to Mathematical Finance with Applications, Springer 2016.
Literatura uzupełniająca
M. Dobija, E. Smaga, Podstawy matematyki finansowej i ubezpieczeniowej, PWN, Warszawa, 1995.
M. Podgórska, J. Klimkowska, Matematyka finansowa, PWN, Warszawa, 2005.
Piasecki K., Modele matematyki finansowej, PWN, Warszawa, 2007.
Chan R.H., Guo Y. ZY., Lee S.T., Li X., Financial Mathematics, Derivatives and Structured Products, Springer 2019.
Uwagi
Zmodyfikowane przez dr Alina Szelecka (ostatnia modyfikacja: 22-11-2020 15:13)
Ta strona używa ciasteczek (cookies), dzięki którym nasz serwis może działać lepiej. Korzystając z niniejszej strony, wyrażasz zgodę na ich używanie. Dowiedz się więcej.