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University of Economics, Faculty of Informatics Dolnozemsk á cesta 1, 852 35 Bratislava

University of Economics, Faculty of Informatics Dolnozemsk á cesta 1, 852 35 Bratislava Slova k Republic. Financial Mathematics in Derivative Securities and Risk Reduction Financial Mathematics. Ass. Prof. Ľu dov í t Pinda, CSc. Department of Mathematics,

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University of Economics, Faculty of Informatics Dolnozemsk á cesta 1, 852 35 Bratislava

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  1. University of Economics, Faculty of Informatics Dolnozemská cesta 1, 852 35 Bratislava Slovak Republic Financial Mathematics in Derivative Securities and Risk Reduction Financial Mathematics Ass. Prof. Ľudovít Pinda, CSc. Department of Mathematics, Tel.:++421 2 67295 813, ++421 2 67295 711 Fax:++421 2 62412195 e-mail: pinda@dec.euba.sk

  2. Sylabus of the lecture ·        Simple and compound interest. ·        Comparison simple interest with compound interest. ·        Nominal interest rates. ·        Accumulation factor, force of interest. ·        Stoodleys formula for the force of interest. ·        The basis compound interest functions. ·        Annuities-certain and annuities-due, present values and accumulations. ·        Continuously payable annuities. ·        Discounted cash flow, net present values.

  3. Simple and compound interest K0– the amount in t = 0, Kn – theamount in t =n, i – the interest rate p. a., n – the time of duration less then one year, d – the time of duration measured in days, K0 n i – theinterest of amount, , Kn K0n i K0 nt Fig. 1 n – thetime of duration is greater then one year,

  4. Kn K0 1t – theinterest of amount, Fig. 2

  5. Comparison simple interest with compound interest Let K0 =1 From the Binomic theorem . . From then ,

  6. Kn K0 n0 = 1n Fig. 3 - the rate of interest for the period (the effective rate of interest for theperiod)

  7. Nominal interest rates

  8. Example 1.

  9. Example 2. Solution.

  10. Example 3. Solution.

  11. Stoodley's formula for the force of interest Using: The model a smoothly decreasing or smoothly increasing force of interest. Situation:

  12. Example 4 , t = 0 the interest rate 0.11, t = 4 the interest rate 0.10, t = ∞ the interest rate 0.08.

  13. The basis compound interest function Tab. 1

  14. Continuously payable annuities

  15. Discounted cash flow, net present values Example 5. Consider the cash flow an initial outlay of 20 000, after one year a futher outlay 10 000, an inflow of 3 000 per annum payable continuously for ten years beginning in three years' time and final inflow of 6 000 in the end of thirteen years' time. Express the net present value. Solution.

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